From 2c7025ed0a472130b19785c3a73712d6fa25d4b4 Mon Sep 17 00:00:00 2001 From: josd Date: Sat, 21 Dec 2024 00:00:02 +0100 Subject: [PATCH] refreshing --- .../proof-by-contradiction/example2-answer.n3 | 10 + .../proof-by-contradiction/example2-proof.n3 | 424 +- reasoning/proof-by-contradiction/example2.n3 | 2 +- .../proof-by-recursion/example2-answer.n3 | 999 + .../proof-by-recursion/example2-proof.n3 | 162529 +++++++++++---- .../proof-by-recursion/example2-query.n3 | 2 +- 6 files changed, 121392 insertions(+), 42574 deletions(-) diff --git a/reasoning/proof-by-contradiction/example2-answer.n3 b/reasoning/proof-by-contradiction/example2-answer.n3 index ee80bafeb..bdeef2828 100644 --- a/reasoning/proof-by-contradiction/example2-answer.n3 +++ b/reasoning/proof-by-contradiction/example2-answer.n3 @@ -11,3 +11,13 @@ 7 a :Positive. 8 a :Positive. 9 a :Positive. +10 a :Positive. +11 a :Positive. +12 a :Positive. +13 a :Positive. +14 a :Positive. +15 a :Positive. +16 a :Positive. +17 a :Positive. +18 a :Positive. +19 a :Positive. diff --git a/reasoning/proof-by-contradiction/example2-proof.n3 b/reasoning/proof-by-contradiction/example2-proof.n3 index 009c7a613..78044bd70 100644 --- a/reasoning/proof-by-contradiction/example2-proof.n3 +++ b/reasoning/proof-by-contradiction/example2-proof.n3 @@ -17,6 +17,16 @@ skolem:proof a r:Proof, r:Conjunction; r:component skolem:lemma8; r:component skolem:lemma9; r:component skolem:lemma10; + r:component skolem:lemma11; + r:component skolem:lemma12; + r:component skolem:lemma13; + r:component skolem:lemma14; + r:component skolem:lemma15; + r:component skolem:lemma16; + r:component skolem:lemma17; + r:component skolem:lemma18; + r:component skolem:lemma19; + r:component skolem:lemma20; r:gives { 0 a :Positive. 1 a :Positive. @@ -28,6 +38,16 @@ skolem:proof a r:Proof, r:Conjunction; 7 a :Positive. 8 a :Positive. 9 a :Positive. + 10 a :Positive. + 11 a :Positive. + 12 a :Positive. + 13 a :Positive. + 14 a :Positive. + 15 a :Positive. + 16 a :Positive. + 17 a :Positive. + 18 a :Positive. + 19 a :Positive. }. skolem:lemma1 a r:Inference; @@ -35,107 +55,207 @@ skolem:lemma1 a r:Inference; 0 a :Positive. }; r:evidence ( - skolem:lemma11 + skolem:lemma21 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:rule skolem:lemma12. + r:rule skolem:lemma22. skolem:lemma2 a r:Inference; r:gives { 1 a :Positive. }; r:evidence ( - skolem:lemma13 + skolem:lemma23 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:rule skolem:lemma12. + r:rule skolem:lemma22. skolem:lemma3 a r:Inference; r:gives { 2 a :Positive. }; r:evidence ( - skolem:lemma14 + skolem:lemma24 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:rule skolem:lemma12. + r:rule skolem:lemma22. skolem:lemma4 a r:Inference; r:gives { 3 a :Positive. }; r:evidence ( - skolem:lemma15 + skolem:lemma25 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; - r:rule skolem:lemma12. + r:rule skolem:lemma22. skolem:lemma5 a r:Inference; r:gives { 4 a :Positive. }; r:evidence ( - skolem:lemma16 + skolem:lemma26 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; - r:rule skolem:lemma12. + r:rule skolem:lemma22. skolem:lemma6 a r:Inference; r:gives { 5 a :Positive. }; r:evidence ( - skolem:lemma17 + skolem:lemma27 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; - r:rule skolem:lemma12. + r:rule skolem:lemma22. skolem:lemma7 a r:Inference; r:gives { 6 a :Positive. }; r:evidence ( - skolem:lemma18 + skolem:lemma28 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; - r:rule skolem:lemma12. + r:rule skolem:lemma22. skolem:lemma8 a r:Inference; r:gives { 7 a :Positive. }; r:evidence ( - skolem:lemma19 + skolem:lemma29 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; - r:rule skolem:lemma12. + r:rule skolem:lemma22. skolem:lemma9 a r:Inference; r:gives { 8 a :Positive. }; r:evidence ( - skolem:lemma20 + skolem:lemma30 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; - r:rule skolem:lemma12. + r:rule skolem:lemma22. skolem:lemma10 a r:Inference; r:gives { 9 a :Positive. }; r:evidence ( - skolem:lemma21 + skolem:lemma31 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; - r:rule skolem:lemma12. + r:rule skolem:lemma22. skolem:lemma11 a r:Inference; + r:gives { + 10 a :Positive. + }; + r:evidence ( + skolem:lemma32 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 10]; + r:rule skolem:lemma22. + +skolem:lemma12 a r:Inference; + r:gives { + 11 a :Positive. + }; + r:evidence ( + skolem:lemma33 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 11]; + r:rule skolem:lemma22. + +skolem:lemma13 a r:Inference; + r:gives { + 12 a :Positive. + }; + r:evidence ( + skolem:lemma34 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 12]; + r:rule skolem:lemma22. + +skolem:lemma14 a r:Inference; + r:gives { + 13 a :Positive. + }; + r:evidence ( + skolem:lemma35 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 13]; + r:rule skolem:lemma22. + +skolem:lemma15 a r:Inference; + r:gives { + 14 a :Positive. + }; + r:evidence ( + skolem:lemma36 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 14]; + r:rule skolem:lemma22. + +skolem:lemma16 a r:Inference; + r:gives { + 15 a :Positive. + }; + r:evidence ( + skolem:lemma37 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 15]; + r:rule skolem:lemma22. + +skolem:lemma17 a r:Inference; + r:gives { + 16 a :Positive. + }; + r:evidence ( + skolem:lemma38 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 16]; + r:rule skolem:lemma22. + +skolem:lemma18 a r:Inference; + r:gives { + 17 a :Positive. + }; + r:evidence ( + skolem:lemma39 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 17]; + r:rule skolem:lemma22. + +skolem:lemma19 a r:Inference; + r:gives { + 18 a :Positive. + }; + r:evidence ( + skolem:lemma40 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 18]; + r:rule skolem:lemma22. + +skolem:lemma20 a r:Inference; + r:gives { + 19 a :Positive. + }; + r:evidence ( + skolem:lemma41 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 19]; + r:rule skolem:lemma22. + +skolem:lemma21 a r:Inference; r:gives { 0 a :Positive. }; r:evidence ( - [ a r:Fact; r:gives {10 log:repeat 0}] + [ a r:Fact; r:gives {20 log:repeat 0}] [ a r:Fact; r:gives {{ { 0 math:notLessThan 0. @@ -148,9 +268,9 @@ skolem:lemma11 a r:Inference; } log:satisfiable false}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:rule skolem:lemma22. + r:rule skolem:lemma42. -skolem:lemma12 a r:Extraction; +skolem:lemma22 a r:Extraction; r:gives { @forAll var:x_0. { var:x_0 a :Positive. @@ -160,12 +280,12 @@ skolem:lemma12 a r:Extraction; }; r:because [ a r:Parsing; r:source ]. -skolem:lemma13 a r:Inference; +skolem:lemma23 a r:Inference; r:gives { 1 a :Positive. }; r:evidence ( - [ a r:Fact; r:gives {10 log:repeat 1}] + [ a r:Fact; r:gives {20 log:repeat 1}] [ a r:Fact; r:gives {{ { 1 math:notLessThan 0. @@ -178,14 +298,14 @@ skolem:lemma13 a r:Inference; } log:satisfiable false}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:rule skolem:lemma22. + r:rule skolem:lemma42. -skolem:lemma14 a r:Inference; +skolem:lemma24 a r:Inference; r:gives { 2 a :Positive. }; r:evidence ( - [ a r:Fact; r:gives {10 log:repeat 2}] + [ a r:Fact; r:gives {20 log:repeat 2}] [ a r:Fact; r:gives {{ { 2 math:notLessThan 0. @@ -198,14 +318,14 @@ skolem:lemma14 a r:Inference; } log:satisfiable false}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:rule skolem:lemma22. + r:rule skolem:lemma42. -skolem:lemma15 a r:Inference; +skolem:lemma25 a r:Inference; r:gives { 3 a :Positive. }; r:evidence ( - [ a r:Fact; r:gives {10 log:repeat 3}] + [ a r:Fact; r:gives {20 log:repeat 3}] [ a r:Fact; r:gives {{ { 3 math:notLessThan 0. @@ -218,14 +338,14 @@ skolem:lemma15 a r:Inference; } log:satisfiable false}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; - r:rule skolem:lemma22. + r:rule skolem:lemma42. -skolem:lemma16 a r:Inference; +skolem:lemma26 a r:Inference; r:gives { 4 a :Positive. }; r:evidence ( - [ a r:Fact; r:gives {10 log:repeat 4}] + [ a r:Fact; r:gives {20 log:repeat 4}] [ a r:Fact; r:gives {{ { 4 math:notLessThan 0. @@ -238,14 +358,14 @@ skolem:lemma16 a r:Inference; } log:satisfiable false}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; - r:rule skolem:lemma22. + r:rule skolem:lemma42. -skolem:lemma17 a r:Inference; +skolem:lemma27 a r:Inference; r:gives { 5 a :Positive. }; r:evidence ( - [ a r:Fact; r:gives {10 log:repeat 5}] + [ a r:Fact; r:gives {20 log:repeat 5}] [ a r:Fact; r:gives {{ { 5 math:notLessThan 0. @@ -258,14 +378,14 @@ skolem:lemma17 a r:Inference; } log:satisfiable false}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; - r:rule skolem:lemma22. + r:rule skolem:lemma42. -skolem:lemma18 a r:Inference; +skolem:lemma28 a r:Inference; r:gives { 6 a :Positive. }; r:evidence ( - [ a r:Fact; r:gives {10 log:repeat 6}] + [ a r:Fact; r:gives {20 log:repeat 6}] [ a r:Fact; r:gives {{ { 6 math:notLessThan 0. @@ -278,14 +398,14 @@ skolem:lemma18 a r:Inference; } log:satisfiable false}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; - r:rule skolem:lemma22. + r:rule skolem:lemma42. -skolem:lemma19 a r:Inference; +skolem:lemma29 a r:Inference; r:gives { 7 a :Positive. }; r:evidence ( - [ a r:Fact; r:gives {10 log:repeat 7}] + [ a r:Fact; r:gives {20 log:repeat 7}] [ a r:Fact; r:gives {{ { 7 math:notLessThan 0. @@ -298,14 +418,14 @@ skolem:lemma19 a r:Inference; } log:satisfiable false}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; - r:rule skolem:lemma22. + r:rule skolem:lemma42. -skolem:lemma20 a r:Inference; +skolem:lemma30 a r:Inference; r:gives { 8 a :Positive. }; r:evidence ( - [ a r:Fact; r:gives {10 log:repeat 8}] + [ a r:Fact; r:gives {20 log:repeat 8}] [ a r:Fact; r:gives {{ { 8 math:notLessThan 0. @@ -318,14 +438,14 @@ skolem:lemma20 a r:Inference; } log:satisfiable false}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; - r:rule skolem:lemma22. + r:rule skolem:lemma42. -skolem:lemma21 a r:Inference; +skolem:lemma31 a r:Inference; r:gives { 9 a :Positive. }; r:evidence ( - [ a r:Fact; r:gives {10 log:repeat 9}] + [ a r:Fact; r:gives {20 log:repeat 9}] [ a r:Fact; r:gives {{ { 9 math:notLessThan 0. @@ -338,12 +458,212 @@ skolem:lemma21 a r:Inference; } log:satisfiable false}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; - r:rule skolem:lemma22. + r:rule skolem:lemma42. -skolem:lemma22 a r:Extraction; +skolem:lemma32 a r:Inference; + r:gives { + 10 a :Positive. + }; + r:evidence ( + [ a r:Fact; r:gives {20 log:repeat 10}] + [ a r:Fact; r:gives {{ + { + 10 math:notLessThan 0. + } => { + 10 a :Positive. + }. + { + 10 a :Positive. + } => false. + } log:satisfiable false}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 10]; + r:rule skolem:lemma42. + +skolem:lemma33 a r:Inference; + r:gives { + 11 a :Positive. + }; + r:evidence ( + [ a r:Fact; r:gives {20 log:repeat 11}] + [ a r:Fact; r:gives {{ + { + 11 math:notLessThan 0. + } => { + 11 a :Positive. + }. + { + 11 a :Positive. + } => false. + } log:satisfiable false}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 11]; + r:rule skolem:lemma42. + +skolem:lemma34 a r:Inference; + r:gives { + 12 a :Positive. + }; + r:evidence ( + [ a r:Fact; r:gives {20 log:repeat 12}] + [ a r:Fact; r:gives {{ + { + 12 math:notLessThan 0. + } => { + 12 a :Positive. + }. + { + 12 a :Positive. + } => false. + } log:satisfiable false}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 12]; + r:rule skolem:lemma42. + +skolem:lemma35 a r:Inference; + r:gives { + 13 a :Positive. + }; + r:evidence ( + [ a r:Fact; r:gives {20 log:repeat 13}] + [ a r:Fact; r:gives {{ + { + 13 math:notLessThan 0. + } => { + 13 a :Positive. + }. + { + 13 a :Positive. + } => false. + } log:satisfiable false}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 13]; + r:rule skolem:lemma42. + +skolem:lemma36 a r:Inference; + r:gives { + 14 a :Positive. + }; + r:evidence ( + [ a r:Fact; r:gives {20 log:repeat 14}] + [ a r:Fact; r:gives {{ + { + 14 math:notLessThan 0. + } => { + 14 a :Positive. + }. + { + 14 a :Positive. + } => false. + } log:satisfiable false}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 14]; + r:rule skolem:lemma42. + +skolem:lemma37 a r:Inference; + r:gives { + 15 a :Positive. + }; + r:evidence ( + [ a r:Fact; r:gives {20 log:repeat 15}] + [ a r:Fact; r:gives {{ + { + 15 math:notLessThan 0. + } => { + 15 a :Positive. + }. + { + 15 a :Positive. + } => false. + } log:satisfiable false}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 15]; + r:rule skolem:lemma42. + +skolem:lemma38 a r:Inference; + r:gives { + 16 a :Positive. + }; + r:evidence ( + [ a r:Fact; r:gives {20 log:repeat 16}] + [ a r:Fact; r:gives {{ + { + 16 math:notLessThan 0. + } => { + 16 a :Positive. + }. + { + 16 a :Positive. + } => false. + } log:satisfiable false}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 16]; + r:rule skolem:lemma42. + +skolem:lemma39 a r:Inference; + r:gives { + 17 a :Positive. + }; + r:evidence ( + [ a r:Fact; r:gives {20 log:repeat 17}] + [ a r:Fact; r:gives {{ + { + 17 math:notLessThan 0. + } => { + 17 a :Positive. + }. + { + 17 a :Positive. + } => false. + } log:satisfiable false}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 17]; + r:rule skolem:lemma42. + +skolem:lemma40 a r:Inference; + r:gives { + 18 a :Positive. + }; + r:evidence ( + [ a r:Fact; r:gives {20 log:repeat 18}] + [ a r:Fact; r:gives {{ + { + 18 math:notLessThan 0. + } => { + 18 a :Positive. + }. + { + 18 a :Positive. + } => false. + } log:satisfiable false}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 18]; + r:rule skolem:lemma42. + +skolem:lemma41 a r:Inference; + r:gives { + 19 a :Positive. + }; + r:evidence ( + [ a r:Fact; r:gives {20 log:repeat 19}] + [ a r:Fact; r:gives {{ + { + 19 math:notLessThan 0. + } => { + 19 a :Positive. + }. + { + 19 a :Positive. + } => false. + } log:satisfiable false}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 19]; + r:rule skolem:lemma42. + +skolem:lemma42 a r:Extraction; r:gives { @forAll var:x_0. { - 10 log:repeat var:x_0. + 20 log:repeat var:x_0. { { var:x_0 math:notLessThan 0. diff --git a/reasoning/proof-by-contradiction/example2.n3 b/reasoning/proof-by-contradiction/example2.n3 index 089b5e7fc..d90c8ee21 100644 --- a/reasoning/proof-by-contradiction/example2.n3 +++ b/reasoning/proof-by-contradiction/example2.n3 @@ -4,7 +4,7 @@ # proof by contradiction { - 10 log:repeat ?X. + 20 log:repeat ?X. { { ?X math:notLessThan 0 } => { ?X a :Positive }. { ?X a :Positive } => false. diff --git a/reasoning/proof-by-recursion/example2-answer.n3 b/reasoning/proof-by-recursion/example2-answer.n3 index 491d0bcdf..5eedc3fae 100644 --- a/reasoning/proof-by-recursion/example2-answer.n3 +++ b/reasoning/proof-by-recursion/example2-answer.n3 @@ -999,3 +999,1002 @@ 2997 :recursionCount 5 . 2998 :recursionCount 3 . 2999 :recursionCount 4 . +3000 :recursionCount 6 . +3001 :recursionCount 3 . +3002 :recursionCount 5 . +3003 :recursionCount 6 . +3004 :recursionCount 3 . +3005 :recursionCount 5 . +3006 :recursionCount 3 . +3007 :recursionCount 6 . +3008 :recursionCount 5 . +3009 :recursionCount 3 . +3010 :recursionCount 3 . +3011 :recursionCount 6 . +3012 :recursionCount 3 . +3013 :recursionCount 5 . +3014 :recursionCount 2 . +3015 :recursionCount 7 . +3016 :recursionCount 1 . +3017 :recursionCount 5 . +3018 :recursionCount 6 . +3019 :recursionCount 3 . +3020 :recursionCount 5 . +3021 :recursionCount 3 . +3022 :recursionCount 6 . +3023 :recursionCount 3 . +3024 :recursionCount 7 . +3025 :recursionCount 7 . +3026 :recursionCount 7 . +3027 :recursionCount 3 . +3028 :recursionCount 3 . +3029 :recursionCount 4 . +3030 :recursionCount 6 . +3031 :recursionCount 5 . +3032 :recursionCount 3 . +3033 :recursionCount 6 . +3034 :recursionCount 4 . +3035 :recursionCount 6 . +3036 :recursionCount 6 . +3037 :recursionCount 4 . +3038 :recursionCount 6 . +3039 :recursionCount 4 . +3040 :recursionCount 3 . +3041 :recursionCount 2 . +3042 :recursionCount 7 . +3043 :recursionCount 4 . +3044 :recursionCount 7 . +3045 :recursionCount 7 . +3046 :recursionCount 7 . +3047 :recursionCount 3 . +3048 :recursionCount 3 . +3049 :recursionCount 4 . +3050 :recursionCount 5 . +3051 :recursionCount 7 . +3052 :recursionCount 7 . +3053 :recursionCount 6 . +3054 :recursionCount 7 . +3055 :recursionCount 7 . +3056 :recursionCount 1 . +3057 :recursionCount 5 . +3058 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:recursionCount 6 . +3934 :recursionCount 7 . +3935 :recursionCount 1 . +3936 :recursionCount 3 . +3937 :recursionCount 4 . +3938 :recursionCount 5 . +3939 :recursionCount 4 . +3940 :recursionCount 4 . +3941 :recursionCount 3 . +3942 :recursionCount 3 . +3943 :recursionCount 7 . +3944 :recursionCount 6 . +3945 :recursionCount 7 . +3946 :recursionCount 1 . +3947 :recursionCount 3 . +3948 :recursionCount 4 . +3949 :recursionCount 5 . +3950 :recursionCount 3 . +3951 :recursionCount 6 . +3952 :recursionCount 5 . +3953 :recursionCount 1 . +3954 :recursionCount 7 . +3955 :recursionCount 6 . +3956 :recursionCount 7 . +3957 :recursionCount 1 . +3958 :recursionCount 3 . +3959 :recursionCount 4 . +3960 :recursionCount 3 . +3961 :recursionCount 5 . +3962 :recursionCount 6 . +3963 :recursionCount 3 . +3964 :recursionCount 1 . +3965 :recursionCount 7 . +3966 :recursionCount 6 . +3967 :recursionCount 7 . +3968 :recursionCount 1 . +3969 :recursionCount 3 . +3970 :recursionCount 7 . +3971 :recursionCount 2 . +3972 :recursionCount 3 . +3973 :recursionCount 4 . +3974 :recursionCount 3 . +3975 :recursionCount 1 . +3976 :recursionCount 7 . +3977 :recursionCount 6 . +3978 :recursionCount 7 . +3979 :recursionCount 1 . +3980 :recursionCount 7 . +3981 :recursionCount 7 . +3982 :recursionCount 5 . +3983 :recursionCount 5 . +3984 :recursionCount 4 . +3985 :recursionCount 3 . +3986 :recursionCount 1 . +3987 :recursionCount 7 . +3988 :recursionCount 6 . +3989 :recursionCount 7 . +3990 :recursionCount 7 . +3991 :recursionCount 2 . +3992 :recursionCount 3 . +3993 :recursionCount 4 . +3994 :recursionCount 5 . +3995 :recursionCount 4 . +3996 :recursionCount 3 . +3997 :recursionCount 1 . +3998 :recursionCount 7 . +3999 :recursionCount 6 . diff --git a/reasoning/proof-by-recursion/example2-proof.n3 b/reasoning/proof-by-recursion/example2-proof.n3 index 435b66ff1..1167fe537 100644 --- a/reasoning/proof-by-recursion/example2-proof.n3 +++ b/reasoning/proof-by-recursion/example2-proof.n3 @@ -1007,6 +1007,1005 @@ skolem:proof a r:Proof, r:Conjunction; r:component skolem:lemma997; r:component skolem:lemma998; r:component skolem:lemma999; + r:component skolem:lemma1000; + r:component skolem:lemma1001; + r:component skolem:lemma1002; + r:component skolem:lemma1003; + r:component skolem:lemma1004; + r:component skolem:lemma1005; + r:component skolem:lemma1006; + r:component skolem:lemma1007; + r:component skolem:lemma1008; + r:component skolem:lemma1009; + r:component skolem:lemma1010; + r:component skolem:lemma1011; + r:component skolem:lemma1012; + r:component skolem:lemma1013; + r:component skolem:lemma1014; + r:component skolem:lemma1015; + r:component skolem:lemma1016; + r:component skolem:lemma1017; + r:component skolem:lemma1018; + r:component skolem:lemma1019; + r:component skolem:lemma1020; + r:component skolem:lemma1021; + r:component skolem:lemma1022; + r:component skolem:lemma1023; + r:component skolem:lemma1024; + r:component skolem:lemma1025; + r:component skolem:lemma1026; + r:component skolem:lemma1027; + r:component skolem:lemma1028; + r:component skolem:lemma1029; + r:component skolem:lemma1030; + r:component skolem:lemma1031; + r:component skolem:lemma1032; + r:component skolem:lemma1033; + r:component skolem:lemma1034; + r:component skolem:lemma1035; + r:component skolem:lemma1036; + r:component skolem:lemma1037; + r:component skolem:lemma1038; + r:component skolem:lemma1039; + r:component skolem:lemma1040; + r:component skolem:lemma1041; + r:component skolem:lemma1042; + r:component skolem:lemma1043; + r:component skolem:lemma1044; + r:component skolem:lemma1045; + r:component skolem:lemma1046; + r:component skolem:lemma1047; + r:component skolem:lemma1048; + r:component skolem:lemma1049; + r:component skolem:lemma1050; + r:component skolem:lemma1051; + r:component skolem:lemma1052; + r:component skolem:lemma1053; + r:component skolem:lemma1054; + r:component skolem:lemma1055; + r:component skolem:lemma1056; + r:component skolem:lemma1057; + r:component skolem:lemma1058; + r:component skolem:lemma1059; + r:component skolem:lemma1060; + r:component skolem:lemma1061; + r:component skolem:lemma1062; + r:component skolem:lemma1063; + r:component skolem:lemma1064; + r:component skolem:lemma1065; + r:component skolem:lemma1066; + r:component skolem:lemma1067; + r:component skolem:lemma1068; + r:component skolem:lemma1069; + r:component skolem:lemma1070; + r:component skolem:lemma1071; + r:component skolem:lemma1072; + r:component skolem:lemma1073; + r:component skolem:lemma1074; + r:component skolem:lemma1075; + r:component skolem:lemma1076; + r:component skolem:lemma1077; + r:component skolem:lemma1078; + r:component skolem:lemma1079; + r:component skolem:lemma1080; + r:component skolem:lemma1081; + r:component skolem:lemma1082; + r:component skolem:lemma1083; + r:component skolem:lemma1084; + r:component skolem:lemma1085; + r:component skolem:lemma1086; + r:component skolem:lemma1087; + r:component skolem:lemma1088; + r:component skolem:lemma1089; + r:component skolem:lemma1090; + r:component skolem:lemma1091; + r:component skolem:lemma1092; + r:component skolem:lemma1093; + r:component skolem:lemma1094; + r:component skolem:lemma1095; + r:component skolem:lemma1096; + r:component skolem:lemma1097; + r:component skolem:lemma1098; + r:component skolem:lemma1099; + r:component skolem:lemma1100; + r:component skolem:lemma1101; + r:component skolem:lemma1102; + r:component skolem:lemma1103; + r:component skolem:lemma1104; + r:component skolem:lemma1105; + r:component skolem:lemma1106; + r:component skolem:lemma1107; + r:component skolem:lemma1108; + r:component skolem:lemma1109; + r:component skolem:lemma1110; + r:component skolem:lemma1111; + r:component skolem:lemma1112; + r:component skolem:lemma1113; + r:component skolem:lemma1114; + r:component skolem:lemma1115; + r:component skolem:lemma1116; + r:component skolem:lemma1117; + r:component skolem:lemma1118; + r:component skolem:lemma1119; + r:component skolem:lemma1120; + r:component skolem:lemma1121; + r:component skolem:lemma1122; + r:component skolem:lemma1123; + r:component skolem:lemma1124; + r:component skolem:lemma1125; + r:component skolem:lemma1126; + r:component skolem:lemma1127; + r:component skolem:lemma1128; + r:component skolem:lemma1129; + r:component skolem:lemma1130; + r:component skolem:lemma1131; + r:component skolem:lemma1132; + r:component skolem:lemma1133; + r:component skolem:lemma1134; + r:component skolem:lemma1135; + r:component skolem:lemma1136; + r:component skolem:lemma1137; + r:component skolem:lemma1138; + r:component skolem:lemma1139; + r:component skolem:lemma1140; + r:component skolem:lemma1141; + r:component skolem:lemma1142; + r:component skolem:lemma1143; + r:component skolem:lemma1144; + r:component skolem:lemma1145; + r:component skolem:lemma1146; + r:component skolem:lemma1147; + r:component skolem:lemma1148; + r:component skolem:lemma1149; + r:component skolem:lemma1150; + r:component skolem:lemma1151; + r:component skolem:lemma1152; + r:component skolem:lemma1153; + r:component skolem:lemma1154; + r:component skolem:lemma1155; + r:component skolem:lemma1156; + r:component skolem:lemma1157; + r:component skolem:lemma1158; + r:component skolem:lemma1159; + r:component skolem:lemma1160; + r:component skolem:lemma1161; + r:component skolem:lemma1162; + r:component skolem:lemma1163; + r:component skolem:lemma1164; + r:component skolem:lemma1165; + r:component skolem:lemma1166; + r:component skolem:lemma1167; + r:component skolem:lemma1168; + r:component skolem:lemma1169; + r:component skolem:lemma1170; + r:component skolem:lemma1171; + r:component skolem:lemma1172; + r:component skolem:lemma1173; + r:component skolem:lemma1174; + r:component skolem:lemma1175; + r:component skolem:lemma1176; + r:component skolem:lemma1177; + r:component skolem:lemma1178; + r:component skolem:lemma1179; + r:component skolem:lemma1180; + r:component skolem:lemma1181; + r:component skolem:lemma1182; + r:component skolem:lemma1183; + r:component skolem:lemma1184; + r:component skolem:lemma1185; + r:component skolem:lemma1186; + r:component skolem:lemma1187; + r:component skolem:lemma1188; + r:component skolem:lemma1189; + r:component skolem:lemma1190; + r:component skolem:lemma1191; + r:component skolem:lemma1192; + r:component skolem:lemma1193; + r:component skolem:lemma1194; + r:component skolem:lemma1195; + r:component skolem:lemma1196; + r:component skolem:lemma1197; + r:component skolem:lemma1198; + r:component skolem:lemma1199; + r:component skolem:lemma1200; + r:component skolem:lemma1201; + r:component skolem:lemma1202; + r:component skolem:lemma1203; + r:component skolem:lemma1204; + r:component skolem:lemma1205; + r:component skolem:lemma1206; + r:component skolem:lemma1207; + r:component skolem:lemma1208; + r:component skolem:lemma1209; + r:component skolem:lemma1210; + r:component skolem:lemma1211; + r:component skolem:lemma1212; + r:component skolem:lemma1213; + r:component skolem:lemma1214; + r:component skolem:lemma1215; + r:component skolem:lemma1216; + r:component skolem:lemma1217; + r:component skolem:lemma1218; + r:component skolem:lemma1219; + r:component skolem:lemma1220; + r:component skolem:lemma1221; + r:component skolem:lemma1222; + r:component skolem:lemma1223; + r:component skolem:lemma1224; + r:component skolem:lemma1225; + r:component skolem:lemma1226; + r:component skolem:lemma1227; + r:component skolem:lemma1228; + r:component skolem:lemma1229; + r:component skolem:lemma1230; + r:component skolem:lemma1231; + r:component skolem:lemma1232; + r:component skolem:lemma1233; + r:component skolem:lemma1234; + r:component skolem:lemma1235; + r:component skolem:lemma1236; + r:component skolem:lemma1237; + r:component skolem:lemma1238; + r:component skolem:lemma1239; + r:component skolem:lemma1240; + r:component skolem:lemma1241; + r:component skolem:lemma1242; + r:component skolem:lemma1243; + r:component skolem:lemma1244; + r:component skolem:lemma1245; + r:component skolem:lemma1246; + r:component skolem:lemma1247; + r:component skolem:lemma1248; + r:component skolem:lemma1249; + r:component skolem:lemma1250; + r:component skolem:lemma1251; + r:component skolem:lemma1252; + r:component skolem:lemma1253; + r:component skolem:lemma1254; + r:component skolem:lemma1255; + r:component skolem:lemma1256; + r:component skolem:lemma1257; + r:component skolem:lemma1258; + r:component skolem:lemma1259; + r:component skolem:lemma1260; + r:component skolem:lemma1261; + r:component skolem:lemma1262; + r:component skolem:lemma1263; + r:component skolem:lemma1264; + r:component skolem:lemma1265; + r:component skolem:lemma1266; + r:component skolem:lemma1267; + r:component skolem:lemma1268; + r:component skolem:lemma1269; + r:component skolem:lemma1270; + r:component skolem:lemma1271; + r:component skolem:lemma1272; + r:component skolem:lemma1273; + r:component skolem:lemma1274; + r:component skolem:lemma1275; + r:component skolem:lemma1276; + r:component skolem:lemma1277; + r:component skolem:lemma1278; + r:component skolem:lemma1279; + r:component skolem:lemma1280; + r:component skolem:lemma1281; + r:component skolem:lemma1282; + r:component skolem:lemma1283; + r:component skolem:lemma1284; + r:component skolem:lemma1285; + r:component skolem:lemma1286; + r:component skolem:lemma1287; + r:component skolem:lemma1288; + r:component skolem:lemma1289; + r:component skolem:lemma1290; + r:component skolem:lemma1291; + r:component skolem:lemma1292; + r:component skolem:lemma1293; + r:component skolem:lemma1294; + r:component skolem:lemma1295; + r:component skolem:lemma1296; + r:component skolem:lemma1297; + r:component skolem:lemma1298; + r:component skolem:lemma1299; + r:component skolem:lemma1300; + r:component skolem:lemma1301; + r:component skolem:lemma1302; + r:component skolem:lemma1303; + r:component skolem:lemma1304; + r:component skolem:lemma1305; + r:component skolem:lemma1306; + r:component skolem:lemma1307; + r:component skolem:lemma1308; + r:component skolem:lemma1309; + r:component skolem:lemma1310; + r:component skolem:lemma1311; + r:component skolem:lemma1312; + r:component skolem:lemma1313; + r:component skolem:lemma1314; + r:component skolem:lemma1315; + r:component skolem:lemma1316; + r:component skolem:lemma1317; + r:component skolem:lemma1318; + r:component skolem:lemma1319; + r:component skolem:lemma1320; + r:component skolem:lemma1321; + r:component skolem:lemma1322; + r:component skolem:lemma1323; + r:component skolem:lemma1324; + r:component skolem:lemma1325; + r:component skolem:lemma1326; + r:component skolem:lemma1327; + r:component skolem:lemma1328; + r:component skolem:lemma1329; + r:component skolem:lemma1330; + r:component skolem:lemma1331; + r:component skolem:lemma1332; + r:component skolem:lemma1333; + r:component skolem:lemma1334; + r:component skolem:lemma1335; + r:component skolem:lemma1336; + r:component skolem:lemma1337; + r:component skolem:lemma1338; + r:component skolem:lemma1339; + r:component skolem:lemma1340; + r:component skolem:lemma1341; + r:component skolem:lemma1342; + r:component skolem:lemma1343; + r:component skolem:lemma1344; + r:component skolem:lemma1345; + r:component skolem:lemma1346; + r:component skolem:lemma1347; + r:component skolem:lemma1348; + r:component skolem:lemma1349; + r:component skolem:lemma1350; + r:component skolem:lemma1351; + r:component skolem:lemma1352; + r:component skolem:lemma1353; + r:component skolem:lemma1354; + r:component skolem:lemma1355; + r:component skolem:lemma1356; + r:component skolem:lemma1357; + r:component skolem:lemma1358; + r:component skolem:lemma1359; + r:component skolem:lemma1360; + r:component skolem:lemma1361; + r:component skolem:lemma1362; + r:component skolem:lemma1363; + r:component skolem:lemma1364; + r:component skolem:lemma1365; + r:component skolem:lemma1366; + r:component skolem:lemma1367; + r:component skolem:lemma1368; + r:component skolem:lemma1369; + r:component skolem:lemma1370; + r:component skolem:lemma1371; + r:component skolem:lemma1372; + r:component skolem:lemma1373; + r:component skolem:lemma1374; + r:component skolem:lemma1375; + r:component skolem:lemma1376; + r:component skolem:lemma1377; + r:component skolem:lemma1378; + r:component skolem:lemma1379; + r:component skolem:lemma1380; + r:component skolem:lemma1381; + r:component skolem:lemma1382; + r:component skolem:lemma1383; + r:component skolem:lemma1384; + r:component skolem:lemma1385; + r:component skolem:lemma1386; + r:component skolem:lemma1387; + r:component skolem:lemma1388; + r:component skolem:lemma1389; + r:component skolem:lemma1390; + r:component skolem:lemma1391; + r:component skolem:lemma1392; + r:component skolem:lemma1393; + r:component skolem:lemma1394; + r:component skolem:lemma1395; + r:component skolem:lemma1396; + r:component skolem:lemma1397; + r:component skolem:lemma1398; + r:component skolem:lemma1399; + r:component skolem:lemma1400; + r:component skolem:lemma1401; + r:component skolem:lemma1402; + r:component skolem:lemma1403; + r:component skolem:lemma1404; + r:component skolem:lemma1405; + r:component skolem:lemma1406; + r:component skolem:lemma1407; + r:component skolem:lemma1408; + r:component skolem:lemma1409; + r:component skolem:lemma1410; + r:component skolem:lemma1411; + r:component skolem:lemma1412; + r:component skolem:lemma1413; + r:component skolem:lemma1414; + r:component skolem:lemma1415; + r:component skolem:lemma1416; + r:component skolem:lemma1417; + r:component skolem:lemma1418; + r:component skolem:lemma1419; + r:component skolem:lemma1420; + r:component skolem:lemma1421; + r:component skolem:lemma1422; + r:component skolem:lemma1423; + r:component skolem:lemma1424; + r:component skolem:lemma1425; + r:component skolem:lemma1426; + r:component skolem:lemma1427; + r:component skolem:lemma1428; + r:component skolem:lemma1429; + r:component skolem:lemma1430; + r:component skolem:lemma1431; + r:component skolem:lemma1432; + r:component skolem:lemma1433; + r:component skolem:lemma1434; + r:component skolem:lemma1435; + r:component skolem:lemma1436; + r:component skolem:lemma1437; + r:component skolem:lemma1438; + r:component skolem:lemma1439; + r:component skolem:lemma1440; + r:component skolem:lemma1441; + r:component skolem:lemma1442; + r:component skolem:lemma1443; + r:component skolem:lemma1444; + r:component skolem:lemma1445; + r:component skolem:lemma1446; + r:component skolem:lemma1447; + r:component skolem:lemma1448; + r:component skolem:lemma1449; + r:component skolem:lemma1450; + r:component skolem:lemma1451; + r:component skolem:lemma1452; + r:component skolem:lemma1453; + r:component skolem:lemma1454; + r:component skolem:lemma1455; + r:component skolem:lemma1456; + r:component skolem:lemma1457; + r:component skolem:lemma1458; + r:component skolem:lemma1459; + r:component skolem:lemma1460; + r:component skolem:lemma1461; + r:component skolem:lemma1462; + r:component skolem:lemma1463; + r:component skolem:lemma1464; + r:component skolem:lemma1465; + r:component skolem:lemma1466; + r:component skolem:lemma1467; + r:component skolem:lemma1468; + r:component skolem:lemma1469; + r:component skolem:lemma1470; + r:component skolem:lemma1471; + r:component skolem:lemma1472; + r:component skolem:lemma1473; + r:component skolem:lemma1474; + r:component skolem:lemma1475; + r:component skolem:lemma1476; + r:component skolem:lemma1477; + r:component skolem:lemma1478; + r:component skolem:lemma1479; + r:component skolem:lemma1480; + r:component skolem:lemma1481; + r:component skolem:lemma1482; + r:component skolem:lemma1483; + r:component skolem:lemma1484; + r:component skolem:lemma1485; + r:component skolem:lemma1486; + r:component skolem:lemma1487; + r:component skolem:lemma1488; + r:component skolem:lemma1489; + r:component skolem:lemma1490; + r:component skolem:lemma1491; + r:component skolem:lemma1492; + r:component skolem:lemma1493; + r:component skolem:lemma1494; + r:component skolem:lemma1495; + r:component skolem:lemma1496; + r:component skolem:lemma1497; + r:component skolem:lemma1498; + r:component skolem:lemma1499; + r:component skolem:lemma1500; + r:component skolem:lemma1501; + r:component skolem:lemma1502; + r:component skolem:lemma1503; + r:component skolem:lemma1504; + r:component skolem:lemma1505; + r:component skolem:lemma1506; + r:component skolem:lemma1507; + r:component skolem:lemma1508; + r:component skolem:lemma1509; + r:component skolem:lemma1510; + r:component skolem:lemma1511; + r:component skolem:lemma1512; + r:component skolem:lemma1513; + r:component skolem:lemma1514; + r:component skolem:lemma1515; + r:component skolem:lemma1516; + r:component skolem:lemma1517; + r:component skolem:lemma1518; + r:component skolem:lemma1519; + r:component skolem:lemma1520; + r:component skolem:lemma1521; + r:component skolem:lemma1522; + r:component skolem:lemma1523; + r:component skolem:lemma1524; + r:component skolem:lemma1525; + r:component skolem:lemma1526; + r:component skolem:lemma1527; + r:component skolem:lemma1528; + r:component skolem:lemma1529; + r:component skolem:lemma1530; + r:component skolem:lemma1531; + r:component skolem:lemma1532; + r:component skolem:lemma1533; + r:component skolem:lemma1534; + r:component skolem:lemma1535; + r:component skolem:lemma1536; + r:component skolem:lemma1537; + r:component skolem:lemma1538; + r:component skolem:lemma1539; + r:component skolem:lemma1540; + r:component skolem:lemma1541; + r:component skolem:lemma1542; + r:component skolem:lemma1543; + r:component skolem:lemma1544; + r:component skolem:lemma1545; + r:component skolem:lemma1546; + r:component skolem:lemma1547; + r:component skolem:lemma1548; + r:component skolem:lemma1549; + r:component skolem:lemma1550; + r:component skolem:lemma1551; + r:component skolem:lemma1552; + r:component skolem:lemma1553; + r:component skolem:lemma1554; + r:component skolem:lemma1555; + r:component skolem:lemma1556; + r:component skolem:lemma1557; + r:component skolem:lemma1558; + r:component skolem:lemma1559; + r:component skolem:lemma1560; + r:component skolem:lemma1561; + r:component skolem:lemma1562; + r:component skolem:lemma1563; + r:component skolem:lemma1564; + r:component skolem:lemma1565; + r:component skolem:lemma1566; + r:component skolem:lemma1567; + r:component skolem:lemma1568; + r:component skolem:lemma1569; + r:component skolem:lemma1570; + r:component skolem:lemma1571; + r:component skolem:lemma1572; + r:component skolem:lemma1573; + r:component skolem:lemma1574; + r:component skolem:lemma1575; + r:component skolem:lemma1576; + r:component skolem:lemma1577; + r:component skolem:lemma1578; + r:component skolem:lemma1579; + r:component skolem:lemma1580; + r:component skolem:lemma1581; + r:component skolem:lemma1582; + r:component skolem:lemma1583; + r:component skolem:lemma1584; + r:component skolem:lemma1585; + r:component skolem:lemma1586; + r:component skolem:lemma1587; + r:component skolem:lemma1588; + r:component skolem:lemma1589; + r:component skolem:lemma1590; + r:component skolem:lemma1591; + r:component skolem:lemma1592; + r:component skolem:lemma1593; + r:component skolem:lemma1594; + r:component skolem:lemma1595; + r:component skolem:lemma1596; + r:component skolem:lemma1597; + r:component skolem:lemma1598; + r:component skolem:lemma1599; + r:component skolem:lemma1600; + r:component skolem:lemma1601; + r:component skolem:lemma1602; + r:component skolem:lemma1603; + r:component skolem:lemma1604; + r:component skolem:lemma1605; + r:component skolem:lemma1606; + r:component skolem:lemma1607; + r:component skolem:lemma1608; + r:component skolem:lemma1609; + r:component skolem:lemma1610; + r:component skolem:lemma1611; + r:component skolem:lemma1612; + r:component skolem:lemma1613; + r:component skolem:lemma1614; + r:component skolem:lemma1615; + r:component skolem:lemma1616; + r:component skolem:lemma1617; + r:component skolem:lemma1618; + r:component skolem:lemma1619; + r:component skolem:lemma1620; + r:component skolem:lemma1621; + r:component skolem:lemma1622; + r:component skolem:lemma1623; + r:component skolem:lemma1624; + r:component skolem:lemma1625; + r:component skolem:lemma1626; + r:component skolem:lemma1627; + r:component skolem:lemma1628; + r:component skolem:lemma1629; + r:component skolem:lemma1630; + r:component skolem:lemma1631; + r:component skolem:lemma1632; + r:component skolem:lemma1633; + r:component skolem:lemma1634; + r:component skolem:lemma1635; + r:component skolem:lemma1636; + r:component skolem:lemma1637; + r:component skolem:lemma1638; + r:component skolem:lemma1639; + r:component skolem:lemma1640; + r:component skolem:lemma1641; + r:component skolem:lemma1642; + r:component skolem:lemma1643; + r:component skolem:lemma1644; + r:component skolem:lemma1645; + r:component skolem:lemma1646; + r:component skolem:lemma1647; + r:component skolem:lemma1648; + r:component skolem:lemma1649; + r:component skolem:lemma1650; + r:component skolem:lemma1651; + r:component skolem:lemma1652; + r:component skolem:lemma1653; + r:component skolem:lemma1654; + r:component skolem:lemma1655; + r:component skolem:lemma1656; + r:component skolem:lemma1657; + r:component skolem:lemma1658; + r:component skolem:lemma1659; + r:component skolem:lemma1660; + r:component skolem:lemma1661; + r:component skolem:lemma1662; + r:component skolem:lemma1663; + r:component skolem:lemma1664; + r:component skolem:lemma1665; + r:component skolem:lemma1666; + r:component skolem:lemma1667; + r:component skolem:lemma1668; + r:component skolem:lemma1669; + r:component skolem:lemma1670; + r:component skolem:lemma1671; + r:component skolem:lemma1672; + r:component skolem:lemma1673; + r:component skolem:lemma1674; + r:component skolem:lemma1675; + r:component skolem:lemma1676; + r:component skolem:lemma1677; + r:component skolem:lemma1678; + r:component skolem:lemma1679; + r:component skolem:lemma1680; + r:component skolem:lemma1681; + r:component skolem:lemma1682; + r:component skolem:lemma1683; + r:component skolem:lemma1684; + r:component skolem:lemma1685; + r:component skolem:lemma1686; + r:component skolem:lemma1687; + r:component skolem:lemma1688; + r:component skolem:lemma1689; + r:component skolem:lemma1690; + r:component skolem:lemma1691; + r:component skolem:lemma1692; + r:component skolem:lemma1693; + r:component skolem:lemma1694; + r:component skolem:lemma1695; + r:component skolem:lemma1696; + r:component skolem:lemma1697; + r:component skolem:lemma1698; + r:component skolem:lemma1699; + r:component skolem:lemma1700; + r:component skolem:lemma1701; + r:component skolem:lemma1702; + r:component skolem:lemma1703; + r:component skolem:lemma1704; + r:component skolem:lemma1705; + r:component skolem:lemma1706; + r:component skolem:lemma1707; + r:component skolem:lemma1708; + r:component skolem:lemma1709; + r:component skolem:lemma1710; + r:component skolem:lemma1711; + r:component skolem:lemma1712; + r:component skolem:lemma1713; + r:component skolem:lemma1714; + r:component skolem:lemma1715; + r:component skolem:lemma1716; + r:component skolem:lemma1717; + r:component skolem:lemma1718; + r:component skolem:lemma1719; + r:component skolem:lemma1720; + r:component skolem:lemma1721; + r:component skolem:lemma1722; + r:component skolem:lemma1723; + r:component skolem:lemma1724; + r:component skolem:lemma1725; + r:component skolem:lemma1726; + r:component skolem:lemma1727; + r:component skolem:lemma1728; + r:component skolem:lemma1729; + r:component skolem:lemma1730; + r:component skolem:lemma1731; + r:component skolem:lemma1732; + r:component skolem:lemma1733; + r:component skolem:lemma1734; + r:component skolem:lemma1735; + r:component skolem:lemma1736; + r:component skolem:lemma1737; + r:component skolem:lemma1738; + r:component skolem:lemma1739; + r:component skolem:lemma1740; + r:component skolem:lemma1741; + r:component skolem:lemma1742; + r:component skolem:lemma1743; + r:component skolem:lemma1744; + r:component skolem:lemma1745; + r:component skolem:lemma1746; + r:component skolem:lemma1747; + r:component skolem:lemma1748; + r:component skolem:lemma1749; + r:component skolem:lemma1750; + r:component skolem:lemma1751; + r:component skolem:lemma1752; + r:component skolem:lemma1753; + r:component skolem:lemma1754; + r:component skolem:lemma1755; + r:component skolem:lemma1756; + r:component skolem:lemma1757; + r:component skolem:lemma1758; + r:component skolem:lemma1759; + r:component skolem:lemma1760; + r:component skolem:lemma1761; + r:component skolem:lemma1762; + r:component skolem:lemma1763; + r:component skolem:lemma1764; + r:component skolem:lemma1765; + r:component skolem:lemma1766; + r:component skolem:lemma1767; + r:component skolem:lemma1768; + r:component skolem:lemma1769; + r:component skolem:lemma1770; + r:component skolem:lemma1771; + r:component skolem:lemma1772; + r:component skolem:lemma1773; + r:component skolem:lemma1774; + r:component skolem:lemma1775; + r:component skolem:lemma1776; + r:component skolem:lemma1777; + r:component skolem:lemma1778; + r:component skolem:lemma1779; + r:component skolem:lemma1780; + r:component skolem:lemma1781; + r:component skolem:lemma1782; + r:component skolem:lemma1783; + r:component skolem:lemma1784; + r:component skolem:lemma1785; + r:component skolem:lemma1786; + r:component skolem:lemma1787; + r:component skolem:lemma1788; + r:component skolem:lemma1789; + r:component skolem:lemma1790; + r:component skolem:lemma1791; + r:component skolem:lemma1792; + r:component skolem:lemma1793; + r:component skolem:lemma1794; + r:component skolem:lemma1795; + r:component skolem:lemma1796; + r:component skolem:lemma1797; + r:component skolem:lemma1798; + r:component skolem:lemma1799; + r:component skolem:lemma1800; + r:component skolem:lemma1801; + r:component skolem:lemma1802; + r:component skolem:lemma1803; + r:component skolem:lemma1804; + r:component skolem:lemma1805; + r:component skolem:lemma1806; + r:component skolem:lemma1807; + r:component skolem:lemma1808; + r:component skolem:lemma1809; + r:component skolem:lemma1810; + r:component skolem:lemma1811; + r:component skolem:lemma1812; + r:component skolem:lemma1813; + r:component skolem:lemma1814; + r:component skolem:lemma1815; + r:component skolem:lemma1816; + r:component skolem:lemma1817; + r:component skolem:lemma1818; + r:component skolem:lemma1819; + r:component skolem:lemma1820; + r:component skolem:lemma1821; + r:component skolem:lemma1822; + r:component skolem:lemma1823; + r:component skolem:lemma1824; + r:component skolem:lemma1825; + r:component skolem:lemma1826; + r:component skolem:lemma1827; + r:component skolem:lemma1828; + r:component skolem:lemma1829; + r:component skolem:lemma1830; + r:component skolem:lemma1831; + r:component skolem:lemma1832; + r:component skolem:lemma1833; + r:component skolem:lemma1834; + r:component skolem:lemma1835; + r:component skolem:lemma1836; + r:component skolem:lemma1837; + r:component skolem:lemma1838; + r:component skolem:lemma1839; + r:component skolem:lemma1840; + r:component skolem:lemma1841; + r:component skolem:lemma1842; + r:component skolem:lemma1843; + r:component skolem:lemma1844; + r:component skolem:lemma1845; + r:component skolem:lemma1846; + r:component skolem:lemma1847; + r:component skolem:lemma1848; + r:component skolem:lemma1849; + r:component skolem:lemma1850; + r:component skolem:lemma1851; + r:component skolem:lemma1852; + r:component skolem:lemma1853; + r:component skolem:lemma1854; + r:component skolem:lemma1855; + r:component skolem:lemma1856; + r:component skolem:lemma1857; + r:component skolem:lemma1858; + r:component skolem:lemma1859; + r:component skolem:lemma1860; + r:component skolem:lemma1861; + r:component skolem:lemma1862; + r:component skolem:lemma1863; + r:component skolem:lemma1864; + r:component skolem:lemma1865; + r:component skolem:lemma1866; + r:component skolem:lemma1867; + r:component skolem:lemma1868; + r:component skolem:lemma1869; + r:component skolem:lemma1870; + r:component skolem:lemma1871; + r:component skolem:lemma1872; + r:component skolem:lemma1873; + r:component skolem:lemma1874; + r:component skolem:lemma1875; + r:component skolem:lemma1876; + r:component skolem:lemma1877; + r:component skolem:lemma1878; + r:component skolem:lemma1879; + r:component skolem:lemma1880; + r:component skolem:lemma1881; + r:component skolem:lemma1882; + r:component skolem:lemma1883; + r:component skolem:lemma1884; + r:component skolem:lemma1885; + r:component skolem:lemma1886; + r:component skolem:lemma1887; + r:component skolem:lemma1888; + r:component skolem:lemma1889; + r:component skolem:lemma1890; + r:component skolem:lemma1891; + r:component skolem:lemma1892; + r:component skolem:lemma1893; + r:component skolem:lemma1894; + r:component skolem:lemma1895; + r:component skolem:lemma1896; + r:component skolem:lemma1897; + r:component skolem:lemma1898; + r:component skolem:lemma1899; + r:component skolem:lemma1900; + r:component skolem:lemma1901; + r:component skolem:lemma1902; + r:component skolem:lemma1903; + r:component skolem:lemma1904; + r:component skolem:lemma1905; + r:component skolem:lemma1906; + r:component skolem:lemma1907; + r:component skolem:lemma1908; + r:component skolem:lemma1909; + r:component skolem:lemma1910; + r:component skolem:lemma1911; + r:component skolem:lemma1912; + r:component skolem:lemma1913; + r:component skolem:lemma1914; + r:component skolem:lemma1915; + r:component skolem:lemma1916; + r:component skolem:lemma1917; + r:component skolem:lemma1918; + r:component skolem:lemma1919; + r:component skolem:lemma1920; + r:component skolem:lemma1921; + r:component skolem:lemma1922; + r:component skolem:lemma1923; + r:component skolem:lemma1924; + r:component skolem:lemma1925; + r:component skolem:lemma1926; + r:component skolem:lemma1927; + r:component skolem:lemma1928; + r:component skolem:lemma1929; + r:component skolem:lemma1930; + r:component skolem:lemma1931; + r:component skolem:lemma1932; + r:component skolem:lemma1933; + r:component skolem:lemma1934; + r:component skolem:lemma1935; + r:component skolem:lemma1936; + r:component skolem:lemma1937; + r:component skolem:lemma1938; + r:component skolem:lemma1939; + r:component skolem:lemma1940; + r:component skolem:lemma1941; + r:component skolem:lemma1942; + r:component skolem:lemma1943; + r:component skolem:lemma1944; + r:component skolem:lemma1945; + r:component skolem:lemma1946; + r:component skolem:lemma1947; + r:component skolem:lemma1948; + r:component skolem:lemma1949; + r:component skolem:lemma1950; + r:component skolem:lemma1951; + r:component skolem:lemma1952; + r:component skolem:lemma1953; + r:component skolem:lemma1954; + r:component skolem:lemma1955; + r:component skolem:lemma1956; + r:component skolem:lemma1957; + r:component skolem:lemma1958; + r:component skolem:lemma1959; + r:component skolem:lemma1960; + r:component skolem:lemma1961; + r:component skolem:lemma1962; + r:component skolem:lemma1963; + r:component skolem:lemma1964; + r:component skolem:lemma1965; + r:component skolem:lemma1966; + r:component skolem:lemma1967; + r:component skolem:lemma1968; + r:component skolem:lemma1969; + r:component skolem:lemma1970; + r:component skolem:lemma1971; + r:component skolem:lemma1972; + r:component skolem:lemma1973; + r:component skolem:lemma1974; + r:component skolem:lemma1975; + r:component skolem:lemma1976; + r:component skolem:lemma1977; + r:component skolem:lemma1978; + r:component skolem:lemma1979; + r:component skolem:lemma1980; + r:component skolem:lemma1981; + r:component skolem:lemma1982; + r:component skolem:lemma1983; + r:component skolem:lemma1984; + r:component skolem:lemma1985; + r:component skolem:lemma1986; + r:component skolem:lemma1987; + r:component skolem:lemma1988; + r:component skolem:lemma1989; + r:component skolem:lemma1990; + r:component skolem:lemma1991; + r:component skolem:lemma1992; + r:component skolem:lemma1993; + r:component skolem:lemma1994; + r:component skolem:lemma1995; + r:component skolem:lemma1996; + r:component skolem:lemma1997; + r:component skolem:lemma1998; r:gives { 2000 :recursionCount 4 . 2001 :recursionCount 3 . @@ -2007,6 +3006,1005 @@ skolem:proof a r:Proof, r:Conjunction; 2997 :recursionCount 5 . 2998 :recursionCount 3 . 2999 :recursionCount 4 . + 3000 :recursionCount 6 . + 3001 :recursionCount 3 . + 3002 :recursionCount 5 . + 3003 :recursionCount 6 . + 3004 :recursionCount 3 . + 3005 :recursionCount 5 . + 3006 :recursionCount 3 . + 3007 :recursionCount 6 . + 3008 :recursionCount 5 . + 3009 :recursionCount 3 . + 3010 :recursionCount 3 . + 3011 :recursionCount 6 . + 3012 :recursionCount 3 . + 3013 :recursionCount 5 . + 3014 :recursionCount 2 . + 3015 :recursionCount 7 . + 3016 :recursionCount 1 . + 3017 :recursionCount 5 . + 3018 :recursionCount 6 . + 3019 :recursionCount 3 . + 3020 :recursionCount 5 . + 3021 :recursionCount 3 . + 3022 :recursionCount 6 . + 3023 :recursionCount 3 . + 3024 :recursionCount 7 . + 3025 :recursionCount 7 . + 3026 :recursionCount 7 . + 3027 :recursionCount 3 . + 3028 :recursionCount 3 . + 3029 :recursionCount 4 . + 3030 :recursionCount 6 . + 3031 :recursionCount 5 . + 3032 :recursionCount 3 . + 3033 :recursionCount 6 . + 3034 :recursionCount 4 . + 3035 :recursionCount 6 . + 3036 :recursionCount 6 . + 3037 :recursionCount 4 . + 3038 :recursionCount 6 . + 3039 :recursionCount 4 . + 3040 :recursionCount 3 . + 3041 :recursionCount 2 . + 3042 :recursionCount 7 . + 3043 :recursionCount 4 . + 3044 :recursionCount 7 . + 3045 :recursionCount 7 . + 3046 :recursionCount 7 . + 3047 :recursionCount 3 . + 3048 :recursionCount 3 . + 3049 :recursionCount 4 . + 3050 :recursionCount 5 . + 3051 :recursionCount 7 . + 3052 :recursionCount 7 . + 3053 :recursionCount 6 . + 3054 :recursionCount 7 . + 3055 :recursionCount 7 . + 3056 :recursionCount 1 . + 3057 :recursionCount 5 . + 3058 :recursionCount 6 . + 3059 :recursionCount 3 . + 3060 :recursionCount 3 . + 3061 :recursionCount 1 . + 3062 :recursionCount 7 . + 3063 :recursionCount 6 . + 3064 :recursionCount 7 . + 3065 :recursionCount 1 . + 3066 :recursionCount 3 . + 3067 :recursionCount 6 . + 3068 :recursionCount 5 . + 3069 :recursionCount 3 . + 3070 :recursionCount 6 . + 3071 :recursionCount 5 . + 3072 :recursionCount 3 . + 3073 :recursionCount 4 . + 3074 :recursionCount 3 . + 3075 :recursionCount 5 . + 3076 :recursionCount 6 . + 3077 :recursionCount 3 . + 3078 :recursionCount 2 . + 3079 :recursionCount 7 . + 3080 :recursionCount 5 . + 3081 :recursionCount 6 . + 3082 :recursionCount 3 . + 3083 :recursionCount 6 . + 3084 :recursionCount 3 . + 3085 :recursionCount 6 . + 3086 :recursionCount 5 . + 3087 :recursionCount 2 . + 3088 :recursionCount 7 . + 3089 :recursionCount 7 . + 3090 :recursionCount 3 . + 3091 :recursionCount 3 . + 3092 :recursionCount 4 . + 3093 :recursionCount 4 . + 3094 :recursionCount 4 . + 3095 :recursionCount 3 . + 3096 :recursionCount 3 . + 3097 :recursionCount 7 . + 3098 :recursionCount 7 . + 3099 :recursionCount 7 . + 3100 :recursionCount 3 . + 3101 :recursionCount 6 . + 3102 :recursionCount 3 . + 3103 :recursionCount 5 . + 3104 :recursionCount 2 . + 3105 :recursionCount 7 . + 3106 :recursionCount 1 . + 3107 :recursionCount 5 . + 3108 :recursionCount 6 . + 3109 :recursionCount 3 . + 3110 :recursionCount 6 . + 3111 :recursionCount 4 . + 3112 :recursionCount 3 . + 3113 :recursionCount 6 . + 3114 :recursionCount 5 . + 3115 :recursionCount 2 . + 3116 :recursionCount 7 . + 3117 :recursionCount 1 . + 3118 :recursionCount 5 . + 3119 :recursionCount 6 . + 3120 :recursionCount 3 . + 3121 :recursionCount 3 . + 3122 :recursionCount 4 . + 3123 :recursionCount 3 . + 3124 :recursionCount 3 . + 3125 :recursionCount 7 . + 3126 :recursionCount 7 . + 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3942 :recursionCount 3 . + 3943 :recursionCount 7 . + 3944 :recursionCount 6 . + 3945 :recursionCount 7 . + 3946 :recursionCount 1 . + 3947 :recursionCount 3 . + 3948 :recursionCount 4 . + 3949 :recursionCount 5 . + 3950 :recursionCount 3 . + 3951 :recursionCount 6 . + 3952 :recursionCount 5 . + 3953 :recursionCount 1 . + 3954 :recursionCount 7 . + 3955 :recursionCount 6 . + 3956 :recursionCount 7 . + 3957 :recursionCount 1 . + 3958 :recursionCount 3 . + 3959 :recursionCount 4 . + 3960 :recursionCount 3 . + 3961 :recursionCount 5 . + 3962 :recursionCount 6 . + 3963 :recursionCount 3 . + 3964 :recursionCount 1 . + 3965 :recursionCount 7 . + 3966 :recursionCount 6 . + 3967 :recursionCount 7 . + 3968 :recursionCount 1 . + 3969 :recursionCount 3 . + 3970 :recursionCount 7 . + 3971 :recursionCount 2 . + 3972 :recursionCount 3 . + 3973 :recursionCount 4 . + 3974 :recursionCount 3 . + 3975 :recursionCount 1 . + 3976 :recursionCount 7 . + 3977 :recursionCount 6 . + 3978 :recursionCount 7 . + 3979 :recursionCount 1 . + 3980 :recursionCount 7 . + 3981 :recursionCount 7 . + 3982 :recursionCount 5 . + 3983 :recursionCount 5 . + 3984 :recursionCount 4 . + 3985 :recursionCount 3 . + 3986 :recursionCount 1 . + 3987 :recursionCount 7 . + 3988 :recursionCount 6 . + 3989 :recursionCount 7 . + 3990 :recursionCount 7 . + 3991 :recursionCount 2 . + 3992 :recursionCount 3 . + 3993 :recursionCount 4 . + 3994 :recursionCount 5 . + 3995 :recursionCount 4 . + 3996 :recursionCount 3 . + 3997 :recursionCount 1 . + 3998 :recursionCount 7 . + 3999 :recursionCount 6 . }. skolem:lemma1 a r:Inference; @@ -2014,47263 +4012,28235 @@ skolem:lemma1 a r:Inference; 2000 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 0}] + [ a r:Fact; r:gives {2000 log:repeat 0}] [ a r:Fact; r:gives {(0 2000) math:sum 2000}] - skolem:lemma1000 + skolem:lemma1999 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma2 a r:Inference; r:gives { 2001 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 1}] + [ a r:Fact; r:gives {2000 log:repeat 1}] [ a r:Fact; r:gives {(1 2000) math:sum 2001}] - skolem:lemma1002 + skolem:lemma2001 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2001]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma3 a r:Inference; r:gives { 2002 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 2}] + [ a r:Fact; r:gives {2000 log:repeat 2}] [ a r:Fact; r:gives {(2 2000) math:sum 2002}] - skolem:lemma1003 + skolem:lemma2002 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2002]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma4 a r:Inference; r:gives { 2003 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 3}] + [ a r:Fact; r:gives {2000 log:repeat 3}] [ a r:Fact; r:gives {(3 2000) math:sum 2003}] - skolem:lemma1004 + skolem:lemma2003 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2003]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma5 a r:Inference; r:gives { 2004 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 4}] + [ a r:Fact; r:gives {2000 log:repeat 4}] [ a r:Fact; r:gives {(4 2000) math:sum 2004}] - skolem:lemma1005 + skolem:lemma2004 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2004]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma6 a r:Inference; r:gives { 2005 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 5}] + [ a r:Fact; r:gives {2000 log:repeat 5}] [ a r:Fact; r:gives {(5 2000) math:sum 2005}] - skolem:lemma1006 + skolem:lemma2005 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2005]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma7 a r:Inference; r:gives { 2006 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 6}] + [ a r:Fact; r:gives {2000 log:repeat 6}] [ a r:Fact; r:gives {(6 2000) math:sum 2006}] - skolem:lemma1007 + skolem:lemma2006 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2006]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma8 a r:Inference; r:gives { 2007 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 7}] + [ a r:Fact; r:gives {2000 log:repeat 7}] [ a r:Fact; r:gives {(7 2000) math:sum 2007}] - skolem:lemma1008 + skolem:lemma2007 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2007]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma9 a r:Inference; r:gives { 2008 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 8}] + [ a r:Fact; r:gives {2000 log:repeat 8}] [ a r:Fact; r:gives {(8 2000) math:sum 2008}] - skolem:lemma1009 + skolem:lemma2008 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2008]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma10 a r:Inference; r:gives { 2009 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 9}] + [ a r:Fact; r:gives {2000 log:repeat 9}] [ a r:Fact; r:gives {(9 2000) math:sum 2009}] - skolem:lemma1010 + skolem:lemma2009 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2009]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma11 a r:Inference; r:gives { 2010 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 10}] + [ a r:Fact; r:gives {2000 log:repeat 10}] [ a r:Fact; r:gives {(10 2000) math:sum 2010}] - skolem:lemma1011 + skolem:lemma2010 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2010]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma12 a r:Inference; r:gives { 2011 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 11}] + [ a r:Fact; r:gives {2000 log:repeat 11}] [ a r:Fact; r:gives {(11 2000) math:sum 2011}] - skolem:lemma1012 + skolem:lemma2011 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 11]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2011]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma13 a r:Inference; r:gives { 2012 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 12}] + [ a r:Fact; r:gives {2000 log:repeat 12}] [ a r:Fact; r:gives {(12 2000) math:sum 2012}] - skolem:lemma1013 + skolem:lemma2012 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 12]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2012]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma14 a r:Inference; r:gives { 2013 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 13}] + [ a r:Fact; r:gives {2000 log:repeat 13}] [ a r:Fact; r:gives {(13 2000) math:sum 2013}] - skolem:lemma1014 + skolem:lemma2013 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 13]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2013]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma15 a r:Inference; r:gives { 2014 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 14}] + [ a r:Fact; r:gives {2000 log:repeat 14}] [ a r:Fact; r:gives {(14 2000) math:sum 2014}] - skolem:lemma1015 + skolem:lemma2014 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 14]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2014]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma16 a r:Inference; r:gives { 2015 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 15}] + [ a r:Fact; r:gives {2000 log:repeat 15}] [ a r:Fact; r:gives {(15 2000) math:sum 2015}] - skolem:lemma1016 + skolem:lemma2015 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 15]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2015]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma17 a r:Inference; r:gives { 2016 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 16}] + [ a r:Fact; r:gives {2000 log:repeat 16}] [ a r:Fact; r:gives {(16 2000) math:sum 2016}] - skolem:lemma1017 + skolem:lemma2016 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 16]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2016]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma18 a r:Inference; r:gives { 2017 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 17}] + [ a r:Fact; r:gives {2000 log:repeat 17}] [ a r:Fact; r:gives {(17 2000) math:sum 2017}] - skolem:lemma1018 + skolem:lemma2017 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 17]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2017]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma19 a r:Inference; r:gives { 2018 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 18}] + [ a r:Fact; r:gives {2000 log:repeat 18}] [ a r:Fact; r:gives {(18 2000) math:sum 2018}] - skolem:lemma1019 + skolem:lemma2018 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 18]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2018]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma20 a r:Inference; r:gives { 2019 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 19}] + [ a r:Fact; r:gives {2000 log:repeat 19}] [ a r:Fact; r:gives {(19 2000) math:sum 2019}] - skolem:lemma1020 + skolem:lemma2019 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 19]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2019]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma21 a r:Inference; r:gives { 2020 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 20}] + [ a r:Fact; r:gives {2000 log:repeat 20}] [ a r:Fact; r:gives {(20 2000) math:sum 2020}] - skolem:lemma1021 + skolem:lemma2020 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 20]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2020]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma22 a r:Inference; r:gives { 2021 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 21}] + [ a r:Fact; r:gives {2000 log:repeat 21}] [ a r:Fact; r:gives {(21 2000) math:sum 2021}] - skolem:lemma1022 + skolem:lemma2021 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 21]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2021]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma23 a r:Inference; r:gives { 2022 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 22}] + [ a r:Fact; r:gives {2000 log:repeat 22}] [ a r:Fact; r:gives {(22 2000) math:sum 2022}] - skolem:lemma1023 + skolem:lemma2022 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 22]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2022]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma24 a r:Inference; r:gives { 2023 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 23}] + [ a r:Fact; r:gives {2000 log:repeat 23}] [ a r:Fact; r:gives {(23 2000) math:sum 2023}] - skolem:lemma1024 + skolem:lemma2023 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 23]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2023]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma25 a r:Inference; r:gives { 2024 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 24}] + [ a r:Fact; r:gives {2000 log:repeat 24}] [ a r:Fact; r:gives {(24 2000) math:sum 2024}] - skolem:lemma1025 + skolem:lemma2024 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 24]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2024]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma26 a r:Inference; r:gives { 2025 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 25}] + [ a r:Fact; r:gives {2000 log:repeat 25}] [ a r:Fact; r:gives {(25 2000) math:sum 2025}] - skolem:lemma1026 + skolem:lemma2025 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 25]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2025]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma27 a r:Inference; r:gives { 2026 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 26}] + [ a r:Fact; r:gives {2000 log:repeat 26}] [ a r:Fact; r:gives {(26 2000) math:sum 2026}] - skolem:lemma1027 + skolem:lemma2026 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 26]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2026]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma28 a r:Inference; r:gives { 2027 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 27}] + [ a r:Fact; r:gives {2000 log:repeat 27}] [ a r:Fact; r:gives {(27 2000) math:sum 2027}] - skolem:lemma1028 + skolem:lemma2027 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 27]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2027]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma29 a r:Inference; r:gives { 2028 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 28}] + [ a r:Fact; r:gives {2000 log:repeat 28}] [ a r:Fact; r:gives {(28 2000) math:sum 2028}] - skolem:lemma1029 + skolem:lemma2028 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 28]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2028]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma30 a r:Inference; r:gives { 2029 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 29}] + [ a r:Fact; r:gives {2000 log:repeat 29}] [ a r:Fact; r:gives {(29 2000) math:sum 2029}] - skolem:lemma1030 + skolem:lemma2029 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 29]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2029]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma31 a r:Inference; r:gives { 2030 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 30}] + [ a r:Fact; r:gives {2000 log:repeat 30}] [ a r:Fact; r:gives {(30 2000) math:sum 2030}] - skolem:lemma1031 + skolem:lemma2030 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2030]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma32 a r:Inference; r:gives { 2031 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 31}] + [ a r:Fact; r:gives {2000 log:repeat 31}] [ a r:Fact; r:gives {(31 2000) math:sum 2031}] - skolem:lemma1032 + skolem:lemma2031 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 31]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2031]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma33 a r:Inference; r:gives { 2032 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 32}] + [ a r:Fact; r:gives {2000 log:repeat 32}] [ a r:Fact; r:gives {(32 2000) math:sum 2032}] - skolem:lemma1033 + skolem:lemma2032 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 32]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2032]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma34 a r:Inference; r:gives { 2033 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 33}] + [ a r:Fact; r:gives {2000 log:repeat 33}] [ a r:Fact; r:gives {(33 2000) math:sum 2033}] - skolem:lemma1034 + skolem:lemma2033 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 33]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2033]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma35 a r:Inference; r:gives { 2034 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 34}] + [ a r:Fact; r:gives {2000 log:repeat 34}] [ a r:Fact; r:gives {(34 2000) math:sum 2034}] - skolem:lemma1035 + skolem:lemma2034 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 34]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2034]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma36 a r:Inference; r:gives { 2035 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 35}] + [ a r:Fact; r:gives {2000 log:repeat 35}] [ a r:Fact; r:gives {(35 2000) math:sum 2035}] - skolem:lemma1036 + skolem:lemma2035 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 35]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2035]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma37 a r:Inference; r:gives { 2036 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 36}] + [ a r:Fact; r:gives {2000 log:repeat 36}] [ a r:Fact; r:gives {(36 2000) math:sum 2036}] - skolem:lemma1037 + skolem:lemma2036 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 36]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2036]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma38 a r:Inference; r:gives { 2037 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 37}] + [ a r:Fact; r:gives {2000 log:repeat 37}] [ a r:Fact; r:gives {(37 2000) math:sum 2037}] - skolem:lemma1038 + skolem:lemma2037 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 37]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2037]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma39 a r:Inference; r:gives { 2038 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 38}] + [ a r:Fact; r:gives {2000 log:repeat 38}] [ a r:Fact; r:gives {(38 2000) math:sum 2038}] - skolem:lemma1039 + skolem:lemma2038 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 38]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2038]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma40 a r:Inference; r:gives { 2039 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 39}] + [ a r:Fact; r:gives {2000 log:repeat 39}] [ a r:Fact; r:gives {(39 2000) math:sum 2039}] - skolem:lemma1040 + skolem:lemma2039 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 39]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2039]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma41 a r:Inference; r:gives { 2040 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 40}] + [ a r:Fact; r:gives {2000 log:repeat 40}] [ a r:Fact; r:gives {(40 2000) math:sum 2040}] - skolem:lemma1041 + skolem:lemma2040 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2040]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma42 a r:Inference; r:gives { 2041 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 41}] + [ a r:Fact; r:gives {2000 log:repeat 41}] [ a r:Fact; r:gives {(41 2000) math:sum 2041}] - skolem:lemma1042 + skolem:lemma2041 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 41]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2041]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma43 a r:Inference; r:gives { 2042 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 42}] + [ a r:Fact; r:gives {2000 log:repeat 42}] [ a r:Fact; r:gives {(42 2000) math:sum 2042}] - skolem:lemma1043 + skolem:lemma2042 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 42]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2042]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma44 a r:Inference; r:gives { 2043 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 43}] + [ a r:Fact; r:gives {2000 log:repeat 43}] [ a r:Fact; r:gives {(43 2000) math:sum 2043}] - skolem:lemma1044 + skolem:lemma2043 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 43]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2043]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma45 a r:Inference; r:gives { 2044 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 44}] + [ a r:Fact; r:gives {2000 log:repeat 44}] [ a r:Fact; r:gives {(44 2000) math:sum 2044}] - skolem:lemma1045 + skolem:lemma2044 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 44]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2044]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma46 a r:Inference; r:gives { 2045 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 45}] + [ a r:Fact; r:gives {2000 log:repeat 45}] [ a r:Fact; r:gives {(45 2000) math:sum 2045}] - skolem:lemma1046 + skolem:lemma2045 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 45]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2045]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma47 a r:Inference; r:gives { 2046 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 46}] + [ a r:Fact; r:gives {2000 log:repeat 46}] [ a r:Fact; r:gives {(46 2000) math:sum 2046}] - skolem:lemma1047 + skolem:lemma2046 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 46]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2046]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma48 a r:Inference; r:gives { 2047 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 47}] + [ a r:Fact; r:gives {2000 log:repeat 47}] [ a r:Fact; r:gives {(47 2000) math:sum 2047}] - skolem:lemma1048 + skolem:lemma2047 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 47]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2047]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma49 a r:Inference; r:gives { 2048 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 48}] + [ a r:Fact; r:gives {2000 log:repeat 48}] [ a r:Fact; r:gives {(48 2000) math:sum 2048}] - skolem:lemma1049 + skolem:lemma2048 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 48]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2048]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma50 a r:Inference; r:gives { 2049 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 49}] + [ a r:Fact; r:gives {2000 log:repeat 49}] [ a r:Fact; r:gives {(49 2000) math:sum 2049}] - skolem:lemma1050 + skolem:lemma2049 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 49]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2049]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma51 a r:Inference; r:gives { 2050 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 50}] + [ a r:Fact; r:gives {2000 log:repeat 50}] [ a r:Fact; r:gives {(50 2000) math:sum 2050}] - skolem:lemma1051 + skolem:lemma2050 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2050]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma52 a r:Inference; r:gives { 2051 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 51}] + [ a r:Fact; r:gives {2000 log:repeat 51}] [ a r:Fact; r:gives {(51 2000) math:sum 2051}] - skolem:lemma1052 + skolem:lemma2051 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 51]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2051]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma53 a r:Inference; r:gives { 2052 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 52}] + [ a r:Fact; r:gives {2000 log:repeat 52}] [ a r:Fact; r:gives {(52 2000) math:sum 2052}] - skolem:lemma1053 + skolem:lemma2052 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 52]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2052]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma54 a r:Inference; r:gives { 2053 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 53}] + [ a r:Fact; r:gives {2000 log:repeat 53}] [ a r:Fact; r:gives {(53 2000) math:sum 2053}] - skolem:lemma1054 + skolem:lemma2053 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 53]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2053]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma55 a r:Inference; r:gives { 2054 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 54}] + [ a r:Fact; r:gives {2000 log:repeat 54}] [ a r:Fact; r:gives {(54 2000) math:sum 2054}] - skolem:lemma1055 + skolem:lemma2054 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 54]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2054]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma56 a r:Inference; r:gives { 2055 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 55}] + [ a r:Fact; r:gives {2000 log:repeat 55}] [ a r:Fact; r:gives {(55 2000) math:sum 2055}] - skolem:lemma1056 + skolem:lemma2055 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 55]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2055]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma57 a r:Inference; r:gives { 2056 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 56}] + [ a r:Fact; r:gives {2000 log:repeat 56}] [ a r:Fact; r:gives {(56 2000) math:sum 2056}] - skolem:lemma1057 + skolem:lemma2056 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 56]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2056]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma58 a r:Inference; r:gives { 2057 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 57}] + [ a r:Fact; r:gives {2000 log:repeat 57}] [ a r:Fact; r:gives {(57 2000) math:sum 2057}] - skolem:lemma1058 + skolem:lemma2057 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 57]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2057]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma59 a r:Inference; r:gives { 2058 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 58}] + [ a r:Fact; r:gives {2000 log:repeat 58}] [ a r:Fact; r:gives {(58 2000) math:sum 2058}] - skolem:lemma1059 + skolem:lemma2058 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 58]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2058]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma60 a r:Inference; r:gives { 2059 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 59}] + [ a r:Fact; r:gives {2000 log:repeat 59}] [ a r:Fact; r:gives {(59 2000) math:sum 2059}] - skolem:lemma1060 + skolem:lemma2059 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 59]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2059]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma61 a r:Inference; r:gives { 2060 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 60}] + [ a r:Fact; r:gives {2000 log:repeat 60}] [ a r:Fact; r:gives {(60 2000) math:sum 2060}] - skolem:lemma1061 + skolem:lemma2060 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2060]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma62 a r:Inference; r:gives { 2061 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 61}] + [ a r:Fact; r:gives {2000 log:repeat 61}] [ a r:Fact; r:gives {(61 2000) math:sum 2061}] - skolem:lemma1062 + skolem:lemma2061 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 61]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2061]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma63 a r:Inference; r:gives { 2062 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 62}] + [ a r:Fact; r:gives {2000 log:repeat 62}] [ a r:Fact; r:gives {(62 2000) math:sum 2062}] - skolem:lemma1063 + skolem:lemma2062 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 62]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2062]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma64 a r:Inference; r:gives { 2063 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 63}] + [ a r:Fact; r:gives {2000 log:repeat 63}] [ a r:Fact; r:gives {(63 2000) math:sum 2063}] - skolem:lemma1064 + skolem:lemma2063 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 63]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2063]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma65 a r:Inference; r:gives { 2064 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 64}] + [ a r:Fact; r:gives {2000 log:repeat 64}] [ a r:Fact; r:gives {(64 2000) math:sum 2064}] - skolem:lemma1065 + skolem:lemma2064 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 64]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2064]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma66 a r:Inference; r:gives { 2065 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 65}] + [ a r:Fact; r:gives {2000 log:repeat 65}] [ a r:Fact; r:gives {(65 2000) math:sum 2065}] - skolem:lemma1066 + skolem:lemma2065 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 65]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2065]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma67 a r:Inference; r:gives { 2066 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 66}] + [ a r:Fact; r:gives {2000 log:repeat 66}] [ a r:Fact; r:gives {(66 2000) math:sum 2066}] - skolem:lemma1067 + skolem:lemma2066 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 66]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2066]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma68 a r:Inference; r:gives { 2067 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 67}] + [ a r:Fact; r:gives {2000 log:repeat 67}] [ a r:Fact; r:gives {(67 2000) math:sum 2067}] - skolem:lemma1068 + skolem:lemma2067 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 67]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2067]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma69 a r:Inference; r:gives { 2068 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 68}] + [ a r:Fact; r:gives {2000 log:repeat 68}] [ a r:Fact; r:gives {(68 2000) math:sum 2068}] - skolem:lemma1069 + skolem:lemma2068 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 68]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2068]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma70 a r:Inference; r:gives { 2069 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 69}] + [ a r:Fact; r:gives {2000 log:repeat 69}] [ a r:Fact; r:gives {(69 2000) math:sum 2069}] - skolem:lemma1070 + skolem:lemma2069 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 69]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2069]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma71 a r:Inference; r:gives { 2070 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 70}] + [ a r:Fact; r:gives {2000 log:repeat 70}] [ a r:Fact; r:gives {(70 2000) math:sum 2070}] - skolem:lemma1071 + skolem:lemma2070 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2070]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma72 a r:Inference; r:gives { 2071 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 71}] + [ a r:Fact; r:gives {2000 log:repeat 71}] [ a r:Fact; r:gives {(71 2000) math:sum 2071}] - skolem:lemma1072 + skolem:lemma2071 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 71]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2071]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma73 a r:Inference; r:gives { 2072 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 72}] + [ a r:Fact; r:gives {2000 log:repeat 72}] [ a r:Fact; r:gives {(72 2000) math:sum 2072}] - skolem:lemma1073 + skolem:lemma2072 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 72]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2072]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma74 a r:Inference; r:gives { 2073 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 73}] + [ a r:Fact; r:gives {2000 log:repeat 73}] [ a r:Fact; r:gives {(73 2000) math:sum 2073}] - skolem:lemma1074 + skolem:lemma2073 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 73]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2073]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma75 a r:Inference; r:gives { 2074 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 74}] + [ a r:Fact; r:gives {2000 log:repeat 74}] [ a r:Fact; r:gives {(74 2000) math:sum 2074}] - skolem:lemma1075 + skolem:lemma2074 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 74]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2074]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma76 a r:Inference; r:gives { 2075 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 75}] + [ a r:Fact; r:gives {2000 log:repeat 75}] [ a r:Fact; r:gives {(75 2000) math:sum 2075}] - skolem:lemma1076 + skolem:lemma2075 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 75]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2075]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma77 a r:Inference; r:gives { 2076 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 76}] + [ a r:Fact; r:gives {2000 log:repeat 76}] [ a r:Fact; r:gives {(76 2000) math:sum 2076}] - skolem:lemma1077 + skolem:lemma2076 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 76]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2076]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma78 a r:Inference; r:gives { 2077 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 77}] + [ a r:Fact; r:gives {2000 log:repeat 77}] [ a r:Fact; r:gives {(77 2000) math:sum 2077}] - skolem:lemma1078 + skolem:lemma2077 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 77]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2077]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma79 a r:Inference; r:gives { 2078 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 78}] + [ a r:Fact; r:gives {2000 log:repeat 78}] [ a r:Fact; r:gives {(78 2000) math:sum 2078}] - skolem:lemma1079 + skolem:lemma2078 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 78]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2078]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma80 a r:Inference; r:gives { 2079 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 79}] + [ a r:Fact; r:gives {2000 log:repeat 79}] [ a r:Fact; r:gives {(79 2000) math:sum 2079}] - skolem:lemma1080 + skolem:lemma2079 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 79]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2079]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma81 a r:Inference; r:gives { 2080 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 80}] + [ a r:Fact; r:gives {2000 log:repeat 80}] [ a r:Fact; r:gives {(80 2000) math:sum 2080}] - skolem:lemma1081 + skolem:lemma2080 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2080]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma82 a r:Inference; r:gives { 2081 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 81}] + [ a r:Fact; r:gives {2000 log:repeat 81}] [ a r:Fact; r:gives {(81 2000) math:sum 2081}] - skolem:lemma1082 + skolem:lemma2081 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 81]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2081]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma83 a r:Inference; r:gives { 2082 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 82}] + [ a r:Fact; r:gives {2000 log:repeat 82}] [ a r:Fact; r:gives {(82 2000) math:sum 2082}] - skolem:lemma1083 + skolem:lemma2082 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 82]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2082]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma84 a r:Inference; r:gives { 2083 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 83}] + [ a r:Fact; r:gives {2000 log:repeat 83}] [ a r:Fact; r:gives {(83 2000) math:sum 2083}] - skolem:lemma1084 + skolem:lemma2083 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 83]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2083]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma85 a r:Inference; r:gives { 2084 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 84}] + [ a r:Fact; r:gives {2000 log:repeat 84}] [ a r:Fact; r:gives {(84 2000) math:sum 2084}] - skolem:lemma1085 + skolem:lemma2084 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 84]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2084]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma86 a r:Inference; r:gives { 2085 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 85}] + [ a r:Fact; r:gives {2000 log:repeat 85}] [ a r:Fact; r:gives {(85 2000) math:sum 2085}] - skolem:lemma1086 + skolem:lemma2085 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 85]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2085]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma87 a r:Inference; r:gives { 2086 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 86}] + [ a r:Fact; r:gives {2000 log:repeat 86}] [ a r:Fact; r:gives {(86 2000) math:sum 2086}] - skolem:lemma1087 + skolem:lemma2086 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 86]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2086]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma88 a r:Inference; r:gives { 2087 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 87}] + [ a r:Fact; r:gives {2000 log:repeat 87}] [ a r:Fact; r:gives {(87 2000) math:sum 2087}] - skolem:lemma1088 + skolem:lemma2087 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 87]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2087]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma89 a r:Inference; r:gives { 2088 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 88}] + [ a r:Fact; r:gives {2000 log:repeat 88}] [ a r:Fact; r:gives {(88 2000) math:sum 2088}] - skolem:lemma1089 + skolem:lemma2088 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 88]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2088]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma90 a r:Inference; r:gives { 2089 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 89}] + [ a r:Fact; r:gives {2000 log:repeat 89}] [ a r:Fact; r:gives {(89 2000) math:sum 2089}] - skolem:lemma1090 + skolem:lemma2089 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 89]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2089]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma91 a r:Inference; r:gives { 2090 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 90}] + [ a r:Fact; r:gives {2000 log:repeat 90}] [ a r:Fact; r:gives {(90 2000) math:sum 2090}] - skolem:lemma1091 + skolem:lemma2090 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 90]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2090]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma92 a r:Inference; r:gives { 2091 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 91}] + [ a r:Fact; r:gives {2000 log:repeat 91}] [ a r:Fact; r:gives {(91 2000) math:sum 2091}] - skolem:lemma1092 + skolem:lemma2091 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 91]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2091]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma93 a r:Inference; r:gives { 2092 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 92}] + [ a r:Fact; r:gives {2000 log:repeat 92}] [ a r:Fact; r:gives {(92 2000) math:sum 2092}] - skolem:lemma1093 + skolem:lemma2092 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 92]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2092]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma94 a r:Inference; r:gives { 2093 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 93}] + [ a r:Fact; r:gives {2000 log:repeat 93}] [ a r:Fact; r:gives {(93 2000) math:sum 2093}] - skolem:lemma1094 + skolem:lemma2093 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 93]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2093]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma95 a r:Inference; r:gives { 2094 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 94}] + [ a r:Fact; r:gives {2000 log:repeat 94}] [ a r:Fact; r:gives {(94 2000) math:sum 2094}] - skolem:lemma1095 + skolem:lemma2094 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 94]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2094]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma96 a r:Inference; r:gives { 2095 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 95}] + [ a r:Fact; r:gives {2000 log:repeat 95}] [ a r:Fact; r:gives {(95 2000) math:sum 2095}] - skolem:lemma1096 + skolem:lemma2095 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 95]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2095]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma97 a r:Inference; r:gives { 2096 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 96}] + [ a r:Fact; r:gives {2000 log:repeat 96}] [ a r:Fact; r:gives {(96 2000) math:sum 2096}] - skolem:lemma1097 + skolem:lemma2096 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 96]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2096]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma98 a r:Inference; r:gives { 2097 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 97}] + [ a r:Fact; r:gives {2000 log:repeat 97}] [ a r:Fact; r:gives {(97 2000) math:sum 2097}] - skolem:lemma1098 + skolem:lemma2097 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 97]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2097]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma99 a r:Inference; r:gives { 2098 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 98}] + [ a r:Fact; r:gives {2000 log:repeat 98}] [ a r:Fact; r:gives {(98 2000) math:sum 2098}] - skolem:lemma1099 + skolem:lemma2098 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 98]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2098]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma100 a r:Inference; r:gives { 2099 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 99}] + [ a r:Fact; r:gives {2000 log:repeat 99}] [ a r:Fact; r:gives {(99 2000) math:sum 2099}] - skolem:lemma1100 + skolem:lemma2099 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 99]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2099]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma101 a r:Inference; r:gives { 2100 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 100}] + [ a r:Fact; r:gives {2000 log:repeat 100}] [ a r:Fact; r:gives {(100 2000) math:sum 2100}] - skolem:lemma1101 + skolem:lemma2100 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 100]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2100]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma102 a r:Inference; r:gives { 2101 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 101}] + [ a r:Fact; r:gives {2000 log:repeat 101}] [ a r:Fact; r:gives {(101 2000) math:sum 2101}] - skolem:lemma1102 + skolem:lemma2101 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 101]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2101]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma103 a r:Inference; r:gives { 2102 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 102}] + [ a r:Fact; r:gives {2000 log:repeat 102}] [ a r:Fact; r:gives {(102 2000) math:sum 2102}] - skolem:lemma1103 + skolem:lemma2102 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 102]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2102]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma104 a r:Inference; r:gives { 2103 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 103}] + [ a r:Fact; r:gives {2000 log:repeat 103}] [ a r:Fact; r:gives {(103 2000) math:sum 2103}] - skolem:lemma1104 + skolem:lemma2103 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 103]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2103]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma105 a r:Inference; r:gives { 2104 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 104}] + [ a r:Fact; r:gives {2000 log:repeat 104}] [ a r:Fact; r:gives {(104 2000) math:sum 2104}] - skolem:lemma1105 + skolem:lemma2104 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 104]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2104]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma106 a r:Inference; r:gives { 2105 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 105}] + [ a r:Fact; r:gives {2000 log:repeat 105}] [ a r:Fact; r:gives {(105 2000) math:sum 2105}] - skolem:lemma1106 + skolem:lemma2105 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 105]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2105]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma107 a r:Inference; r:gives { 2106 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 106}] + [ a r:Fact; r:gives {2000 log:repeat 106}] [ a r:Fact; r:gives {(106 2000) math:sum 2106}] - skolem:lemma1107 + skolem:lemma2106 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 106]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2106]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma108 a r:Inference; r:gives { 2107 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 107}] + [ a r:Fact; r:gives {2000 log:repeat 107}] [ a r:Fact; r:gives {(107 2000) math:sum 2107}] - skolem:lemma1108 + skolem:lemma2107 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 107]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2107]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma109 a r:Inference; r:gives { 2108 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 108}] + [ a r:Fact; r:gives {2000 log:repeat 108}] [ a r:Fact; r:gives {(108 2000) math:sum 2108}] - skolem:lemma1109 + skolem:lemma2108 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 108]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2108]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma110 a r:Inference; r:gives { 2109 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 109}] + [ a r:Fact; r:gives {2000 log:repeat 109}] [ a r:Fact; r:gives {(109 2000) math:sum 2109}] - skolem:lemma1110 + skolem:lemma2109 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 109]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2109]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma111 a r:Inference; r:gives { 2110 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 110}] + [ a r:Fact; r:gives {2000 log:repeat 110}] [ a r:Fact; r:gives {(110 2000) math:sum 2110}] - skolem:lemma1111 + skolem:lemma2110 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 110]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2110]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma112 a r:Inference; r:gives { 2111 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 111}] + [ a r:Fact; r:gives {2000 log:repeat 111}] [ a r:Fact; r:gives {(111 2000) math:sum 2111}] - skolem:lemma1112 + skolem:lemma2111 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 111]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2111]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma113 a r:Inference; r:gives { 2112 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 112}] + [ a r:Fact; r:gives {2000 log:repeat 112}] [ a r:Fact; r:gives {(112 2000) math:sum 2112}] - skolem:lemma1113 + skolem:lemma2112 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 112]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2112]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma114 a r:Inference; r:gives { 2113 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 113}] + [ a r:Fact; r:gives {2000 log:repeat 113}] [ a r:Fact; r:gives {(113 2000) math:sum 2113}] - skolem:lemma1114 + skolem:lemma2113 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 113]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2113]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma115 a r:Inference; r:gives { 2114 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 114}] + [ a r:Fact; r:gives {2000 log:repeat 114}] [ a r:Fact; r:gives {(114 2000) math:sum 2114}] - skolem:lemma1115 + skolem:lemma2114 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 114]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2114]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma116 a r:Inference; r:gives { 2115 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 115}] + [ a r:Fact; r:gives {2000 log:repeat 115}] [ a r:Fact; r:gives {(115 2000) math:sum 2115}] - skolem:lemma1116 + skolem:lemma2115 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 115]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2115]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma117 a r:Inference; r:gives { 2116 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 116}] + [ a r:Fact; r:gives {2000 log:repeat 116}] [ a r:Fact; r:gives {(116 2000) math:sum 2116}] - skolem:lemma1117 + skolem:lemma2116 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 116]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2116]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma118 a r:Inference; r:gives { 2117 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 117}] + [ a r:Fact; r:gives {2000 log:repeat 117}] [ a r:Fact; r:gives {(117 2000) math:sum 2117}] - skolem:lemma1118 + skolem:lemma2117 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 117]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2117]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma119 a r:Inference; r:gives { 2118 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 118}] + [ a r:Fact; r:gives {2000 log:repeat 118}] [ a r:Fact; r:gives {(118 2000) math:sum 2118}] - skolem:lemma1119 + skolem:lemma2118 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 118]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2118]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma120 a r:Inference; r:gives { 2119 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 119}] + [ a r:Fact; r:gives {2000 log:repeat 119}] [ a r:Fact; r:gives {(119 2000) math:sum 2119}] - skolem:lemma1120 + skolem:lemma2119 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 119]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2119]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma121 a r:Inference; r:gives { 2120 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 120}] + [ a r:Fact; r:gives {2000 log:repeat 120}] [ a r:Fact; r:gives {(120 2000) math:sum 2120}] - skolem:lemma1121 + skolem:lemma2120 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 120]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2120]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma122 a r:Inference; r:gives { 2121 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 121}] + [ a r:Fact; r:gives {2000 log:repeat 121}] [ a r:Fact; r:gives {(121 2000) math:sum 2121}] - skolem:lemma1122 + skolem:lemma2121 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 121]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2121]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma123 a r:Inference; r:gives { 2122 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 122}] + [ a r:Fact; r:gives {2000 log:repeat 122}] [ a r:Fact; r:gives {(122 2000) math:sum 2122}] - skolem:lemma1123 + skolem:lemma2122 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 122]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2122]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma124 a r:Inference; r:gives { 2123 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 123}] + [ a r:Fact; r:gives {2000 log:repeat 123}] [ a r:Fact; r:gives {(123 2000) math:sum 2123}] - skolem:lemma1124 + skolem:lemma2123 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 123]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2123]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma125 a r:Inference; r:gives { 2124 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 124}] + [ a r:Fact; r:gives {2000 log:repeat 124}] [ a r:Fact; r:gives {(124 2000) math:sum 2124}] - skolem:lemma1125 + skolem:lemma2124 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 124]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2124]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma126 a r:Inference; r:gives { 2125 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 125}] + [ a r:Fact; r:gives {2000 log:repeat 125}] [ a r:Fact; r:gives {(125 2000) math:sum 2125}] - skolem:lemma1126 + skolem:lemma2125 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 125]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2125]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma127 a r:Inference; r:gives { 2126 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 126}] + [ a r:Fact; r:gives {2000 log:repeat 126}] [ a r:Fact; r:gives {(126 2000) math:sum 2126}] - skolem:lemma1127 + skolem:lemma2126 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 126]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2126]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma128 a r:Inference; r:gives { 2127 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 127}] + [ a r:Fact; r:gives {2000 log:repeat 127}] [ a r:Fact; r:gives {(127 2000) math:sum 2127}] - skolem:lemma1128 + skolem:lemma2127 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 127]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2127]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma129 a r:Inference; r:gives { 2128 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 128}] + [ a r:Fact; r:gives {2000 log:repeat 128}] [ a r:Fact; r:gives {(128 2000) math:sum 2128}] - skolem:lemma1129 + skolem:lemma2128 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 128]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2128]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma130 a r:Inference; r:gives { 2129 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 129}] + [ a r:Fact; r:gives {2000 log:repeat 129}] [ a r:Fact; r:gives {(129 2000) math:sum 2129}] - skolem:lemma1130 + skolem:lemma2129 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 129]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2129]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma131 a r:Inference; r:gives { 2130 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 130}] + [ a r:Fact; r:gives {2000 log:repeat 130}] [ a r:Fact; r:gives {(130 2000) math:sum 2130}] - skolem:lemma1131 + skolem:lemma2130 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 130]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2130]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma132 a r:Inference; r:gives { 2131 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 131}] + [ a r:Fact; r:gives {2000 log:repeat 131}] [ a r:Fact; r:gives {(131 2000) math:sum 2131}] - skolem:lemma1132 + skolem:lemma2131 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 131]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2131]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma133 a r:Inference; r:gives { 2132 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 132}] + [ a r:Fact; r:gives {2000 log:repeat 132}] [ a r:Fact; r:gives {(132 2000) math:sum 2132}] - skolem:lemma1133 + skolem:lemma2132 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 132]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2132]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma134 a r:Inference; r:gives { 2133 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 133}] + [ a r:Fact; r:gives {2000 log:repeat 133}] [ a r:Fact; r:gives {(133 2000) math:sum 2133}] - skolem:lemma1134 + skolem:lemma2133 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 133]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2133]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma135 a r:Inference; r:gives { 2134 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 134}] + [ a r:Fact; r:gives {2000 log:repeat 134}] [ a r:Fact; r:gives {(134 2000) math:sum 2134}] - skolem:lemma1135 + skolem:lemma2134 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 134]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2134]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma136 a r:Inference; r:gives { 2135 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 135}] + [ a r:Fact; r:gives {2000 log:repeat 135}] [ a r:Fact; r:gives {(135 2000) math:sum 2135}] - skolem:lemma1136 + skolem:lemma2135 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 135]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2135]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma137 a r:Inference; r:gives { 2136 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 136}] + [ a r:Fact; r:gives {2000 log:repeat 136}] [ a r:Fact; r:gives {(136 2000) math:sum 2136}] - skolem:lemma1137 + skolem:lemma2136 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 136]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2136]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma138 a r:Inference; r:gives { 2137 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 137}] + [ a r:Fact; r:gives {2000 log:repeat 137}] [ a r:Fact; r:gives {(137 2000) math:sum 2137}] - skolem:lemma1138 + skolem:lemma2137 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 137]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2137]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma139 a r:Inference; r:gives { 2138 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 138}] + [ a r:Fact; r:gives {2000 log:repeat 138}] [ a r:Fact; r:gives {(138 2000) math:sum 2138}] - skolem:lemma1139 + skolem:lemma2138 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 138]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2138]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma140 a r:Inference; r:gives { 2139 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 139}] + [ a r:Fact; r:gives {2000 log:repeat 139}] [ a r:Fact; r:gives {(139 2000) math:sum 2139}] - skolem:lemma1140 + skolem:lemma2139 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 139]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2139]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma141 a r:Inference; r:gives { 2140 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 140}] + [ a r:Fact; r:gives {2000 log:repeat 140}] [ a r:Fact; r:gives {(140 2000) math:sum 2140}] - skolem:lemma1141 + skolem:lemma2140 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 140]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2140]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma142 a r:Inference; r:gives { 2141 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 141}] + [ a r:Fact; r:gives {2000 log:repeat 141}] [ a r:Fact; r:gives {(141 2000) math:sum 2141}] - skolem:lemma1142 + skolem:lemma2141 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 141]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2141]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma143 a r:Inference; r:gives { 2142 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 142}] + [ a r:Fact; r:gives {2000 log:repeat 142}] [ a r:Fact; r:gives {(142 2000) math:sum 2142}] - skolem:lemma1143 + skolem:lemma2142 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 142]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2142]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma144 a r:Inference; r:gives { 2143 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 143}] + [ a r:Fact; r:gives {2000 log:repeat 143}] [ a r:Fact; r:gives {(143 2000) math:sum 2143}] - skolem:lemma1144 + skolem:lemma2143 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 143]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2143]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma145 a r:Inference; r:gives { 2144 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 144}] + [ a r:Fact; r:gives {2000 log:repeat 144}] [ a r:Fact; r:gives {(144 2000) math:sum 2144}] - skolem:lemma1145 + skolem:lemma2144 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 144]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2144]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma146 a r:Inference; r:gives { 2145 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 145}] + [ a r:Fact; r:gives {2000 log:repeat 145}] [ a r:Fact; r:gives {(145 2000) math:sum 2145}] - skolem:lemma1146 + skolem:lemma2145 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 145]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2145]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma147 a r:Inference; r:gives { 2146 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 146}] + [ a r:Fact; r:gives {2000 log:repeat 146}] [ a r:Fact; r:gives {(146 2000) math:sum 2146}] - skolem:lemma1147 + skolem:lemma2146 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 146]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2146]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma148 a r:Inference; r:gives { 2147 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 147}] + [ a r:Fact; r:gives {2000 log:repeat 147}] [ a r:Fact; r:gives {(147 2000) math:sum 2147}] - skolem:lemma1148 + skolem:lemma2147 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 147]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2147]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma149 a r:Inference; r:gives { 2148 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 148}] + [ a r:Fact; r:gives {2000 log:repeat 148}] [ a r:Fact; r:gives {(148 2000) math:sum 2148}] - skolem:lemma1149 + skolem:lemma2148 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 148]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2148]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma150 a r:Inference; r:gives { 2149 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 149}] + [ a r:Fact; r:gives {2000 log:repeat 149}] [ a r:Fact; r:gives {(149 2000) math:sum 2149}] - skolem:lemma1150 + skolem:lemma2149 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 149]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2149]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma151 a r:Inference; r:gives { 2150 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 150}] + [ a r:Fact; r:gives {2000 log:repeat 150}] [ a r:Fact; r:gives {(150 2000) math:sum 2150}] - skolem:lemma1151 + skolem:lemma2150 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 150]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2150]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma152 a r:Inference; r:gives { 2151 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 151}] + [ a r:Fact; r:gives {2000 log:repeat 151}] [ a r:Fact; r:gives {(151 2000) math:sum 2151}] - skolem:lemma1152 + skolem:lemma2151 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 151]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2151]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma153 a r:Inference; r:gives { 2152 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 152}] + [ a r:Fact; r:gives {2000 log:repeat 152}] [ a r:Fact; r:gives {(152 2000) math:sum 2152}] - skolem:lemma1153 + skolem:lemma2152 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 152]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2152]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma154 a r:Inference; r:gives { 2153 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 153}] + [ a r:Fact; r:gives {2000 log:repeat 153}] [ a r:Fact; r:gives {(153 2000) math:sum 2153}] - skolem:lemma1154 + skolem:lemma2153 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 153]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2153]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma155 a r:Inference; r:gives { 2154 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 154}] + [ a r:Fact; r:gives {2000 log:repeat 154}] [ a r:Fact; r:gives {(154 2000) math:sum 2154}] - skolem:lemma1155 + skolem:lemma2154 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 154]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2154]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma156 a r:Inference; r:gives { 2155 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 155}] + [ a r:Fact; r:gives {2000 log:repeat 155}] [ a r:Fact; r:gives {(155 2000) math:sum 2155}] - skolem:lemma1156 + skolem:lemma2155 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 155]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2155]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma157 a r:Inference; r:gives { 2156 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 156}] + [ a r:Fact; r:gives {2000 log:repeat 156}] [ a r:Fact; r:gives {(156 2000) math:sum 2156}] - skolem:lemma1157 + skolem:lemma2156 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 156]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2156]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma158 a r:Inference; r:gives { 2157 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 157}] + [ a r:Fact; r:gives {2000 log:repeat 157}] [ a r:Fact; r:gives {(157 2000) math:sum 2157}] - skolem:lemma1158 + skolem:lemma2157 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 157]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2157]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma159 a r:Inference; r:gives { 2158 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 158}] + [ a r:Fact; r:gives {2000 log:repeat 158}] [ a r:Fact; r:gives {(158 2000) math:sum 2158}] - skolem:lemma1159 + skolem:lemma2158 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 158]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2158]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma160 a r:Inference; r:gives { 2159 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 159}] + [ a r:Fact; r:gives {2000 log:repeat 159}] [ a r:Fact; r:gives {(159 2000) math:sum 2159}] - skolem:lemma1160 + skolem:lemma2159 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 159]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2159]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma161 a r:Inference; r:gives { 2160 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 160}] + [ a r:Fact; r:gives {2000 log:repeat 160}] [ a r:Fact; r:gives {(160 2000) math:sum 2160}] - skolem:lemma1161 + skolem:lemma2160 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 160]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2160]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma162 a r:Inference; r:gives { 2161 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 161}] + [ a r:Fact; r:gives {2000 log:repeat 161}] [ a r:Fact; r:gives {(161 2000) math:sum 2161}] - skolem:lemma1162 + skolem:lemma2161 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 161]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2161]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma163 a r:Inference; r:gives { 2162 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 162}] + [ a r:Fact; r:gives {2000 log:repeat 162}] [ a r:Fact; r:gives {(162 2000) math:sum 2162}] - skolem:lemma1163 + skolem:lemma2162 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 162]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2162]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma164 a r:Inference; r:gives { 2163 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 163}] + [ a r:Fact; r:gives {2000 log:repeat 163}] [ a r:Fact; r:gives {(163 2000) math:sum 2163}] - skolem:lemma1164 + skolem:lemma2163 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 163]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2163]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma165 a r:Inference; r:gives { 2164 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 164}] + [ a r:Fact; r:gives {2000 log:repeat 164}] [ a r:Fact; r:gives {(164 2000) math:sum 2164}] - skolem:lemma1165 + skolem:lemma2164 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 164]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2164]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma166 a r:Inference; r:gives { 2165 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 165}] + [ a r:Fact; r:gives {2000 log:repeat 165}] [ a r:Fact; r:gives {(165 2000) math:sum 2165}] - skolem:lemma1166 + skolem:lemma2165 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 165]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2165]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma167 a r:Inference; r:gives { 2166 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 166}] + [ a r:Fact; r:gives {2000 log:repeat 166}] [ a r:Fact; r:gives {(166 2000) math:sum 2166}] - skolem:lemma1167 + skolem:lemma2166 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 166]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2166]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma168 a r:Inference; r:gives { 2167 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 167}] + [ a r:Fact; r:gives {2000 log:repeat 167}] [ a r:Fact; r:gives {(167 2000) math:sum 2167}] - skolem:lemma1168 + skolem:lemma2167 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 167]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2167]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma169 a r:Inference; r:gives { 2168 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 168}] + [ a r:Fact; r:gives {2000 log:repeat 168}] [ a r:Fact; r:gives {(168 2000) math:sum 2168}] - skolem:lemma1169 + skolem:lemma2168 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 168]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2168]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma170 a r:Inference; r:gives { 2169 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 169}] + [ a r:Fact; r:gives {2000 log:repeat 169}] [ a r:Fact; r:gives {(169 2000) math:sum 2169}] - skolem:lemma1170 + skolem:lemma2169 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 169]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2169]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma171 a r:Inference; r:gives { 2170 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 170}] + [ a r:Fact; r:gives {2000 log:repeat 170}] [ a r:Fact; r:gives {(170 2000) math:sum 2170}] - skolem:lemma1171 + skolem:lemma2170 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 170]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2170]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma172 a r:Inference; r:gives { 2171 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 171}] + [ a r:Fact; r:gives {2000 log:repeat 171}] [ a r:Fact; r:gives {(171 2000) math:sum 2171}] - skolem:lemma1172 + skolem:lemma2171 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 171]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2171]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma173 a r:Inference; r:gives { 2172 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 172}] + [ a r:Fact; r:gives {2000 log:repeat 172}] [ a r:Fact; r:gives {(172 2000) math:sum 2172}] - skolem:lemma1173 + skolem:lemma2172 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 172]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2172]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma174 a r:Inference; r:gives { 2173 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 173}] + [ a r:Fact; r:gives {2000 log:repeat 173}] [ a r:Fact; r:gives {(173 2000) math:sum 2173}] - skolem:lemma1174 + skolem:lemma2173 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 173]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2173]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma175 a r:Inference; r:gives { 2174 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 174}] + [ a r:Fact; r:gives {2000 log:repeat 174}] [ a r:Fact; r:gives {(174 2000) math:sum 2174}] - skolem:lemma1175 + skolem:lemma2174 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 174]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2174]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma176 a r:Inference; r:gives { 2175 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 175}] + [ a r:Fact; r:gives {2000 log:repeat 175}] [ a r:Fact; r:gives {(175 2000) math:sum 2175}] - skolem:lemma1176 + skolem:lemma2175 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 175]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2175]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma177 a r:Inference; r:gives { 2176 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 176}] + [ a r:Fact; r:gives {2000 log:repeat 176}] [ a r:Fact; r:gives {(176 2000) math:sum 2176}] - skolem:lemma1177 + skolem:lemma2176 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 176]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2176]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma178 a r:Inference; r:gives { 2177 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 177}] + [ a r:Fact; r:gives {2000 log:repeat 177}] [ a r:Fact; r:gives {(177 2000) math:sum 2177}] - skolem:lemma1178 + skolem:lemma2177 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 177]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2177]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma179 a r:Inference; r:gives { 2178 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 178}] + [ a r:Fact; r:gives {2000 log:repeat 178}] [ a r:Fact; r:gives {(178 2000) math:sum 2178}] - skolem:lemma1179 + skolem:lemma2178 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 178]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2178]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma180 a r:Inference; r:gives { 2179 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 179}] + [ a r:Fact; r:gives {2000 log:repeat 179}] [ a r:Fact; r:gives {(179 2000) math:sum 2179}] - skolem:lemma1180 + skolem:lemma2179 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 179]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2179]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma181 a r:Inference; r:gives { 2180 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 180}] + [ a r:Fact; r:gives {2000 log:repeat 180}] [ a r:Fact; r:gives {(180 2000) math:sum 2180}] - skolem:lemma1181 + skolem:lemma2180 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 180]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2180]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma182 a r:Inference; r:gives { 2181 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 181}] + [ a r:Fact; r:gives {2000 log:repeat 181}] [ a r:Fact; r:gives {(181 2000) math:sum 2181}] - skolem:lemma1182 + skolem:lemma2181 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 181]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2181]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma183 a r:Inference; r:gives { 2182 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 182}] + [ a r:Fact; r:gives {2000 log:repeat 182}] [ a r:Fact; r:gives {(182 2000) math:sum 2182}] - skolem:lemma1183 + skolem:lemma2182 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 182]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2182]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma184 a r:Inference; r:gives { 2183 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 183}] + [ a r:Fact; r:gives {2000 log:repeat 183}] [ a r:Fact; r:gives {(183 2000) math:sum 2183}] - skolem:lemma1184 + skolem:lemma2183 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 183]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2183]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma185 a r:Inference; r:gives { 2184 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 184}] + [ a r:Fact; r:gives {2000 log:repeat 184}] [ a r:Fact; r:gives {(184 2000) math:sum 2184}] - skolem:lemma1185 + skolem:lemma2184 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 184]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2184]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma186 a r:Inference; r:gives { 2185 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 185}] + [ a r:Fact; r:gives {2000 log:repeat 185}] [ a r:Fact; r:gives {(185 2000) math:sum 2185}] - skolem:lemma1186 + skolem:lemma2185 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 185]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2185]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma187 a r:Inference; r:gives { 2186 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 186}] + [ a r:Fact; r:gives {2000 log:repeat 186}] [ a r:Fact; r:gives {(186 2000) math:sum 2186}] - skolem:lemma1187 + skolem:lemma2186 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 186]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2186]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma188 a r:Inference; r:gives { 2187 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 187}] + [ a r:Fact; r:gives {2000 log:repeat 187}] [ a r:Fact; r:gives {(187 2000) math:sum 2187}] - skolem:lemma1188 + skolem:lemma2187 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 187]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2187]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma189 a r:Inference; r:gives { 2188 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 188}] + [ a r:Fact; r:gives {2000 log:repeat 188}] [ a r:Fact; r:gives {(188 2000) math:sum 2188}] - skolem:lemma1189 + skolem:lemma2188 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 188]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2188]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma190 a r:Inference; r:gives { 2189 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 189}] + [ a r:Fact; r:gives {2000 log:repeat 189}] [ a r:Fact; r:gives {(189 2000) math:sum 2189}] - skolem:lemma1190 + skolem:lemma2189 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 189]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2189]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma191 a r:Inference; r:gives { 2190 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 190}] + [ a r:Fact; r:gives {2000 log:repeat 190}] [ a r:Fact; r:gives {(190 2000) math:sum 2190}] - skolem:lemma1191 + skolem:lemma2190 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 190]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2190]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma192 a r:Inference; r:gives { 2191 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 191}] + [ a r:Fact; r:gives {2000 log:repeat 191}] [ a r:Fact; r:gives {(191 2000) math:sum 2191}] - skolem:lemma1192 + skolem:lemma2191 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 191]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2191]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma193 a r:Inference; r:gives { 2192 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 192}] + [ a r:Fact; r:gives {2000 log:repeat 192}] [ a r:Fact; r:gives {(192 2000) math:sum 2192}] - skolem:lemma1193 + skolem:lemma2192 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 192]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2192]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma194 a r:Inference; r:gives { 2193 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 193}] + [ a r:Fact; r:gives {2000 log:repeat 193}] [ a r:Fact; r:gives {(193 2000) math:sum 2193}] - skolem:lemma1194 + skolem:lemma2193 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 193]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2193]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma195 a r:Inference; r:gives { 2194 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 194}] + [ a r:Fact; r:gives {2000 log:repeat 194}] [ a r:Fact; r:gives {(194 2000) math:sum 2194}] - skolem:lemma1195 + skolem:lemma2194 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 194]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2194]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma196 a r:Inference; r:gives { 2195 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 195}] + [ a r:Fact; r:gives {2000 log:repeat 195}] [ a r:Fact; r:gives {(195 2000) math:sum 2195}] - skolem:lemma1196 + skolem:lemma2195 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 195]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2195]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma197 a r:Inference; r:gives { 2196 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 196}] + [ a r:Fact; r:gives {2000 log:repeat 196}] [ a r:Fact; r:gives {(196 2000) math:sum 2196}] - skolem:lemma1197 + skolem:lemma2196 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 196]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2196]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma198 a r:Inference; r:gives { 2197 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 197}] + [ a r:Fact; r:gives {2000 log:repeat 197}] [ a r:Fact; r:gives {(197 2000) math:sum 2197}] - skolem:lemma1198 + skolem:lemma2197 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 197]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2197]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma199 a r:Inference; r:gives { 2198 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 198}] + [ a r:Fact; r:gives {2000 log:repeat 198}] [ a r:Fact; r:gives {(198 2000) math:sum 2198}] - skolem:lemma1199 + skolem:lemma2198 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 198]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2198]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma200 a r:Inference; r:gives { 2199 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 199}] + [ a r:Fact; r:gives {2000 log:repeat 199}] [ a r:Fact; r:gives {(199 2000) math:sum 2199}] - skolem:lemma1200 + skolem:lemma2199 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 199]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2199]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma201 a r:Inference; r:gives { 2200 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 200}] + [ a r:Fact; r:gives {2000 log:repeat 200}] [ a r:Fact; r:gives {(200 2000) math:sum 2200}] - skolem:lemma1201 + skolem:lemma2200 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 200]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2200]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma202 a r:Inference; r:gives { 2201 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 201}] + [ a r:Fact; r:gives {2000 log:repeat 201}] [ a r:Fact; r:gives {(201 2000) math:sum 2201}] - skolem:lemma1202 + skolem:lemma2201 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 201]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2201]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma203 a r:Inference; r:gives { 2202 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 202}] + [ a r:Fact; r:gives {2000 log:repeat 202}] [ a r:Fact; r:gives {(202 2000) math:sum 2202}] - skolem:lemma1203 + skolem:lemma2202 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 202]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2202]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma204 a r:Inference; r:gives { 2203 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 203}] + [ a r:Fact; r:gives {2000 log:repeat 203}] [ a r:Fact; r:gives {(203 2000) math:sum 2203}] - skolem:lemma1204 + skolem:lemma2203 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 203]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2203]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma205 a r:Inference; r:gives { 2204 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 204}] + [ a r:Fact; r:gives {2000 log:repeat 204}] [ a r:Fact; r:gives {(204 2000) math:sum 2204}] - skolem:lemma1205 + skolem:lemma2204 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 204]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2204]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma206 a r:Inference; r:gives { 2205 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 205}] + [ a r:Fact; r:gives {2000 log:repeat 205}] [ a r:Fact; r:gives {(205 2000) math:sum 2205}] - skolem:lemma1206 + skolem:lemma2205 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 205]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2205]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma207 a r:Inference; r:gives { 2206 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 206}] + [ a r:Fact; r:gives {2000 log:repeat 206}] [ a r:Fact; r:gives {(206 2000) math:sum 2206}] - skolem:lemma1207 + skolem:lemma2206 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 206]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2206]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma208 a r:Inference; r:gives { 2207 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 207}] + [ a r:Fact; r:gives {2000 log:repeat 207}] [ a r:Fact; r:gives {(207 2000) math:sum 2207}] - skolem:lemma1208 + skolem:lemma2207 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 207]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2207]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma209 a r:Inference; r:gives { 2208 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 208}] + [ a r:Fact; r:gives {2000 log:repeat 208}] [ a r:Fact; r:gives {(208 2000) math:sum 2208}] - skolem:lemma1209 + skolem:lemma2208 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 208]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2208]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma210 a r:Inference; r:gives { 2209 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 209}] + [ a r:Fact; r:gives {2000 log:repeat 209}] [ a r:Fact; r:gives {(209 2000) math:sum 2209}] - skolem:lemma1210 + skolem:lemma2209 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 209]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2209]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma211 a r:Inference; r:gives { 2210 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 210}] + [ a r:Fact; r:gives {2000 log:repeat 210}] [ a r:Fact; r:gives {(210 2000) math:sum 2210}] - skolem:lemma1211 + skolem:lemma2210 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 210]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2210]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma212 a r:Inference; r:gives { 2211 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 211}] + [ a r:Fact; r:gives {2000 log:repeat 211}] [ a r:Fact; r:gives {(211 2000) math:sum 2211}] - skolem:lemma1212 + skolem:lemma2211 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 211]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2211]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma213 a r:Inference; r:gives { 2212 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 212}] + [ a r:Fact; r:gives {2000 log:repeat 212}] [ a r:Fact; r:gives {(212 2000) math:sum 2212}] - skolem:lemma1213 + skolem:lemma2212 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 212]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2212]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma214 a r:Inference; r:gives { 2213 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 213}] + [ a r:Fact; r:gives {2000 log:repeat 213}] [ a r:Fact; r:gives {(213 2000) math:sum 2213}] - skolem:lemma1214 + skolem:lemma2213 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 213]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2213]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma215 a r:Inference; r:gives { 2214 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 214}] + [ a r:Fact; r:gives {2000 log:repeat 214}] [ a r:Fact; r:gives {(214 2000) math:sum 2214}] - skolem:lemma1215 + skolem:lemma2214 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 214]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2214]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma216 a r:Inference; r:gives { 2215 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 215}] + [ a r:Fact; r:gives {2000 log:repeat 215}] [ a r:Fact; r:gives {(215 2000) math:sum 2215}] - skolem:lemma1216 + skolem:lemma2215 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 215]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2215]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma217 a r:Inference; r:gives { 2216 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 216}] + [ a r:Fact; r:gives {2000 log:repeat 216}] [ a r:Fact; r:gives {(216 2000) math:sum 2216}] - skolem:lemma1217 + skolem:lemma2216 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 216]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2216]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma218 a r:Inference; r:gives { 2217 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 217}] + [ a r:Fact; r:gives {2000 log:repeat 217}] [ a r:Fact; r:gives {(217 2000) math:sum 2217}] - skolem:lemma1218 + skolem:lemma2217 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 217]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2217]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma219 a r:Inference; r:gives { 2218 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 218}] + [ a r:Fact; r:gives {2000 log:repeat 218}] [ a r:Fact; r:gives {(218 2000) math:sum 2218}] - skolem:lemma1219 + skolem:lemma2218 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 218]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2218]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma220 a r:Inference; r:gives { 2219 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 219}] + [ a r:Fact; r:gives {2000 log:repeat 219}] [ a r:Fact; r:gives {(219 2000) math:sum 2219}] - skolem:lemma1220 + skolem:lemma2219 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 219]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2219]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma221 a r:Inference; r:gives { 2220 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 220}] + [ a r:Fact; r:gives {2000 log:repeat 220}] [ a r:Fact; r:gives {(220 2000) math:sum 2220}] - skolem:lemma1221 + skolem:lemma2220 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 220]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2220]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma222 a r:Inference; r:gives { 2221 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 221}] + [ a r:Fact; r:gives {2000 log:repeat 221}] [ a r:Fact; r:gives {(221 2000) math:sum 2221}] - skolem:lemma1222 + skolem:lemma2221 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 221]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2221]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma223 a r:Inference; r:gives { 2223 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 223}] + [ a r:Fact; r:gives {2000 log:repeat 223}] [ a r:Fact; r:gives {(223 2000) math:sum 2223}] - skolem:lemma1223 + skolem:lemma2222 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 223]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2223]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma224 a r:Inference; r:gives { 2224 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 224}] + [ a r:Fact; r:gives {2000 log:repeat 224}] [ a r:Fact; r:gives {(224 2000) math:sum 2224}] - skolem:lemma1224 + skolem:lemma2223 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 224]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2224]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma225 a r:Inference; r:gives { 2225 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 225}] + [ a r:Fact; r:gives {2000 log:repeat 225}] [ a r:Fact; r:gives {(225 2000) math:sum 2225}] - skolem:lemma1225 + skolem:lemma2224 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 225]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2225]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma226 a r:Inference; r:gives { 2226 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 226}] + [ a r:Fact; r:gives {2000 log:repeat 226}] [ a r:Fact; r:gives {(226 2000) math:sum 2226}] - skolem:lemma1226 + skolem:lemma2225 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 226]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2226]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma227 a r:Inference; r:gives { 2227 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 227}] + [ a r:Fact; r:gives {2000 log:repeat 227}] [ a r:Fact; r:gives {(227 2000) math:sum 2227}] - skolem:lemma1227 + skolem:lemma2226 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 227]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2227]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma228 a r:Inference; r:gives { 2228 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 228}] + [ a r:Fact; r:gives {2000 log:repeat 228}] [ a r:Fact; r:gives {(228 2000) math:sum 2228}] - skolem:lemma1228 + skolem:lemma2227 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 228]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2228]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma229 a r:Inference; r:gives { 2229 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 229}] + [ a r:Fact; r:gives {2000 log:repeat 229}] [ a r:Fact; r:gives {(229 2000) math:sum 2229}] - skolem:lemma1229 + skolem:lemma2228 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 229]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2229]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma230 a r:Inference; r:gives { 2230 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 230}] + [ a r:Fact; r:gives {2000 log:repeat 230}] [ a r:Fact; r:gives {(230 2000) math:sum 2230}] - skolem:lemma1230 + skolem:lemma2229 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 230]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2230]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma231 a r:Inference; r:gives { 2231 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 231}] + [ a r:Fact; r:gives {2000 log:repeat 231}] [ a r:Fact; r:gives {(231 2000) math:sum 2231}] - skolem:lemma1231 + skolem:lemma2230 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 231]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2231]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma232 a r:Inference; r:gives { 2232 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 232}] + [ a r:Fact; r:gives {2000 log:repeat 232}] [ a r:Fact; r:gives {(232 2000) math:sum 2232}] - skolem:lemma1232 + skolem:lemma2231 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 232]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2232]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma233 a r:Inference; r:gives { 2233 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 233}] + [ a r:Fact; r:gives {2000 log:repeat 233}] [ a r:Fact; r:gives {(233 2000) math:sum 2233}] - skolem:lemma1233 + skolem:lemma2232 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 233]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2233]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma234 a r:Inference; r:gives { 2234 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 234}] + [ a r:Fact; r:gives {2000 log:repeat 234}] [ a r:Fact; r:gives {(234 2000) math:sum 2234}] - skolem:lemma1234 + skolem:lemma2233 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 234]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2234]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma235 a r:Inference; r:gives { 2235 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 235}] + [ a r:Fact; r:gives {2000 log:repeat 235}] [ a r:Fact; r:gives {(235 2000) math:sum 2235}] - skolem:lemma1235 + skolem:lemma2234 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 235]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2235]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma236 a r:Inference; r:gives { 2236 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 236}] + [ a r:Fact; r:gives {2000 log:repeat 236}] [ a r:Fact; r:gives {(236 2000) math:sum 2236}] - skolem:lemma1236 + skolem:lemma2235 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 236]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2236]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma237 a r:Inference; r:gives { 2237 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 237}] + [ a r:Fact; r:gives {2000 log:repeat 237}] [ a r:Fact; r:gives {(237 2000) math:sum 2237}] - skolem:lemma1237 + skolem:lemma2236 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 237]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2237]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma238 a r:Inference; r:gives { 2238 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 238}] + [ a r:Fact; r:gives {2000 log:repeat 238}] [ a r:Fact; r:gives {(238 2000) math:sum 2238}] - skolem:lemma1238 + skolem:lemma2237 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 238]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2238]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma239 a r:Inference; r:gives { 2239 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 239}] + [ a r:Fact; r:gives {2000 log:repeat 239}] [ a r:Fact; r:gives {(239 2000) math:sum 2239}] - skolem:lemma1239 + skolem:lemma2238 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 239]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2239]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma240 a r:Inference; r:gives { 2240 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 240}] + [ a r:Fact; r:gives {2000 log:repeat 240}] [ a r:Fact; r:gives {(240 2000) math:sum 2240}] - skolem:lemma1240 + skolem:lemma2239 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 240]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2240]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma241 a r:Inference; r:gives { 2241 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 241}] + [ a r:Fact; r:gives {2000 log:repeat 241}] [ a r:Fact; r:gives {(241 2000) math:sum 2241}] - skolem:lemma1241 + skolem:lemma2240 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 241]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2241]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma242 a r:Inference; r:gives { 2242 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 242}] + [ a r:Fact; r:gives {2000 log:repeat 242}] [ a r:Fact; r:gives {(242 2000) math:sum 2242}] - skolem:lemma1242 + skolem:lemma2241 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 242]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2242]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma243 a r:Inference; r:gives { 2243 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 243}] + [ a r:Fact; r:gives {2000 log:repeat 243}] [ a r:Fact; r:gives {(243 2000) math:sum 2243}] - skolem:lemma1243 + skolem:lemma2242 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 243]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2243]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma244 a r:Inference; r:gives { 2244 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 244}] + [ a r:Fact; r:gives {2000 log:repeat 244}] [ a r:Fact; r:gives {(244 2000) math:sum 2244}] - skolem:lemma1244 + skolem:lemma2243 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 244]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2244]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma245 a r:Inference; r:gives { 2245 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 245}] + [ a r:Fact; r:gives {2000 log:repeat 245}] [ a r:Fact; r:gives {(245 2000) math:sum 2245}] - skolem:lemma1245 + skolem:lemma2244 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 245]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2245]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma246 a r:Inference; r:gives { 2246 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 246}] + [ a r:Fact; r:gives {2000 log:repeat 246}] [ a r:Fact; r:gives {(246 2000) math:sum 2246}] - skolem:lemma1246 + skolem:lemma2245 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 246]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2246]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma247 a r:Inference; r:gives { 2247 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 247}] + [ a r:Fact; r:gives {2000 log:repeat 247}] [ a r:Fact; r:gives {(247 2000) math:sum 2247}] - skolem:lemma1247 + skolem:lemma2246 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 247]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2247]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma248 a r:Inference; r:gives { 2248 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 248}] + [ a r:Fact; r:gives {2000 log:repeat 248}] [ a r:Fact; r:gives {(248 2000) math:sum 2248}] - skolem:lemma1248 + skolem:lemma2247 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 248]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2248]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma249 a r:Inference; r:gives { 2249 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 249}] + [ a r:Fact; r:gives {2000 log:repeat 249}] [ a r:Fact; r:gives {(249 2000) math:sum 2249}] - skolem:lemma1249 + skolem:lemma2248 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 249]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2249]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma250 a r:Inference; r:gives { 2250 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 250}] + [ a r:Fact; r:gives {2000 log:repeat 250}] [ a r:Fact; r:gives {(250 2000) math:sum 2250}] - skolem:lemma1250 + skolem:lemma2249 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 250]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2250]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma251 a r:Inference; r:gives { 2251 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 251}] + [ a r:Fact; r:gives {2000 log:repeat 251}] [ a r:Fact; r:gives {(251 2000) math:sum 2251}] - skolem:lemma1251 + skolem:lemma2250 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 251]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2251]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma252 a r:Inference; r:gives { 2252 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 252}] + [ a r:Fact; r:gives {2000 log:repeat 252}] [ a r:Fact; r:gives {(252 2000) math:sum 2252}] - skolem:lemma1252 + skolem:lemma2251 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 252]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2252]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma253 a r:Inference; r:gives { 2253 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 253}] + [ a r:Fact; r:gives {2000 log:repeat 253}] [ a r:Fact; r:gives {(253 2000) math:sum 2253}] - skolem:lemma1253 + skolem:lemma2252 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 253]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2253]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma254 a r:Inference; r:gives { 2254 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 254}] + [ a r:Fact; r:gives {2000 log:repeat 254}] [ a r:Fact; r:gives {(254 2000) math:sum 2254}] - skolem:lemma1254 + skolem:lemma2253 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 254]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2254]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma255 a r:Inference; r:gives { 2255 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 255}] + [ a r:Fact; r:gives {2000 log:repeat 255}] [ a r:Fact; r:gives {(255 2000) math:sum 2255}] - skolem:lemma1255 + skolem:lemma2254 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 255]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2255]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma256 a r:Inference; r:gives { 2256 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 256}] + [ a r:Fact; r:gives {2000 log:repeat 256}] [ a r:Fact; r:gives {(256 2000) math:sum 2256}] - skolem:lemma1256 + skolem:lemma2255 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 256]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2256]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma257 a r:Inference; r:gives { 2257 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 257}] + [ a r:Fact; r:gives {2000 log:repeat 257}] [ a r:Fact; r:gives {(257 2000) math:sum 2257}] - skolem:lemma1257 + skolem:lemma2256 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 257]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2257]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma258 a r:Inference; r:gives { 2258 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 258}] + [ a r:Fact; r:gives {2000 log:repeat 258}] [ a r:Fact; r:gives {(258 2000) math:sum 2258}] - skolem:lemma1258 + skolem:lemma2257 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 258]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2258]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma259 a r:Inference; r:gives { 2259 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 259}] + [ a r:Fact; r:gives {2000 log:repeat 259}] [ a r:Fact; r:gives {(259 2000) math:sum 2259}] - skolem:lemma1259 + skolem:lemma2258 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 259]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2259]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma260 a r:Inference; r:gives { 2260 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 260}] + [ a r:Fact; r:gives {2000 log:repeat 260}] [ a r:Fact; r:gives {(260 2000) math:sum 2260}] - skolem:lemma1260 + skolem:lemma2259 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 260]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2260]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma261 a r:Inference; r:gives { 2261 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 261}] + [ a r:Fact; r:gives {2000 log:repeat 261}] [ a r:Fact; r:gives {(261 2000) math:sum 2261}] - skolem:lemma1261 + skolem:lemma2260 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 261]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2261]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma262 a r:Inference; r:gives { 2262 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 262}] + [ a r:Fact; r:gives {2000 log:repeat 262}] [ a r:Fact; r:gives {(262 2000) math:sum 2262}] - skolem:lemma1262 + skolem:lemma2261 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 262]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2262]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma263 a r:Inference; r:gives { 2263 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 263}] + [ a r:Fact; r:gives {2000 log:repeat 263}] [ a r:Fact; r:gives {(263 2000) math:sum 2263}] - skolem:lemma1263 + skolem:lemma2262 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 263]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2263]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma264 a r:Inference; r:gives { 2264 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 264}] + [ a r:Fact; r:gives {2000 log:repeat 264}] [ a r:Fact; r:gives {(264 2000) math:sum 2264}] - skolem:lemma1264 + skolem:lemma2263 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 264]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2264]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma265 a r:Inference; r:gives { 2265 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 265}] + [ a r:Fact; r:gives {2000 log:repeat 265}] [ a r:Fact; r:gives {(265 2000) math:sum 2265}] - skolem:lemma1265 + skolem:lemma2264 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 265]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2265]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma266 a r:Inference; r:gives { 2266 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 266}] + [ a r:Fact; r:gives {2000 log:repeat 266}] [ a r:Fact; r:gives {(266 2000) math:sum 2266}] - skolem:lemma1266 + skolem:lemma2265 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 266]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2266]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma267 a r:Inference; r:gives { 2267 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 267}] + [ a r:Fact; r:gives {2000 log:repeat 267}] [ a r:Fact; r:gives {(267 2000) math:sum 2267}] - skolem:lemma1267 + skolem:lemma2266 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 267]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2267]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma268 a r:Inference; r:gives { 2268 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 268}] + [ a r:Fact; r:gives {2000 log:repeat 268}] [ a r:Fact; r:gives {(268 2000) math:sum 2268}] - skolem:lemma1268 + skolem:lemma2267 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 268]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2268]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma269 a r:Inference; r:gives { 2269 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 269}] + [ a r:Fact; r:gives {2000 log:repeat 269}] [ a r:Fact; r:gives {(269 2000) math:sum 2269}] - skolem:lemma1269 + skolem:lemma2268 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 269]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2269]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma270 a r:Inference; r:gives { 2270 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 270}] + [ a r:Fact; r:gives {2000 log:repeat 270}] [ a r:Fact; r:gives {(270 2000) math:sum 2270}] - skolem:lemma1270 + skolem:lemma2269 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 270]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2270]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma271 a r:Inference; r:gives { 2271 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 271}] + [ a r:Fact; r:gives {2000 log:repeat 271}] [ a r:Fact; r:gives {(271 2000) math:sum 2271}] - skolem:lemma1271 + skolem:lemma2270 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 271]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2271]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma272 a r:Inference; r:gives { 2272 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 272}] + [ a r:Fact; r:gives {2000 log:repeat 272}] [ a r:Fact; r:gives {(272 2000) math:sum 2272}] - skolem:lemma1272 + skolem:lemma2271 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 272]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2272]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma273 a r:Inference; r:gives { 2273 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 273}] + [ a r:Fact; r:gives {2000 log:repeat 273}] [ a r:Fact; r:gives {(273 2000) math:sum 2273}] - skolem:lemma1273 + skolem:lemma2272 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 273]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2273]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma274 a r:Inference; r:gives { 2274 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 274}] + [ a r:Fact; r:gives {2000 log:repeat 274}] [ a r:Fact; r:gives {(274 2000) math:sum 2274}] - skolem:lemma1274 + skolem:lemma2273 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 274]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2274]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma275 a r:Inference; r:gives { 2275 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 275}] + [ a r:Fact; r:gives {2000 log:repeat 275}] [ a r:Fact; r:gives {(275 2000) math:sum 2275}] - skolem:lemma1275 + skolem:lemma2274 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 275]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2275]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma276 a r:Inference; r:gives { 2276 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 276}] + [ a r:Fact; r:gives {2000 log:repeat 276}] [ a r:Fact; r:gives {(276 2000) math:sum 2276}] - skolem:lemma1276 + skolem:lemma2275 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 276]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2276]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma277 a r:Inference; r:gives { 2277 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 277}] + [ a r:Fact; r:gives {2000 log:repeat 277}] [ a r:Fact; r:gives {(277 2000) math:sum 2277}] - skolem:lemma1277 + skolem:lemma2276 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 277]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2277]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma278 a r:Inference; r:gives { 2278 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 278}] + [ a r:Fact; r:gives {2000 log:repeat 278}] [ a r:Fact; r:gives {(278 2000) math:sum 2278}] - skolem:lemma1278 + skolem:lemma2277 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 278]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2278]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma279 a r:Inference; r:gives { 2279 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 279}] + [ a r:Fact; r:gives {2000 log:repeat 279}] [ a r:Fact; r:gives {(279 2000) math:sum 2279}] - skolem:lemma1279 + skolem:lemma2278 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 279]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2279]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma280 a r:Inference; r:gives { 2280 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 280}] + [ a r:Fact; r:gives {2000 log:repeat 280}] [ a r:Fact; r:gives {(280 2000) math:sum 2280}] - skolem:lemma1280 + skolem:lemma2279 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 280]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2280]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma281 a r:Inference; r:gives { 2281 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 281}] + [ a r:Fact; r:gives {2000 log:repeat 281}] [ a r:Fact; r:gives {(281 2000) math:sum 2281}] - skolem:lemma1281 + skolem:lemma2280 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 281]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2281]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma282 a r:Inference; r:gives { 2282 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 282}] + [ a r:Fact; r:gives {2000 log:repeat 282}] [ a r:Fact; r:gives {(282 2000) math:sum 2282}] - skolem:lemma1282 + skolem:lemma2281 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 282]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2282]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma283 a r:Inference; r:gives { 2283 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 283}] + [ a r:Fact; r:gives {2000 log:repeat 283}] [ a r:Fact; r:gives {(283 2000) math:sum 2283}] - skolem:lemma1283 + skolem:lemma2282 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 283]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2283]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma284 a r:Inference; r:gives { 2284 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 284}] + [ a r:Fact; r:gives {2000 log:repeat 284}] [ a r:Fact; r:gives {(284 2000) math:sum 2284}] - skolem:lemma1284 + skolem:lemma2283 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 284]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2284]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma285 a r:Inference; r:gives { 2285 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 285}] + [ a r:Fact; r:gives {2000 log:repeat 285}] [ a r:Fact; r:gives {(285 2000) math:sum 2285}] - skolem:lemma1285 + skolem:lemma2284 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 285]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2285]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma286 a r:Inference; r:gives { 2286 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 286}] + [ a r:Fact; r:gives {2000 log:repeat 286}] [ a r:Fact; r:gives {(286 2000) math:sum 2286}] - skolem:lemma1286 + skolem:lemma2285 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 286]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2286]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma287 a r:Inference; r:gives { 2287 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 287}] + [ a r:Fact; r:gives {2000 log:repeat 287}] [ a r:Fact; r:gives {(287 2000) math:sum 2287}] - skolem:lemma1287 + skolem:lemma2286 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 287]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2287]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma288 a r:Inference; r:gives { 2288 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 288}] + [ a r:Fact; r:gives {2000 log:repeat 288}] [ a r:Fact; r:gives {(288 2000) math:sum 2288}] - skolem:lemma1288 + skolem:lemma2287 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 288]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2288]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma289 a r:Inference; r:gives { 2289 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 289}] + [ a r:Fact; r:gives {2000 log:repeat 289}] [ a r:Fact; r:gives {(289 2000) math:sum 2289}] - skolem:lemma1289 + skolem:lemma2288 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 289]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2289]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma290 a r:Inference; r:gives { 2290 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 290}] + [ a r:Fact; r:gives {2000 log:repeat 290}] [ a r:Fact; r:gives {(290 2000) math:sum 2290}] - skolem:lemma1290 + skolem:lemma2289 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 290]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2290]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma291 a r:Inference; r:gives { 2291 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 291}] + [ a r:Fact; r:gives {2000 log:repeat 291}] [ a r:Fact; r:gives {(291 2000) math:sum 2291}] - skolem:lemma1291 + skolem:lemma2290 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 291]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2291]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma292 a r:Inference; r:gives { 2292 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 292}] + [ a r:Fact; r:gives {2000 log:repeat 292}] [ a r:Fact; r:gives {(292 2000) math:sum 2292}] - skolem:lemma1292 + skolem:lemma2291 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 292]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2292]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma293 a r:Inference; r:gives { 2293 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 293}] + [ a r:Fact; r:gives {2000 log:repeat 293}] [ a r:Fact; r:gives {(293 2000) math:sum 2293}] - skolem:lemma1293 + skolem:lemma2292 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 293]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2293]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma294 a r:Inference; r:gives { 2294 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 294}] + [ a r:Fact; r:gives {2000 log:repeat 294}] [ a r:Fact; r:gives {(294 2000) math:sum 2294}] - skolem:lemma1294 + skolem:lemma2293 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 294]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2294]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma295 a r:Inference; r:gives { 2295 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 295}] + [ a r:Fact; r:gives {2000 log:repeat 295}] [ a r:Fact; r:gives {(295 2000) math:sum 2295}] - skolem:lemma1295 + skolem:lemma2294 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 295]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2295]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma296 a r:Inference; r:gives { 2296 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 296}] + [ a r:Fact; r:gives {2000 log:repeat 296}] [ a r:Fact; r:gives {(296 2000) math:sum 2296}] - skolem:lemma1296 + skolem:lemma2295 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 296]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2296]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma297 a r:Inference; r:gives { 2297 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 297}] + [ a r:Fact; r:gives {2000 log:repeat 297}] [ a r:Fact; r:gives {(297 2000) math:sum 2297}] - skolem:lemma1297 + skolem:lemma2296 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 297]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2297]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma298 a r:Inference; r:gives { 2298 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 298}] + [ a r:Fact; r:gives {2000 log:repeat 298}] [ a r:Fact; r:gives {(298 2000) math:sum 2298}] - skolem:lemma1298 + skolem:lemma2297 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 298]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2298]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma299 a r:Inference; r:gives { 2299 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 299}] + [ a r:Fact; r:gives {2000 log:repeat 299}] [ a r:Fact; r:gives {(299 2000) math:sum 2299}] - skolem:lemma1299 + skolem:lemma2298 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 299]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2299]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma300 a r:Inference; r:gives { 2300 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 300}] + [ a r:Fact; r:gives {2000 log:repeat 300}] [ a r:Fact; r:gives {(300 2000) math:sum 2300}] - skolem:lemma1300 + skolem:lemma2299 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma301 a r:Inference; r:gives { 2301 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 301}] + [ a r:Fact; r:gives {2000 log:repeat 301}] [ a r:Fact; r:gives {(301 2000) math:sum 2301}] - skolem:lemma1301 + skolem:lemma2300 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 301]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2301]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma302 a r:Inference; r:gives { 2302 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 302}] + [ a r:Fact; r:gives {2000 log:repeat 302}] [ a r:Fact; r:gives {(302 2000) math:sum 2302}] - skolem:lemma1302 + skolem:lemma2301 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 302]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2302]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma303 a r:Inference; r:gives { 2303 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 303}] + [ a r:Fact; r:gives {2000 log:repeat 303}] [ a r:Fact; r:gives {(303 2000) math:sum 2303}] - skolem:lemma1303 + skolem:lemma2302 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 303]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2303]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma304 a r:Inference; r:gives { 2304 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 304}] + [ a r:Fact; r:gives {2000 log:repeat 304}] [ a r:Fact; r:gives {(304 2000) math:sum 2304}] - skolem:lemma1304 + skolem:lemma2303 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 304]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2304]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma305 a r:Inference; r:gives { 2305 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 305}] + [ a r:Fact; r:gives {2000 log:repeat 305}] [ a r:Fact; r:gives {(305 2000) math:sum 2305}] - skolem:lemma1305 + skolem:lemma2304 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 305]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2305]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma306 a r:Inference; r:gives { 2306 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 306}] + [ a r:Fact; r:gives {2000 log:repeat 306}] [ a r:Fact; r:gives {(306 2000) math:sum 2306}] - skolem:lemma1306 + skolem:lemma2305 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 306]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2306]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma307 a r:Inference; r:gives { 2307 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 307}] + [ a r:Fact; r:gives {2000 log:repeat 307}] [ a r:Fact; r:gives {(307 2000) math:sum 2307}] - skolem:lemma1307 + skolem:lemma2306 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 307]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2307]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma308 a r:Inference; r:gives { 2308 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 308}] + [ a r:Fact; r:gives {2000 log:repeat 308}] [ a r:Fact; r:gives {(308 2000) math:sum 2308}] - skolem:lemma1308 + skolem:lemma2307 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 308]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2308]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma309 a r:Inference; r:gives { 2309 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 309}] + [ a r:Fact; r:gives {2000 log:repeat 309}] [ a r:Fact; r:gives {(309 2000) math:sum 2309}] - skolem:lemma1309 + skolem:lemma2308 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 309]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2309]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma310 a r:Inference; r:gives { 2310 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 310}] + [ a r:Fact; r:gives {2000 log:repeat 310}] [ a r:Fact; r:gives {(310 2000) math:sum 2310}] - skolem:lemma1310 + skolem:lemma2309 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 310]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2310]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma311 a r:Inference; r:gives { 2311 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 311}] + [ a r:Fact; r:gives {2000 log:repeat 311}] [ a r:Fact; r:gives {(311 2000) math:sum 2311}] - skolem:lemma1311 + skolem:lemma2310 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 311]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2311]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma312 a r:Inference; r:gives { 2312 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 312}] + [ a r:Fact; r:gives {2000 log:repeat 312}] [ a r:Fact; r:gives {(312 2000) math:sum 2312}] - skolem:lemma1312 + skolem:lemma2311 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 312]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2312]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma313 a r:Inference; r:gives { 2313 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 313}] + [ a r:Fact; r:gives {2000 log:repeat 313}] [ a r:Fact; r:gives {(313 2000) math:sum 2313}] - skolem:lemma1313 + skolem:lemma2312 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 313]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2313]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma314 a r:Inference; r:gives { 2314 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 314}] + [ a r:Fact; r:gives {2000 log:repeat 314}] [ a r:Fact; r:gives {(314 2000) math:sum 2314}] - skolem:lemma1314 + skolem:lemma2313 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 314]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2314]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma315 a r:Inference; r:gives { 2315 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 315}] + [ a r:Fact; r:gives {2000 log:repeat 315}] [ a r:Fact; r:gives {(315 2000) math:sum 2315}] - skolem:lemma1315 + skolem:lemma2314 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 315]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2315]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma316 a r:Inference; r:gives { 2316 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 316}] + [ a r:Fact; r:gives {2000 log:repeat 316}] [ a r:Fact; r:gives {(316 2000) math:sum 2316}] - skolem:lemma1316 + skolem:lemma2315 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 316]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2316]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma317 a r:Inference; r:gives { 2317 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 317}] + [ a r:Fact; r:gives {2000 log:repeat 317}] [ a r:Fact; r:gives {(317 2000) math:sum 2317}] - skolem:lemma1317 + skolem:lemma2316 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 317]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2317]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma318 a r:Inference; r:gives { 2318 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 318}] + [ a r:Fact; r:gives {2000 log:repeat 318}] [ a r:Fact; r:gives {(318 2000) math:sum 2318}] - skolem:lemma1318 + skolem:lemma2317 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 318]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2318]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma319 a r:Inference; r:gives { 2319 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 319}] + [ a r:Fact; r:gives {2000 log:repeat 319}] [ a r:Fact; r:gives {(319 2000) math:sum 2319}] - skolem:lemma1319 + skolem:lemma2318 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 319]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2319]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma320 a r:Inference; r:gives { 2320 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 320}] + [ a r:Fact; r:gives {2000 log:repeat 320}] [ a r:Fact; r:gives {(320 2000) math:sum 2320}] - skolem:lemma1320 + skolem:lemma2319 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 320]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2320]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma321 a r:Inference; r:gives { 2321 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 321}] + [ a r:Fact; r:gives {2000 log:repeat 321}] [ a r:Fact; r:gives {(321 2000) math:sum 2321}] - skolem:lemma1321 + skolem:lemma2320 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 321]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2321]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma322 a r:Inference; r:gives { 2322 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 322}] + [ a r:Fact; r:gives {2000 log:repeat 322}] [ a r:Fact; r:gives {(322 2000) math:sum 2322}] - skolem:lemma1322 + skolem:lemma2321 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 322]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2322]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma323 a r:Inference; r:gives { 2323 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 323}] + [ a r:Fact; r:gives {2000 log:repeat 323}] [ a r:Fact; r:gives {(323 2000) math:sum 2323}] - skolem:lemma1323 + skolem:lemma2322 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 323]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2323]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma324 a r:Inference; r:gives { 2324 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 324}] + [ a r:Fact; r:gives {2000 log:repeat 324}] [ a r:Fact; r:gives {(324 2000) math:sum 2324}] - skolem:lemma1324 + skolem:lemma2323 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 324]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2324]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma325 a r:Inference; r:gives { 2325 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 325}] + [ a r:Fact; r:gives {2000 log:repeat 325}] [ a r:Fact; r:gives {(325 2000) math:sum 2325}] - skolem:lemma1325 + skolem:lemma2324 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 325]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2325]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma326 a r:Inference; r:gives { 2326 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 326}] + [ a r:Fact; r:gives {2000 log:repeat 326}] [ a r:Fact; r:gives {(326 2000) math:sum 2326}] - skolem:lemma1326 + skolem:lemma2325 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 326]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2326]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma327 a r:Inference; r:gives { 2327 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 327}] + [ a r:Fact; r:gives {2000 log:repeat 327}] [ a r:Fact; r:gives {(327 2000) math:sum 2327}] - skolem:lemma1327 + skolem:lemma2326 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 327]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2327]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma328 a r:Inference; r:gives { 2328 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 328}] + [ a r:Fact; r:gives {2000 log:repeat 328}] [ a r:Fact; r:gives {(328 2000) math:sum 2328}] - skolem:lemma1328 + skolem:lemma2327 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 328]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2328]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma329 a r:Inference; r:gives { 2329 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 329}] + [ a r:Fact; r:gives {2000 log:repeat 329}] [ a r:Fact; r:gives {(329 2000) math:sum 2329}] - skolem:lemma1329 + skolem:lemma2328 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 329]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2329]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma330 a r:Inference; r:gives { 2330 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 330}] + [ a r:Fact; r:gives {2000 log:repeat 330}] [ a r:Fact; r:gives {(330 2000) math:sum 2330}] - skolem:lemma1330 + skolem:lemma2329 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 330]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2330]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma331 a r:Inference; r:gives { 2331 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 331}] + [ a r:Fact; r:gives {2000 log:repeat 331}] [ a r:Fact; r:gives {(331 2000) math:sum 2331}] - skolem:lemma1331 + skolem:lemma2330 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 331]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2331]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma332 a r:Inference; r:gives { 2332 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 332}] + [ a r:Fact; r:gives {2000 log:repeat 332}] [ a r:Fact; r:gives {(332 2000) math:sum 2332}] - skolem:lemma1332 + skolem:lemma2331 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 332]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2332]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma333 a r:Inference; r:gives { 2333 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 333}] + [ a r:Fact; r:gives {2000 log:repeat 333}] [ a r:Fact; r:gives {(333 2000) math:sum 2333}] - skolem:lemma1333 + skolem:lemma2332 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 333]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2333]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma334 a r:Inference; r:gives { 2334 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 334}] + [ a r:Fact; r:gives {2000 log:repeat 334}] [ a r:Fact; r:gives {(334 2000) math:sum 2334}] - skolem:lemma1334 + skolem:lemma2333 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 334]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2334]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma335 a r:Inference; r:gives { 2335 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 335}] + [ a r:Fact; r:gives {2000 log:repeat 335}] [ a r:Fact; r:gives {(335 2000) math:sum 2335}] - skolem:lemma1335 + skolem:lemma2334 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 335]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2335]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma336 a r:Inference; r:gives { 2336 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 336}] + [ a r:Fact; r:gives {2000 log:repeat 336}] [ a r:Fact; r:gives {(336 2000) math:sum 2336}] - skolem:lemma1336 + skolem:lemma2335 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 336]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2336]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma337 a r:Inference; r:gives { 2337 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 337}] + [ a r:Fact; r:gives {2000 log:repeat 337}] [ a r:Fact; r:gives {(337 2000) math:sum 2337}] - skolem:lemma1337 + skolem:lemma2336 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 337]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2337]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma338 a r:Inference; r:gives { 2338 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 338}] + [ a r:Fact; r:gives {2000 log:repeat 338}] [ a r:Fact; r:gives {(338 2000) math:sum 2338}] - skolem:lemma1338 + skolem:lemma2337 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 338]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2338]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma339 a r:Inference; r:gives { 2339 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 339}] + [ a r:Fact; r:gives {2000 log:repeat 339}] [ a r:Fact; r:gives {(339 2000) math:sum 2339}] - skolem:lemma1339 + skolem:lemma2338 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 339]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2339]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma340 a r:Inference; r:gives { 2340 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 340}] + [ a r:Fact; r:gives {2000 log:repeat 340}] [ a r:Fact; r:gives {(340 2000) math:sum 2340}] - skolem:lemma1340 + skolem:lemma2339 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 340]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2340]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma341 a r:Inference; r:gives { 2341 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 341}] + [ a r:Fact; r:gives {2000 log:repeat 341}] [ a r:Fact; r:gives {(341 2000) math:sum 2341}] - skolem:lemma1341 + skolem:lemma2340 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 341]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2341]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma342 a r:Inference; r:gives { 2342 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 342}] + [ a r:Fact; r:gives {2000 log:repeat 342}] [ a r:Fact; r:gives {(342 2000) math:sum 2342}] - skolem:lemma1342 + skolem:lemma2341 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 342]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2342]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma343 a r:Inference; r:gives { 2343 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 343}] + [ a r:Fact; r:gives {2000 log:repeat 343}] [ a r:Fact; r:gives {(343 2000) math:sum 2343}] - skolem:lemma1343 + skolem:lemma2342 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 343]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2343]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma344 a r:Inference; r:gives { 2344 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 344}] + [ a r:Fact; r:gives {2000 log:repeat 344}] [ a r:Fact; r:gives {(344 2000) math:sum 2344}] - skolem:lemma1344 + skolem:lemma2343 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 344]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2344]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma345 a r:Inference; r:gives { 2345 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 345}] + [ a r:Fact; r:gives {2000 log:repeat 345}] [ a r:Fact; r:gives {(345 2000) math:sum 2345}] - skolem:lemma1345 + skolem:lemma2344 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 345]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2345]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma346 a r:Inference; r:gives { 2346 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 346}] + [ a r:Fact; r:gives {2000 log:repeat 346}] [ a r:Fact; r:gives {(346 2000) math:sum 2346}] - skolem:lemma1346 + skolem:lemma2345 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 346]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2346]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma347 a r:Inference; r:gives { 2347 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 347}] + [ a r:Fact; r:gives {2000 log:repeat 347}] [ a r:Fact; r:gives {(347 2000) math:sum 2347}] - skolem:lemma1347 + skolem:lemma2346 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 347]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2347]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma348 a r:Inference; r:gives { 2348 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 348}] + [ a r:Fact; r:gives {2000 log:repeat 348}] [ a r:Fact; r:gives {(348 2000) math:sum 2348}] - skolem:lemma1348 + skolem:lemma2347 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 348]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2348]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma349 a r:Inference; r:gives { 2349 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 349}] + [ a r:Fact; r:gives {2000 log:repeat 349}] [ a r:Fact; r:gives {(349 2000) math:sum 2349}] - skolem:lemma1349 + skolem:lemma2348 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 349]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2349]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma350 a r:Inference; r:gives { 2350 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 350}] + [ a r:Fact; r:gives {2000 log:repeat 350}] [ a r:Fact; r:gives {(350 2000) math:sum 2350}] - skolem:lemma1350 + skolem:lemma2349 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 350]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2350]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma351 a r:Inference; r:gives { 2351 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 351}] + [ a r:Fact; r:gives {2000 log:repeat 351}] [ a r:Fact; r:gives {(351 2000) math:sum 2351}] - skolem:lemma1351 + skolem:lemma2350 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 351]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2351]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma352 a r:Inference; r:gives { 2352 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 352}] + [ a r:Fact; r:gives {2000 log:repeat 352}] [ a r:Fact; r:gives {(352 2000) math:sum 2352}] - skolem:lemma1352 + skolem:lemma2351 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 352]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2352]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma353 a r:Inference; r:gives { 2353 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 353}] + [ a r:Fact; r:gives {2000 log:repeat 353}] [ a r:Fact; r:gives {(353 2000) math:sum 2353}] - skolem:lemma1353 + skolem:lemma2352 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 353]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2353]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma354 a r:Inference; r:gives { 2354 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 354}] + [ a r:Fact; r:gives {2000 log:repeat 354}] [ a r:Fact; r:gives {(354 2000) math:sum 2354}] - skolem:lemma1354 + skolem:lemma2353 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 354]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2354]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma355 a r:Inference; r:gives { 2355 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 355}] + [ a r:Fact; r:gives {2000 log:repeat 355}] [ a r:Fact; r:gives {(355 2000) math:sum 2355}] - skolem:lemma1355 + skolem:lemma2354 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 355]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2355]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma356 a r:Inference; r:gives { 2356 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 356}] + [ a r:Fact; r:gives {2000 log:repeat 356}] [ a r:Fact; r:gives {(356 2000) math:sum 2356}] - skolem:lemma1356 + skolem:lemma2355 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 356]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2356]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma357 a r:Inference; r:gives { 2357 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 357}] + [ a r:Fact; r:gives {2000 log:repeat 357}] [ a r:Fact; r:gives {(357 2000) math:sum 2357}] - skolem:lemma1357 + skolem:lemma2356 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 357]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2357]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma358 a r:Inference; r:gives { 2358 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 358}] + [ a r:Fact; r:gives {2000 log:repeat 358}] [ a r:Fact; r:gives {(358 2000) math:sum 2358}] - skolem:lemma1358 + skolem:lemma2357 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 358]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2358]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma359 a r:Inference; r:gives { 2359 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 359}] + [ a r:Fact; r:gives {2000 log:repeat 359}] [ a r:Fact; r:gives {(359 2000) math:sum 2359}] - skolem:lemma1359 + skolem:lemma2358 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 359]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2359]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma360 a r:Inference; r:gives { 2360 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 360}] + [ a r:Fact; r:gives {2000 log:repeat 360}] [ a r:Fact; r:gives {(360 2000) math:sum 2360}] - skolem:lemma1360 + skolem:lemma2359 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 360]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2360]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma361 a r:Inference; r:gives { 2361 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 361}] + [ a r:Fact; r:gives {2000 log:repeat 361}] [ a r:Fact; r:gives {(361 2000) math:sum 2361}] - skolem:lemma1361 + skolem:lemma2360 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 361]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2361]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma362 a r:Inference; r:gives { 2362 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 362}] + [ a r:Fact; r:gives {2000 log:repeat 362}] [ a r:Fact; r:gives {(362 2000) math:sum 2362}] - skolem:lemma1362 + skolem:lemma2361 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 362]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2362]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma363 a r:Inference; r:gives { 2363 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 363}] + [ a r:Fact; r:gives {2000 log:repeat 363}] [ a r:Fact; r:gives {(363 2000) math:sum 2363}] - skolem:lemma1363 + skolem:lemma2362 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 363]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2363]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma364 a r:Inference; r:gives { 2364 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 364}] + [ a r:Fact; r:gives {2000 log:repeat 364}] [ a r:Fact; r:gives {(364 2000) math:sum 2364}] - skolem:lemma1364 + skolem:lemma2363 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 364]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2364]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma365 a r:Inference; r:gives { 2365 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 365}] + [ a r:Fact; r:gives {2000 log:repeat 365}] [ a r:Fact; r:gives {(365 2000) math:sum 2365}] - skolem:lemma1365 + skolem:lemma2364 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 365]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2365]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma366 a r:Inference; r:gives { 2366 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 366}] + [ a r:Fact; r:gives {2000 log:repeat 366}] [ a r:Fact; r:gives {(366 2000) math:sum 2366}] - skolem:lemma1366 + skolem:lemma2365 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 366]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2366]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma367 a r:Inference; r:gives { 2367 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 367}] + [ a r:Fact; r:gives {2000 log:repeat 367}] [ a r:Fact; r:gives {(367 2000) math:sum 2367}] - skolem:lemma1367 + skolem:lemma2366 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 367]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2367]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma368 a r:Inference; r:gives { 2368 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 368}] + [ a r:Fact; r:gives {2000 log:repeat 368}] [ a r:Fact; r:gives {(368 2000) math:sum 2368}] - skolem:lemma1368 + skolem:lemma2367 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 368]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2368]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma369 a r:Inference; r:gives { 2369 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 369}] + [ a r:Fact; r:gives {2000 log:repeat 369}] [ a r:Fact; r:gives {(369 2000) math:sum 2369}] - skolem:lemma1369 + skolem:lemma2368 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 369]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2369]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma370 a r:Inference; r:gives { 2370 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 370}] + [ a r:Fact; r:gives {2000 log:repeat 370}] [ a r:Fact; r:gives {(370 2000) math:sum 2370}] - skolem:lemma1370 + skolem:lemma2369 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 370]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2370]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma371 a r:Inference; r:gives { 2371 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 371}] + [ a r:Fact; r:gives {2000 log:repeat 371}] [ a r:Fact; r:gives {(371 2000) math:sum 2371}] - skolem:lemma1371 + skolem:lemma2370 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 371]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2371]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma372 a r:Inference; r:gives { 2372 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 372}] + [ a r:Fact; r:gives {2000 log:repeat 372}] [ a r:Fact; r:gives {(372 2000) math:sum 2372}] - skolem:lemma1372 + skolem:lemma2371 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 372]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2372]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma373 a r:Inference; r:gives { 2373 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 373}] + [ a r:Fact; r:gives {2000 log:repeat 373}] [ a r:Fact; r:gives {(373 2000) math:sum 2373}] - skolem:lemma1373 + skolem:lemma2372 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 373]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2373]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma374 a r:Inference; r:gives { 2374 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 374}] + [ a r:Fact; r:gives {2000 log:repeat 374}] [ a r:Fact; r:gives {(374 2000) math:sum 2374}] - skolem:lemma1374 + skolem:lemma2373 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 374]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2374]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma375 a r:Inference; r:gives { 2375 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 375}] + [ a r:Fact; r:gives {2000 log:repeat 375}] [ a r:Fact; r:gives {(375 2000) math:sum 2375}] - skolem:lemma1375 + skolem:lemma2374 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 375]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2375]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma376 a r:Inference; r:gives { 2376 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 376}] + [ a r:Fact; r:gives {2000 log:repeat 376}] [ a r:Fact; r:gives {(376 2000) math:sum 2376}] - skolem:lemma1376 + skolem:lemma2375 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 376]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2376]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma377 a r:Inference; r:gives { 2377 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 377}] + [ a r:Fact; r:gives {2000 log:repeat 377}] [ a r:Fact; r:gives {(377 2000) math:sum 2377}] - skolem:lemma1377 + skolem:lemma2376 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 377]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2377]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma378 a r:Inference; r:gives { 2378 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 378}] + [ a r:Fact; r:gives {2000 log:repeat 378}] [ a r:Fact; r:gives {(378 2000) math:sum 2378}] - skolem:lemma1378 + skolem:lemma2377 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 378]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2378]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma379 a r:Inference; r:gives { 2379 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 379}] + [ a r:Fact; r:gives {2000 log:repeat 379}] [ a r:Fact; r:gives {(379 2000) math:sum 2379}] - skolem:lemma1379 + skolem:lemma2378 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 379]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2379]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma380 a r:Inference; r:gives { 2380 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 380}] + [ a r:Fact; r:gives {2000 log:repeat 380}] [ a r:Fact; r:gives {(380 2000) math:sum 2380}] - skolem:lemma1380 + skolem:lemma2379 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 380]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2380]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma381 a r:Inference; r:gives { 2381 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 381}] + [ a r:Fact; r:gives {2000 log:repeat 381}] [ a r:Fact; r:gives {(381 2000) math:sum 2381}] - skolem:lemma1381 + skolem:lemma2380 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 381]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2381]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma382 a r:Inference; r:gives { 2382 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 382}] + [ a r:Fact; r:gives {2000 log:repeat 382}] [ a r:Fact; r:gives {(382 2000) math:sum 2382}] - skolem:lemma1382 + skolem:lemma2381 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 382]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2382]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma383 a r:Inference; r:gives { 2383 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 383}] + [ a r:Fact; r:gives {2000 log:repeat 383}] [ a r:Fact; r:gives {(383 2000) math:sum 2383}] - skolem:lemma1383 + skolem:lemma2382 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 383]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2383]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma384 a r:Inference; r:gives { 2384 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 384}] + [ a r:Fact; r:gives {2000 log:repeat 384}] [ a r:Fact; r:gives {(384 2000) math:sum 2384}] - skolem:lemma1384 + skolem:lemma2383 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 384]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2384]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma385 a r:Inference; r:gives { 2385 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 385}] + [ a r:Fact; r:gives {2000 log:repeat 385}] [ a r:Fact; r:gives {(385 2000) math:sum 2385}] - skolem:lemma1385 + skolem:lemma2384 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 385]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2385]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma386 a r:Inference; r:gives { 2386 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 386}] + [ a r:Fact; r:gives {2000 log:repeat 386}] [ a r:Fact; r:gives {(386 2000) math:sum 2386}] - skolem:lemma1386 + skolem:lemma2385 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 386]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2386]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma387 a r:Inference; r:gives { 2387 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 387}] + [ a r:Fact; r:gives {2000 log:repeat 387}] [ a r:Fact; r:gives {(387 2000) math:sum 2387}] - skolem:lemma1387 + skolem:lemma2386 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 387]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2387]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma388 a r:Inference; r:gives { 2388 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 388}] + [ a r:Fact; r:gives {2000 log:repeat 388}] [ a r:Fact; r:gives {(388 2000) math:sum 2388}] - skolem:lemma1388 + skolem:lemma2387 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 388]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2388]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma389 a r:Inference; r:gives { 2389 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 389}] + [ a r:Fact; r:gives {2000 log:repeat 389}] [ a r:Fact; r:gives {(389 2000) math:sum 2389}] - skolem:lemma1389 + skolem:lemma2388 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 389]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2389]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma390 a r:Inference; r:gives { 2390 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 390}] + [ a r:Fact; r:gives {2000 log:repeat 390}] [ a r:Fact; r:gives {(390 2000) math:sum 2390}] - skolem:lemma1390 + skolem:lemma2389 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 390]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2390]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma391 a r:Inference; r:gives { 2391 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 391}] + [ a r:Fact; r:gives {2000 log:repeat 391}] [ a r:Fact; r:gives {(391 2000) math:sum 2391}] - skolem:lemma1391 + skolem:lemma2390 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 391]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2391]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma392 a r:Inference; r:gives { 2392 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 392}] + [ a r:Fact; r:gives {2000 log:repeat 392}] [ a r:Fact; r:gives {(392 2000) math:sum 2392}] - skolem:lemma1392 + skolem:lemma2391 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 392]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2392]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma393 a r:Inference; r:gives { 2393 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 393}] + [ a r:Fact; r:gives {2000 log:repeat 393}] [ a r:Fact; r:gives {(393 2000) math:sum 2393}] - skolem:lemma1393 + skolem:lemma2392 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 393]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2393]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma394 a r:Inference; r:gives { 2394 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 394}] + [ a r:Fact; r:gives {2000 log:repeat 394}] [ a r:Fact; r:gives {(394 2000) math:sum 2394}] - skolem:lemma1394 + skolem:lemma2393 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 394]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2394]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma395 a r:Inference; r:gives { 2395 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 395}] + [ a r:Fact; r:gives {2000 log:repeat 395}] [ a r:Fact; r:gives {(395 2000) math:sum 2395}] - skolem:lemma1395 + skolem:lemma2394 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 395]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2395]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma396 a r:Inference; r:gives { 2396 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 396}] + [ a r:Fact; r:gives {2000 log:repeat 396}] [ a r:Fact; r:gives {(396 2000) math:sum 2396}] - skolem:lemma1396 + skolem:lemma2395 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 396]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2396]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma397 a r:Inference; r:gives { 2397 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 397}] + [ a r:Fact; r:gives {2000 log:repeat 397}] [ a r:Fact; r:gives {(397 2000) math:sum 2397}] - skolem:lemma1397 + skolem:lemma2396 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 397]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2397]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma398 a r:Inference; r:gives { 2398 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 398}] + [ a r:Fact; r:gives {2000 log:repeat 398}] [ a r:Fact; r:gives {(398 2000) math:sum 2398}] - skolem:lemma1398 + skolem:lemma2397 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 398]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2398]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma399 a r:Inference; r:gives { 2399 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 399}] + [ a r:Fact; r:gives {2000 log:repeat 399}] [ a r:Fact; r:gives {(399 2000) math:sum 2399}] - skolem:lemma1399 + skolem:lemma2398 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 399]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2399]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma400 a r:Inference; r:gives { 2400 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 400}] + [ a r:Fact; r:gives {2000 log:repeat 400}] [ a r:Fact; r:gives {(400 2000) math:sum 2400}] - skolem:lemma1400 + skolem:lemma2399 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma401 a r:Inference; r:gives { 2401 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 401}] + [ a r:Fact; r:gives {2000 log:repeat 401}] [ a r:Fact; r:gives {(401 2000) math:sum 2401}] - skolem:lemma1401 + skolem:lemma2400 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 401]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2401]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma402 a r:Inference; r:gives { 2402 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 402}] + [ a r:Fact; r:gives {2000 log:repeat 402}] [ a r:Fact; r:gives {(402 2000) math:sum 2402}] - skolem:lemma1402 + skolem:lemma2401 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 402]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2402]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma403 a r:Inference; r:gives { 2403 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 403}] + [ a r:Fact; r:gives {2000 log:repeat 403}] [ a r:Fact; r:gives {(403 2000) math:sum 2403}] - skolem:lemma1403 + skolem:lemma2402 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 403]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2403]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma404 a r:Inference; r:gives { 2404 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 404}] + [ a r:Fact; r:gives {2000 log:repeat 404}] [ a r:Fact; r:gives {(404 2000) math:sum 2404}] - skolem:lemma1404 + skolem:lemma2403 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 404]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2404]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma405 a r:Inference; r:gives { 2405 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 405}] + [ a r:Fact; r:gives {2000 log:repeat 405}] [ a r:Fact; r:gives {(405 2000) math:sum 2405}] - skolem:lemma1405 + skolem:lemma2404 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 405]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2405]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma406 a r:Inference; r:gives { 2406 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 406}] + [ a r:Fact; r:gives {2000 log:repeat 406}] [ a r:Fact; r:gives {(406 2000) math:sum 2406}] - skolem:lemma1406 + skolem:lemma2405 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 406]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2406]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma407 a r:Inference; r:gives { 2407 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 407}] + [ a r:Fact; r:gives {2000 log:repeat 407}] [ a r:Fact; r:gives {(407 2000) math:sum 2407}] - skolem:lemma1407 + skolem:lemma2406 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 407]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2407]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma408 a r:Inference; r:gives { 2408 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 408}] + [ a r:Fact; r:gives {2000 log:repeat 408}] [ a r:Fact; r:gives {(408 2000) math:sum 2408}] - skolem:lemma1408 + skolem:lemma2407 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 408]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2408]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma409 a r:Inference; r:gives { 2409 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 409}] + [ a r:Fact; r:gives {2000 log:repeat 409}] [ a r:Fact; r:gives {(409 2000) math:sum 2409}] - skolem:lemma1409 + skolem:lemma2408 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 409]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2409]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma410 a r:Inference; r:gives { 2410 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 410}] + [ a r:Fact; r:gives {2000 log:repeat 410}] [ a r:Fact; r:gives {(410 2000) math:sum 2410}] - skolem:lemma1410 + skolem:lemma2409 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 410]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2410]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma411 a r:Inference; r:gives { 2411 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 411}] + [ a r:Fact; r:gives {2000 log:repeat 411}] [ a r:Fact; r:gives {(411 2000) math:sum 2411}] - skolem:lemma1411 + skolem:lemma2410 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 411]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2411]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma412 a r:Inference; r:gives { 2412 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 412}] + [ a r:Fact; r:gives {2000 log:repeat 412}] [ a r:Fact; r:gives {(412 2000) math:sum 2412}] - skolem:lemma1412 + skolem:lemma2411 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 412]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2412]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma413 a r:Inference; r:gives { 2413 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 413}] + [ a r:Fact; r:gives {2000 log:repeat 413}] [ a r:Fact; r:gives {(413 2000) math:sum 2413}] - skolem:lemma1413 + skolem:lemma2412 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 413]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2413]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma414 a r:Inference; r:gives { 2414 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 414}] + [ a r:Fact; r:gives {2000 log:repeat 414}] [ a r:Fact; r:gives {(414 2000) math:sum 2414}] - skolem:lemma1414 + skolem:lemma2413 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 414]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2414]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma415 a r:Inference; r:gives { 2415 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 415}] + [ a r:Fact; r:gives {2000 log:repeat 415}] [ a r:Fact; r:gives {(415 2000) math:sum 2415}] - skolem:lemma1415 + skolem:lemma2414 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 415]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2415]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma416 a r:Inference; r:gives { 2416 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 416}] + [ a r:Fact; r:gives {2000 log:repeat 416}] [ a r:Fact; r:gives {(416 2000) math:sum 2416}] - skolem:lemma1416 + skolem:lemma2415 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 416]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2416]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma417 a r:Inference; r:gives { 2417 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 417}] + [ a r:Fact; r:gives {2000 log:repeat 417}] [ a r:Fact; r:gives {(417 2000) math:sum 2417}] - skolem:lemma1417 + skolem:lemma2416 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 417]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2417]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma418 a r:Inference; r:gives { 2418 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 418}] + [ a r:Fact; r:gives {2000 log:repeat 418}] [ a r:Fact; r:gives {(418 2000) math:sum 2418}] - skolem:lemma1418 + skolem:lemma2417 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 418]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2418]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma419 a r:Inference; r:gives { 2419 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 419}] + [ a r:Fact; r:gives {2000 log:repeat 419}] [ a r:Fact; r:gives {(419 2000) math:sum 2419}] - skolem:lemma1419 + skolem:lemma2418 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 419]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2419]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma420 a r:Inference; r:gives { 2420 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 420}] + [ a r:Fact; r:gives {2000 log:repeat 420}] [ a r:Fact; r:gives {(420 2000) math:sum 2420}] - skolem:lemma1420 + skolem:lemma2419 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 420]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2420]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma421 a r:Inference; r:gives { 2421 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 421}] + [ a r:Fact; r:gives {2000 log:repeat 421}] [ a r:Fact; r:gives {(421 2000) math:sum 2421}] - skolem:lemma1421 + skolem:lemma2420 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 421]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2421]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma422 a r:Inference; r:gives { 2422 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 422}] + [ a r:Fact; r:gives {2000 log:repeat 422}] [ a r:Fact; r:gives {(422 2000) math:sum 2422}] - skolem:lemma1422 + skolem:lemma2421 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 422]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2422]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma423 a r:Inference; r:gives { 2423 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 423}] + [ a r:Fact; r:gives {2000 log:repeat 423}] [ a r:Fact; r:gives {(423 2000) math:sum 2423}] - skolem:lemma1423 + skolem:lemma2422 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 423]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2423]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma424 a r:Inference; r:gives { 2424 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 424}] + [ a r:Fact; r:gives {2000 log:repeat 424}] [ a r:Fact; r:gives {(424 2000) math:sum 2424}] - skolem:lemma1424 + skolem:lemma2423 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 424]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2424]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma425 a r:Inference; r:gives { 2425 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 425}] + [ a r:Fact; r:gives {2000 log:repeat 425}] [ a r:Fact; r:gives {(425 2000) math:sum 2425}] - skolem:lemma1425 + skolem:lemma2424 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 425]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2425]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma426 a r:Inference; r:gives { 2426 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 426}] + [ a r:Fact; r:gives {2000 log:repeat 426}] [ a r:Fact; r:gives {(426 2000) math:sum 2426}] - skolem:lemma1426 + skolem:lemma2425 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 426]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2426]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma427 a r:Inference; r:gives { 2427 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 427}] + [ a r:Fact; r:gives {2000 log:repeat 427}] [ a r:Fact; r:gives {(427 2000) math:sum 2427}] - skolem:lemma1427 + skolem:lemma2426 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 427]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2427]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma428 a r:Inference; r:gives { 2428 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 428}] + [ a r:Fact; r:gives {2000 log:repeat 428}] [ a r:Fact; r:gives {(428 2000) math:sum 2428}] - skolem:lemma1428 + skolem:lemma2427 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 428]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2428]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma429 a r:Inference; r:gives { 2429 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 429}] + [ a r:Fact; r:gives {2000 log:repeat 429}] [ a r:Fact; r:gives {(429 2000) math:sum 2429}] - skolem:lemma1429 + skolem:lemma2428 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 429]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2429]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma430 a r:Inference; r:gives { 2430 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 430}] + [ a r:Fact; r:gives {2000 log:repeat 430}] [ a r:Fact; r:gives {(430 2000) math:sum 2430}] - skolem:lemma1430 + skolem:lemma2429 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 430]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2430]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma431 a r:Inference; r:gives { 2431 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 431}] + [ a r:Fact; r:gives {2000 log:repeat 431}] [ a r:Fact; r:gives {(431 2000) math:sum 2431}] - skolem:lemma1431 + skolem:lemma2430 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 431]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2431]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma432 a r:Inference; r:gives { 2432 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 432}] + [ a r:Fact; r:gives {2000 log:repeat 432}] [ a r:Fact; r:gives {(432 2000) math:sum 2432}] - skolem:lemma1432 + skolem:lemma2431 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 432]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2432]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma433 a r:Inference; r:gives { 2433 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 433}] + [ a r:Fact; r:gives {2000 log:repeat 433}] [ a r:Fact; r:gives {(433 2000) math:sum 2433}] - skolem:lemma1433 + skolem:lemma2432 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 433]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2433]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma434 a r:Inference; r:gives { 2434 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 434}] + [ a r:Fact; r:gives {2000 log:repeat 434}] [ a r:Fact; r:gives {(434 2000) math:sum 2434}] - skolem:lemma1434 + skolem:lemma2433 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 434]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2434]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma435 a r:Inference; r:gives { 2435 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 435}] + [ a r:Fact; r:gives {2000 log:repeat 435}] [ a r:Fact; r:gives {(435 2000) math:sum 2435}] - skolem:lemma1435 + skolem:lemma2434 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 435]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2435]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma436 a r:Inference; r:gives { 2436 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 436}] + [ a r:Fact; r:gives {2000 log:repeat 436}] [ a r:Fact; r:gives {(436 2000) math:sum 2436}] - skolem:lemma1436 + skolem:lemma2435 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 436]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2436]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma437 a r:Inference; r:gives { 2437 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 437}] + [ a r:Fact; r:gives {2000 log:repeat 437}] [ a r:Fact; r:gives {(437 2000) math:sum 2437}] - skolem:lemma1437 + skolem:lemma2436 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 437]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2437]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma438 a r:Inference; r:gives { 2438 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 438}] + [ a r:Fact; r:gives {2000 log:repeat 438}] [ a r:Fact; r:gives {(438 2000) math:sum 2438}] - skolem:lemma1438 + skolem:lemma2437 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 438]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2438]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma439 a r:Inference; r:gives { 2439 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 439}] + [ a r:Fact; r:gives {2000 log:repeat 439}] [ a r:Fact; r:gives {(439 2000) math:sum 2439}] - skolem:lemma1439 + skolem:lemma2438 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 439]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2439]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma440 a r:Inference; r:gives { 2440 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 440}] + [ a r:Fact; r:gives {2000 log:repeat 440}] [ a r:Fact; r:gives {(440 2000) math:sum 2440}] - skolem:lemma1440 + skolem:lemma2439 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 440]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2440]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma441 a r:Inference; r:gives { 2441 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 441}] + [ a r:Fact; r:gives {2000 log:repeat 441}] [ a r:Fact; r:gives {(441 2000) math:sum 2441}] - skolem:lemma1441 + skolem:lemma2440 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 441]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2441]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma442 a r:Inference; r:gives { 2442 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 442}] + [ a r:Fact; r:gives {2000 log:repeat 442}] [ a r:Fact; r:gives {(442 2000) math:sum 2442}] - skolem:lemma1442 + skolem:lemma2441 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 442]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2442]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma443 a r:Inference; r:gives { 2443 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 443}] + [ a r:Fact; r:gives {2000 log:repeat 443}] [ a r:Fact; r:gives {(443 2000) math:sum 2443}] - skolem:lemma1443 + skolem:lemma2442 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 443]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2443]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma444 a r:Inference; r:gives { 2444 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 444}] + [ a r:Fact; r:gives {2000 log:repeat 444}] [ a r:Fact; r:gives {(444 2000) math:sum 2444}] - skolem:lemma1444 + skolem:lemma2443 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 444]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2444]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma445 a r:Inference; r:gives { 2445 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 445}] + [ a r:Fact; r:gives {2000 log:repeat 445}] [ a r:Fact; r:gives {(445 2000) math:sum 2445}] - skolem:lemma1445 + skolem:lemma2444 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 445]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2445]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma446 a r:Inference; r:gives { 2446 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 446}] + [ a r:Fact; r:gives {2000 log:repeat 446}] [ a r:Fact; r:gives {(446 2000) math:sum 2446}] - skolem:lemma1446 + skolem:lemma2445 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 446]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2446]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma447 a r:Inference; r:gives { 2447 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 447}] + [ a r:Fact; r:gives {2000 log:repeat 447}] [ a r:Fact; r:gives {(447 2000) math:sum 2447}] - skolem:lemma1447 + skolem:lemma2446 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 447]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2447]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma448 a r:Inference; r:gives { 2448 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 448}] + [ a r:Fact; r:gives {2000 log:repeat 448}] [ a r:Fact; r:gives {(448 2000) math:sum 2448}] - skolem:lemma1448 + skolem:lemma2447 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 448]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2448]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma449 a r:Inference; r:gives { 2449 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 449}] + [ a r:Fact; r:gives {2000 log:repeat 449}] [ a r:Fact; r:gives {(449 2000) math:sum 2449}] - skolem:lemma1449 + skolem:lemma2448 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 449]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2449]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma450 a r:Inference; r:gives { 2450 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 450}] + [ a r:Fact; r:gives {2000 log:repeat 450}] [ a r:Fact; r:gives {(450 2000) math:sum 2450}] - skolem:lemma1450 + skolem:lemma2449 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 450]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2450]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma451 a r:Inference; r:gives { 2451 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 451}] + [ a r:Fact; r:gives {2000 log:repeat 451}] [ a r:Fact; r:gives {(451 2000) math:sum 2451}] - skolem:lemma1451 + skolem:lemma2450 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 451]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2451]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma452 a r:Inference; r:gives { 2452 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 452}] + [ a r:Fact; r:gives {2000 log:repeat 452}] [ a r:Fact; r:gives {(452 2000) math:sum 2452}] - skolem:lemma1452 + skolem:lemma2451 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 452]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2452]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma453 a r:Inference; r:gives { 2453 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 453}] + [ a r:Fact; r:gives {2000 log:repeat 453}] [ a r:Fact; r:gives {(453 2000) math:sum 2453}] - skolem:lemma1453 + skolem:lemma2452 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 453]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2453]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma454 a r:Inference; r:gives { 2454 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 454}] + [ a r:Fact; r:gives {2000 log:repeat 454}] [ a r:Fact; r:gives {(454 2000) math:sum 2454}] - skolem:lemma1454 + skolem:lemma2453 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 454]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2454]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma455 a r:Inference; r:gives { 2455 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 455}] + [ a r:Fact; r:gives {2000 log:repeat 455}] [ a r:Fact; r:gives {(455 2000) math:sum 2455}] - skolem:lemma1455 + skolem:lemma2454 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 455]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2455]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma456 a r:Inference; r:gives { 2456 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 456}] + [ a r:Fact; r:gives {2000 log:repeat 456}] [ a r:Fact; r:gives {(456 2000) math:sum 2456}] - skolem:lemma1456 + skolem:lemma2455 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 456]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2456]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma457 a r:Inference; r:gives { 2457 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 457}] + [ a r:Fact; r:gives {2000 log:repeat 457}] [ a r:Fact; r:gives {(457 2000) math:sum 2457}] - skolem:lemma1457 + skolem:lemma2456 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 457]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2457]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma458 a r:Inference; r:gives { 2458 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 458}] + [ a r:Fact; r:gives {2000 log:repeat 458}] [ a r:Fact; r:gives {(458 2000) math:sum 2458}] - skolem:lemma1458 + skolem:lemma2457 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 458]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2458]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma459 a r:Inference; r:gives { 2459 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 459}] + [ a r:Fact; r:gives {2000 log:repeat 459}] [ a r:Fact; r:gives {(459 2000) math:sum 2459}] - skolem:lemma1459 + skolem:lemma2458 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 459]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2459]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma460 a r:Inference; r:gives { 2460 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 460}] + [ a r:Fact; r:gives {2000 log:repeat 460}] [ a r:Fact; r:gives {(460 2000) math:sum 2460}] - skolem:lemma1460 + skolem:lemma2459 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 460]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2460]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma461 a r:Inference; r:gives { 2461 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 461}] + [ a r:Fact; r:gives {2000 log:repeat 461}] [ a r:Fact; r:gives {(461 2000) math:sum 2461}] - skolem:lemma1461 + skolem:lemma2460 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 461]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2461]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma462 a r:Inference; r:gives { 2462 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 462}] + [ a r:Fact; r:gives {2000 log:repeat 462}] [ a r:Fact; r:gives {(462 2000) math:sum 2462}] - skolem:lemma1462 + skolem:lemma2461 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 462]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2462]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma463 a r:Inference; r:gives { 2463 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 463}] + [ a r:Fact; r:gives {2000 log:repeat 463}] [ a r:Fact; r:gives {(463 2000) math:sum 2463}] - skolem:lemma1463 + skolem:lemma2462 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 463]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2463]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma464 a r:Inference; r:gives { 2464 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 464}] + [ a r:Fact; r:gives {2000 log:repeat 464}] [ a r:Fact; r:gives {(464 2000) math:sum 2464}] - skolem:lemma1464 + skolem:lemma2463 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 464]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2464]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma465 a r:Inference; r:gives { 2465 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 465}] + [ a r:Fact; r:gives {2000 log:repeat 465}] [ a r:Fact; r:gives {(465 2000) math:sum 2465}] - skolem:lemma1465 + skolem:lemma2464 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 465]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2465]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma466 a r:Inference; r:gives { 2466 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 466}] + [ a r:Fact; r:gives {2000 log:repeat 466}] [ a r:Fact; r:gives {(466 2000) math:sum 2466}] - skolem:lemma1466 + skolem:lemma2465 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 466]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2466]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma467 a r:Inference; r:gives { 2467 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 467}] + [ a r:Fact; r:gives {2000 log:repeat 467}] [ a r:Fact; r:gives {(467 2000) math:sum 2467}] - skolem:lemma1467 + skolem:lemma2466 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 467]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2467]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma468 a r:Inference; r:gives { 2468 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 468}] + [ a r:Fact; r:gives {2000 log:repeat 468}] [ a r:Fact; r:gives {(468 2000) math:sum 2468}] - skolem:lemma1468 + skolem:lemma2467 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 468]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2468]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma469 a r:Inference; r:gives { 2469 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 469}] + [ a r:Fact; r:gives {2000 log:repeat 469}] [ a r:Fact; r:gives {(469 2000) math:sum 2469}] - skolem:lemma1469 + skolem:lemma2468 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 469]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2469]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma470 a r:Inference; r:gives { 2470 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 470}] + [ a r:Fact; r:gives {2000 log:repeat 470}] [ a r:Fact; r:gives {(470 2000) math:sum 2470}] - skolem:lemma1470 + skolem:lemma2469 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 470]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2470]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma471 a r:Inference; r:gives { 2471 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 471}] + [ a r:Fact; r:gives {2000 log:repeat 471}] [ a r:Fact; r:gives {(471 2000) math:sum 2471}] - skolem:lemma1471 + skolem:lemma2470 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 471]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2471]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma472 a r:Inference; r:gives { 2472 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 472}] + [ a r:Fact; r:gives {2000 log:repeat 472}] [ a r:Fact; r:gives {(472 2000) math:sum 2472}] - skolem:lemma1472 + skolem:lemma2471 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 472]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2472]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma473 a r:Inference; r:gives { 2473 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 473}] + [ a r:Fact; r:gives {2000 log:repeat 473}] [ a r:Fact; r:gives {(473 2000) math:sum 2473}] - skolem:lemma1473 + skolem:lemma2472 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 473]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2473]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma474 a r:Inference; r:gives { 2474 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 474}] + [ a r:Fact; r:gives {2000 log:repeat 474}] [ a r:Fact; r:gives {(474 2000) math:sum 2474}] - skolem:lemma1474 + skolem:lemma2473 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 474]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2474]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma475 a r:Inference; r:gives { 2475 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 475}] + [ a r:Fact; r:gives {2000 log:repeat 475}] [ a r:Fact; r:gives {(475 2000) math:sum 2475}] - skolem:lemma1475 + skolem:lemma2474 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 475]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2475]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma476 a r:Inference; r:gives { 2476 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 476}] + [ a r:Fact; r:gives {2000 log:repeat 476}] [ a r:Fact; r:gives {(476 2000) math:sum 2476}] - skolem:lemma1476 + skolem:lemma2475 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 476]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2476]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma477 a r:Inference; r:gives { 2477 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 477}] + [ a r:Fact; r:gives {2000 log:repeat 477}] [ a r:Fact; r:gives {(477 2000) math:sum 2477}] - skolem:lemma1477 + skolem:lemma2476 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 477]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2477]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma478 a r:Inference; r:gives { 2478 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 478}] + [ a r:Fact; r:gives {2000 log:repeat 478}] [ a r:Fact; r:gives {(478 2000) math:sum 2478}] - skolem:lemma1478 + skolem:lemma2477 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 478]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2478]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma479 a r:Inference; r:gives { 2479 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 479}] + [ a r:Fact; r:gives {2000 log:repeat 479}] [ a r:Fact; r:gives {(479 2000) math:sum 2479}] - skolem:lemma1479 + skolem:lemma2478 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 479]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2479]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma480 a r:Inference; r:gives { 2480 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 480}] + [ a r:Fact; r:gives {2000 log:repeat 480}] [ a r:Fact; r:gives {(480 2000) math:sum 2480}] - skolem:lemma1480 + skolem:lemma2479 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 480]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2480]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma481 a r:Inference; r:gives { 2481 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 481}] + [ a r:Fact; r:gives {2000 log:repeat 481}] [ a r:Fact; r:gives {(481 2000) math:sum 2481}] - skolem:lemma1481 + skolem:lemma2480 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 481]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2481]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma482 a r:Inference; r:gives { 2482 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 482}] + [ a r:Fact; r:gives {2000 log:repeat 482}] [ a r:Fact; r:gives {(482 2000) math:sum 2482}] - skolem:lemma1482 + skolem:lemma2481 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 482]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2482]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma483 a r:Inference; r:gives { 2483 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 483}] + [ a r:Fact; r:gives {2000 log:repeat 483}] [ a r:Fact; r:gives {(483 2000) math:sum 2483}] - skolem:lemma1483 + skolem:lemma2482 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 483]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2483]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma484 a r:Inference; r:gives { 2484 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 484}] + [ a r:Fact; r:gives {2000 log:repeat 484}] [ a r:Fact; r:gives {(484 2000) math:sum 2484}] - skolem:lemma1484 + skolem:lemma2483 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 484]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2484]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma485 a r:Inference; r:gives { 2485 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 485}] + [ a r:Fact; r:gives {2000 log:repeat 485}] [ a r:Fact; r:gives {(485 2000) math:sum 2485}] - skolem:lemma1485 + skolem:lemma2484 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 485]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2485]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma486 a r:Inference; r:gives { 2486 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 486}] + [ a r:Fact; r:gives {2000 log:repeat 486}] [ a r:Fact; r:gives {(486 2000) math:sum 2486}] - skolem:lemma1486 + skolem:lemma2485 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 486]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2486]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma487 a r:Inference; r:gives { 2487 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 487}] + [ a r:Fact; r:gives {2000 log:repeat 487}] [ a r:Fact; r:gives {(487 2000) math:sum 2487}] - skolem:lemma1487 + skolem:lemma2486 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 487]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2487]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma488 a r:Inference; r:gives { 2488 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 488}] + [ a r:Fact; r:gives {2000 log:repeat 488}] [ a r:Fact; r:gives {(488 2000) math:sum 2488}] - skolem:lemma1488 + skolem:lemma2487 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 488]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2488]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma489 a r:Inference; r:gives { 2489 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 489}] + [ a r:Fact; r:gives {2000 log:repeat 489}] [ a r:Fact; r:gives {(489 2000) math:sum 2489}] - skolem:lemma1489 + skolem:lemma2488 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 489]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2489]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma490 a r:Inference; r:gives { 2490 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 490}] + [ a r:Fact; r:gives {2000 log:repeat 490}] [ a r:Fact; r:gives {(490 2000) math:sum 2490}] - skolem:lemma1490 + skolem:lemma2489 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 490]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2490]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma491 a r:Inference; r:gives { 2491 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 491}] + [ a r:Fact; r:gives {2000 log:repeat 491}] [ a r:Fact; r:gives {(491 2000) math:sum 2491}] - skolem:lemma1491 + skolem:lemma2490 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 491]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2491]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma492 a r:Inference; r:gives { 2492 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 492}] + [ a r:Fact; r:gives {2000 log:repeat 492}] [ a r:Fact; r:gives {(492 2000) math:sum 2492}] - skolem:lemma1492 + skolem:lemma2491 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 492]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2492]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma493 a r:Inference; r:gives { 2493 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 493}] + [ a r:Fact; r:gives {2000 log:repeat 493}] [ a r:Fact; r:gives {(493 2000) math:sum 2493}] - skolem:lemma1493 + skolem:lemma2492 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 493]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2493]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma494 a r:Inference; r:gives { 2494 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 494}] + [ a r:Fact; r:gives {2000 log:repeat 494}] [ a r:Fact; r:gives {(494 2000) math:sum 2494}] - skolem:lemma1494 + skolem:lemma2493 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 494]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2494]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma495 a r:Inference; r:gives { 2495 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 495}] + [ a r:Fact; r:gives {2000 log:repeat 495}] [ a r:Fact; r:gives {(495 2000) math:sum 2495}] - skolem:lemma1495 + skolem:lemma2494 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 495]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2495]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma496 a r:Inference; r:gives { 2496 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 496}] + [ a r:Fact; r:gives {2000 log:repeat 496}] [ a r:Fact; r:gives {(496 2000) math:sum 2496}] - skolem:lemma1496 + skolem:lemma2495 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 496]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2496]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma497 a r:Inference; r:gives { 2497 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 497}] + [ a r:Fact; r:gives {2000 log:repeat 497}] [ a r:Fact; r:gives {(497 2000) math:sum 2497}] - skolem:lemma1497 + skolem:lemma2496 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 497]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2497]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma498 a r:Inference; r:gives { 2498 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 498}] + [ a r:Fact; r:gives {2000 log:repeat 498}] [ a r:Fact; r:gives {(498 2000) math:sum 2498}] - skolem:lemma1498 + skolem:lemma2497 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 498]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2498]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma499 a r:Inference; r:gives { 2499 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 499}] + [ a r:Fact; r:gives {2000 log:repeat 499}] [ a r:Fact; r:gives {(499 2000) math:sum 2499}] - skolem:lemma1499 + skolem:lemma2498 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 499]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2499]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma500 a r:Inference; r:gives { 2500 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 500}] + [ a r:Fact; r:gives {2000 log:repeat 500}] [ a r:Fact; r:gives {(500 2000) math:sum 2500}] - skolem:lemma1500 + skolem:lemma2499 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma501 a r:Inference; r:gives { 2501 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 501}] + [ a r:Fact; r:gives {2000 log:repeat 501}] [ a r:Fact; r:gives {(501 2000) math:sum 2501}] - skolem:lemma1501 + skolem:lemma2500 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 501]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2501]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma502 a r:Inference; r:gives { 2502 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 502}] + [ a r:Fact; r:gives {2000 log:repeat 502}] [ a r:Fact; r:gives {(502 2000) math:sum 2502}] - skolem:lemma1502 + skolem:lemma2501 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 502]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2502]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma503 a r:Inference; r:gives { 2503 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 503}] + [ a r:Fact; r:gives {2000 log:repeat 503}] [ a r:Fact; r:gives {(503 2000) math:sum 2503}] - skolem:lemma1503 + skolem:lemma2502 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 503]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2503]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma504 a r:Inference; r:gives { 2504 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 504}] + [ a r:Fact; r:gives {2000 log:repeat 504}] [ a r:Fact; r:gives {(504 2000) math:sum 2504}] - skolem:lemma1504 + skolem:lemma2503 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 504]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2504]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma505 a r:Inference; r:gives { 2505 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 505}] + [ a r:Fact; r:gives {2000 log:repeat 505}] [ a r:Fact; r:gives {(505 2000) math:sum 2505}] - skolem:lemma1505 + skolem:lemma2504 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 505]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2505]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma506 a r:Inference; r:gives { 2506 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 506}] + [ a r:Fact; r:gives {2000 log:repeat 506}] [ a r:Fact; r:gives {(506 2000) math:sum 2506}] - skolem:lemma1506 + skolem:lemma2505 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 506]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2506]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma507 a r:Inference; r:gives { 2507 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 507}] + [ a r:Fact; r:gives {2000 log:repeat 507}] [ a r:Fact; r:gives {(507 2000) math:sum 2507}] - skolem:lemma1507 + skolem:lemma2506 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 507]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2507]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma508 a r:Inference; r:gives { 2508 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 508}] + [ a r:Fact; r:gives {2000 log:repeat 508}] [ a r:Fact; r:gives {(508 2000) math:sum 2508}] - skolem:lemma1508 + skolem:lemma2507 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 508]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2508]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma509 a r:Inference; r:gives { 2509 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 509}] + [ a r:Fact; r:gives {2000 log:repeat 509}] [ a r:Fact; r:gives {(509 2000) math:sum 2509}] - skolem:lemma1509 + skolem:lemma2508 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 509]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2509]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma510 a r:Inference; r:gives { 2510 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 510}] + [ a r:Fact; r:gives {2000 log:repeat 510}] [ a r:Fact; r:gives {(510 2000) math:sum 2510}] - skolem:lemma1510 + skolem:lemma2509 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 510]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2510]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma511 a r:Inference; r:gives { 2511 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 511}] + [ a r:Fact; r:gives {2000 log:repeat 511}] [ a r:Fact; r:gives {(511 2000) math:sum 2511}] - skolem:lemma1511 + skolem:lemma2510 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 511]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2511]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma512 a r:Inference; r:gives { 2512 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 512}] + [ a r:Fact; r:gives {2000 log:repeat 512}] [ a r:Fact; r:gives {(512 2000) math:sum 2512}] - skolem:lemma1512 + skolem:lemma2511 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 512]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2512]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma513 a r:Inference; r:gives { 2513 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 513}] + [ a r:Fact; r:gives {2000 log:repeat 513}] [ a r:Fact; r:gives {(513 2000) math:sum 2513}] - skolem:lemma1513 + skolem:lemma2512 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 513]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2513]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma514 a r:Inference; r:gives { 2514 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 514}] + [ a r:Fact; r:gives {2000 log:repeat 514}] [ a r:Fact; r:gives {(514 2000) math:sum 2514}] - skolem:lemma1514 + skolem:lemma2513 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 514]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2514]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma515 a r:Inference; r:gives { 2515 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 515}] + [ a r:Fact; r:gives {2000 log:repeat 515}] [ a r:Fact; r:gives {(515 2000) math:sum 2515}] - skolem:lemma1515 + skolem:lemma2514 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 515]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2515]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma516 a r:Inference; r:gives { 2516 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 516}] + [ a r:Fact; r:gives {2000 log:repeat 516}] [ a r:Fact; r:gives {(516 2000) math:sum 2516}] - skolem:lemma1516 + skolem:lemma2515 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 516]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2516]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma517 a r:Inference; r:gives { 2517 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 517}] + [ a r:Fact; r:gives {2000 log:repeat 517}] [ a r:Fact; r:gives {(517 2000) math:sum 2517}] - skolem:lemma1517 + skolem:lemma2516 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 517]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2517]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma518 a r:Inference; r:gives { 2518 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 518}] + [ a r:Fact; r:gives {2000 log:repeat 518}] [ a r:Fact; r:gives {(518 2000) math:sum 2518}] - skolem:lemma1518 + skolem:lemma2517 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 518]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2518]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma519 a r:Inference; r:gives { 2519 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 519}] + [ a r:Fact; r:gives {2000 log:repeat 519}] [ a r:Fact; r:gives {(519 2000) math:sum 2519}] - skolem:lemma1519 + skolem:lemma2518 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 519]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2519]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma520 a r:Inference; r:gives { 2520 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 520}] + [ a r:Fact; r:gives {2000 log:repeat 520}] [ a r:Fact; r:gives {(520 2000) math:sum 2520}] - skolem:lemma1520 + skolem:lemma2519 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 520]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2520]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma521 a r:Inference; r:gives { 2521 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 521}] + [ a r:Fact; r:gives {2000 log:repeat 521}] [ a r:Fact; r:gives {(521 2000) math:sum 2521}] - skolem:lemma1521 + skolem:lemma2520 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 521]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2521]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma522 a r:Inference; r:gives { 2522 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 522}] + [ a r:Fact; r:gives {2000 log:repeat 522}] [ a r:Fact; r:gives {(522 2000) math:sum 2522}] - skolem:lemma1522 + skolem:lemma2521 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 522]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2522]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma523 a r:Inference; r:gives { 2523 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 523}] + [ a r:Fact; r:gives {2000 log:repeat 523}] [ a r:Fact; r:gives {(523 2000) math:sum 2523}] - skolem:lemma1523 + skolem:lemma2522 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 523]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2523]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma524 a r:Inference; r:gives { 2524 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 524}] + [ a r:Fact; r:gives {2000 log:repeat 524}] [ a r:Fact; r:gives {(524 2000) math:sum 2524}] - skolem:lemma1524 + skolem:lemma2523 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 524]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2524]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma525 a r:Inference; r:gives { 2525 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 525}] + [ a r:Fact; r:gives {2000 log:repeat 525}] [ a r:Fact; r:gives {(525 2000) math:sum 2525}] - skolem:lemma1525 + skolem:lemma2524 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 525]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2525]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma526 a r:Inference; r:gives { 2526 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 526}] + [ a r:Fact; r:gives {2000 log:repeat 526}] [ a r:Fact; r:gives {(526 2000) math:sum 2526}] - skolem:lemma1526 + skolem:lemma2525 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 526]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2526]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma527 a r:Inference; r:gives { 2527 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 527}] + [ a r:Fact; r:gives {2000 log:repeat 527}] [ a r:Fact; r:gives {(527 2000) math:sum 2527}] - skolem:lemma1527 + skolem:lemma2526 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 527]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2527]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma528 a r:Inference; r:gives { 2528 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 528}] + [ a r:Fact; r:gives {2000 log:repeat 528}] [ a r:Fact; r:gives {(528 2000) math:sum 2528}] - skolem:lemma1528 + skolem:lemma2527 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 528]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2528]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma529 a r:Inference; r:gives { 2529 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 529}] + [ a r:Fact; r:gives {2000 log:repeat 529}] [ a r:Fact; r:gives {(529 2000) math:sum 2529}] - skolem:lemma1529 + skolem:lemma2528 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 529]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2529]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma530 a r:Inference; r:gives { 2530 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 530}] + [ a r:Fact; r:gives {2000 log:repeat 530}] [ a r:Fact; r:gives {(530 2000) math:sum 2530}] - skolem:lemma1530 + skolem:lemma2529 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 530]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2530]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma531 a r:Inference; r:gives { 2531 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 531}] + [ a r:Fact; r:gives {2000 log:repeat 531}] [ a r:Fact; r:gives {(531 2000) math:sum 2531}] - skolem:lemma1531 + skolem:lemma2530 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 531]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2531]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma532 a r:Inference; r:gives { 2532 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 532}] + [ a r:Fact; r:gives {2000 log:repeat 532}] [ a r:Fact; r:gives {(532 2000) math:sum 2532}] - skolem:lemma1532 + skolem:lemma2531 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 532]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2532]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma533 a r:Inference; r:gives { 2533 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 533}] + [ a r:Fact; r:gives {2000 log:repeat 533}] [ a r:Fact; r:gives {(533 2000) math:sum 2533}] - skolem:lemma1533 + skolem:lemma2532 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 533]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2533]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma534 a r:Inference; r:gives { 2534 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 534}] + [ a r:Fact; r:gives {2000 log:repeat 534}] [ a r:Fact; r:gives {(534 2000) math:sum 2534}] - skolem:lemma1534 + skolem:lemma2533 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 534]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2534]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma535 a r:Inference; r:gives { 2535 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 535}] + [ a r:Fact; r:gives {2000 log:repeat 535}] [ a r:Fact; r:gives {(535 2000) math:sum 2535}] - skolem:lemma1535 + skolem:lemma2534 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 535]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2535]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma536 a r:Inference; r:gives { 2536 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 536}] + [ a r:Fact; r:gives {2000 log:repeat 536}] [ a r:Fact; r:gives {(536 2000) math:sum 2536}] - skolem:lemma1536 + skolem:lemma2535 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 536]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2536]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma537 a r:Inference; r:gives { 2537 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 537}] + [ a r:Fact; r:gives {2000 log:repeat 537}] [ a r:Fact; r:gives {(537 2000) math:sum 2537}] - skolem:lemma1537 + skolem:lemma2536 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 537]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2537]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma538 a r:Inference; r:gives { 2538 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 538}] + [ a r:Fact; r:gives {2000 log:repeat 538}] [ a r:Fact; r:gives {(538 2000) math:sum 2538}] - skolem:lemma1538 + skolem:lemma2537 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 538]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2538]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma539 a r:Inference; r:gives { 2539 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 539}] + [ a r:Fact; r:gives {2000 log:repeat 539}] [ a r:Fact; r:gives {(539 2000) math:sum 2539}] - skolem:lemma1539 + skolem:lemma2538 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 539]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2539]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma540 a r:Inference; r:gives { 2540 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 540}] + [ a r:Fact; r:gives {2000 log:repeat 540}] [ a r:Fact; r:gives {(540 2000) math:sum 2540}] - skolem:lemma1540 + skolem:lemma2539 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 540]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2540]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma541 a r:Inference; r:gives { 2541 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 541}] + [ a r:Fact; r:gives {2000 log:repeat 541}] [ a r:Fact; r:gives {(541 2000) math:sum 2541}] - skolem:lemma1541 + skolem:lemma2540 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 541]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2541]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma542 a r:Inference; r:gives { 2542 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 542}] + [ a r:Fact; r:gives {2000 log:repeat 542}] [ a r:Fact; r:gives {(542 2000) math:sum 2542}] - skolem:lemma1542 + skolem:lemma2541 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 542]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2542]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma543 a r:Inference; r:gives { 2543 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 543}] + [ a r:Fact; r:gives {2000 log:repeat 543}] [ a r:Fact; r:gives {(543 2000) math:sum 2543}] - skolem:lemma1543 + skolem:lemma2542 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 543]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2543]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma544 a r:Inference; r:gives { 2544 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 544}] + [ a r:Fact; r:gives {2000 log:repeat 544}] [ a r:Fact; r:gives {(544 2000) math:sum 2544}] - skolem:lemma1544 + skolem:lemma2543 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 544]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2544]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma545 a r:Inference; r:gives { 2545 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 545}] + [ a r:Fact; r:gives {2000 log:repeat 545}] [ a r:Fact; r:gives {(545 2000) math:sum 2545}] - skolem:lemma1545 + skolem:lemma2544 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 545]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2545]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma546 a r:Inference; r:gives { 2546 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 546}] + [ a r:Fact; r:gives {2000 log:repeat 546}] [ a r:Fact; r:gives {(546 2000) math:sum 2546}] - skolem:lemma1546 + skolem:lemma2545 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 546]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2546]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma547 a r:Inference; r:gives { 2547 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 547}] + [ a r:Fact; r:gives {2000 log:repeat 547}] [ a r:Fact; r:gives {(547 2000) math:sum 2547}] - skolem:lemma1547 + skolem:lemma2546 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 547]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2547]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma548 a r:Inference; r:gives { 2548 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 548}] + [ a r:Fact; r:gives {2000 log:repeat 548}] [ a r:Fact; r:gives {(548 2000) math:sum 2548}] - skolem:lemma1548 + skolem:lemma2547 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 548]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2548]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma549 a r:Inference; r:gives { 2549 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 549}] + [ a r:Fact; r:gives {2000 log:repeat 549}] [ a r:Fact; r:gives {(549 2000) math:sum 2549}] - skolem:lemma1549 + skolem:lemma2548 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 549]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2549]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma550 a r:Inference; r:gives { 2550 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 550}] + [ a r:Fact; r:gives {2000 log:repeat 550}] [ a r:Fact; r:gives {(550 2000) math:sum 2550}] - skolem:lemma1550 + skolem:lemma2549 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 550]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2550]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma551 a r:Inference; r:gives { 2551 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 551}] + [ a r:Fact; r:gives {2000 log:repeat 551}] [ a r:Fact; r:gives {(551 2000) math:sum 2551}] - skolem:lemma1551 + skolem:lemma2550 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 551]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2551]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma552 a r:Inference; r:gives { 2552 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 552}] + [ a r:Fact; r:gives {2000 log:repeat 552}] [ a r:Fact; r:gives {(552 2000) math:sum 2552}] - skolem:lemma1552 + skolem:lemma2551 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 552]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2552]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma553 a r:Inference; r:gives { 2553 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 553}] + [ a r:Fact; r:gives {2000 log:repeat 553}] [ a r:Fact; r:gives {(553 2000) math:sum 2553}] - skolem:lemma1553 + skolem:lemma2552 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 553]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2553]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma554 a r:Inference; r:gives { 2554 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 554}] + [ a r:Fact; r:gives {2000 log:repeat 554}] [ a r:Fact; r:gives {(554 2000) math:sum 2554}] - skolem:lemma1554 + skolem:lemma2553 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 554]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2554]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma555 a r:Inference; r:gives { 2555 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 555}] + [ a r:Fact; r:gives {2000 log:repeat 555}] [ a r:Fact; r:gives {(555 2000) math:sum 2555}] - skolem:lemma1555 + skolem:lemma2554 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 555]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2555]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma556 a r:Inference; r:gives { 2556 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 556}] + [ a r:Fact; r:gives {2000 log:repeat 556}] [ a r:Fact; r:gives {(556 2000) math:sum 2556}] - skolem:lemma1556 + skolem:lemma2555 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 556]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2556]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma557 a r:Inference; r:gives { 2557 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 557}] + [ a r:Fact; r:gives {2000 log:repeat 557}] [ a r:Fact; r:gives {(557 2000) math:sum 2557}] - skolem:lemma1557 + skolem:lemma2556 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 557]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2557]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma558 a r:Inference; r:gives { 2558 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 558}] + [ a r:Fact; r:gives {2000 log:repeat 558}] [ a r:Fact; r:gives {(558 2000) math:sum 2558}] - skolem:lemma1558 + skolem:lemma2557 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 558]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2558]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma559 a r:Inference; r:gives { 2559 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 559}] + [ a r:Fact; r:gives {2000 log:repeat 559}] [ a r:Fact; r:gives {(559 2000) math:sum 2559}] - skolem:lemma1559 + skolem:lemma2558 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 559]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2559]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma560 a r:Inference; r:gives { 2560 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 560}] + [ a r:Fact; r:gives {2000 log:repeat 560}] [ a r:Fact; r:gives {(560 2000) math:sum 2560}] - skolem:lemma1560 + skolem:lemma2559 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 560]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2560]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma561 a r:Inference; r:gives { 2561 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 561}] + [ a r:Fact; r:gives {2000 log:repeat 561}] [ a r:Fact; r:gives {(561 2000) math:sum 2561}] - skolem:lemma1561 + skolem:lemma2560 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 561]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2561]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma562 a r:Inference; r:gives { 2562 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 562}] + [ a r:Fact; r:gives {2000 log:repeat 562}] [ a r:Fact; r:gives {(562 2000) math:sum 2562}] - skolem:lemma1562 + skolem:lemma2561 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 562]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2562]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma563 a r:Inference; r:gives { 2563 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 563}] + [ a r:Fact; r:gives {2000 log:repeat 563}] [ a r:Fact; r:gives {(563 2000) math:sum 2563}] - skolem:lemma1563 + skolem:lemma2562 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 563]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2563]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma564 a r:Inference; r:gives { 2564 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 564}] + [ a r:Fact; r:gives {2000 log:repeat 564}] [ a r:Fact; r:gives {(564 2000) math:sum 2564}] - skolem:lemma1564 + skolem:lemma2563 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 564]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2564]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma565 a r:Inference; r:gives { 2565 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 565}] + [ a r:Fact; r:gives {2000 log:repeat 565}] [ a r:Fact; r:gives {(565 2000) math:sum 2565}] - skolem:lemma1565 + skolem:lemma2564 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 565]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2565]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma566 a r:Inference; r:gives { 2566 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 566}] + [ a r:Fact; r:gives {2000 log:repeat 566}] [ a r:Fact; r:gives {(566 2000) math:sum 2566}] - skolem:lemma1566 + skolem:lemma2565 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 566]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2566]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma567 a r:Inference; r:gives { 2567 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 567}] + [ a r:Fact; r:gives {2000 log:repeat 567}] [ a r:Fact; r:gives {(567 2000) math:sum 2567}] - skolem:lemma1567 + skolem:lemma2566 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 567]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2567]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma568 a r:Inference; r:gives { 2568 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 568}] + [ a r:Fact; r:gives {2000 log:repeat 568}] [ a r:Fact; r:gives {(568 2000) math:sum 2568}] - skolem:lemma1568 + skolem:lemma2567 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 568]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2568]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma569 a r:Inference; r:gives { 2569 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 569}] + [ a r:Fact; r:gives {2000 log:repeat 569}] [ a r:Fact; r:gives {(569 2000) math:sum 2569}] - skolem:lemma1569 + skolem:lemma2568 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 569]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2569]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma570 a r:Inference; r:gives { 2570 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 570}] + [ a r:Fact; r:gives {2000 log:repeat 570}] [ a r:Fact; r:gives {(570 2000) math:sum 2570}] - skolem:lemma1570 + skolem:lemma2569 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 570]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2570]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma571 a r:Inference; r:gives { 2571 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 571}] + [ a r:Fact; r:gives {2000 log:repeat 571}] [ a r:Fact; r:gives {(571 2000) math:sum 2571}] - skolem:lemma1571 + skolem:lemma2570 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 571]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2571]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma572 a r:Inference; r:gives { 2572 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 572}] + [ a r:Fact; r:gives {2000 log:repeat 572}] [ a r:Fact; r:gives {(572 2000) math:sum 2572}] - skolem:lemma1572 + skolem:lemma2571 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 572]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2572]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma573 a r:Inference; r:gives { 2573 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 573}] + [ a r:Fact; r:gives {2000 log:repeat 573}] [ a r:Fact; r:gives {(573 2000) math:sum 2573}] - skolem:lemma1573 + skolem:lemma2572 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 573]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2573]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma574 a r:Inference; r:gives { 2574 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 574}] + [ a r:Fact; r:gives {2000 log:repeat 574}] [ a r:Fact; r:gives {(574 2000) math:sum 2574}] - skolem:lemma1574 + skolem:lemma2573 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 574]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2574]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma575 a r:Inference; r:gives { 2575 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 575}] + [ a r:Fact; r:gives {2000 log:repeat 575}] [ a r:Fact; r:gives {(575 2000) math:sum 2575}] - skolem:lemma1575 + skolem:lemma2574 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 575]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2575]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma576 a r:Inference; r:gives { 2576 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 576}] + [ a r:Fact; r:gives {2000 log:repeat 576}] [ a r:Fact; r:gives {(576 2000) math:sum 2576}] - skolem:lemma1576 + skolem:lemma2575 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 576]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2576]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma577 a r:Inference; r:gives { 2577 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 577}] + [ a r:Fact; r:gives {2000 log:repeat 577}] [ a r:Fact; r:gives {(577 2000) math:sum 2577}] - skolem:lemma1577 + skolem:lemma2576 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 577]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2577]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma578 a r:Inference; r:gives { 2578 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 578}] + [ a r:Fact; r:gives {2000 log:repeat 578}] [ a r:Fact; r:gives {(578 2000) math:sum 2578}] - skolem:lemma1578 + skolem:lemma2577 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 578]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2578]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma579 a r:Inference; r:gives { 2579 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 579}] + [ a r:Fact; r:gives {2000 log:repeat 579}] [ a r:Fact; r:gives {(579 2000) math:sum 2579}] - skolem:lemma1579 + skolem:lemma2578 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 579]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2579]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma580 a r:Inference; r:gives { 2580 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 580}] + [ a r:Fact; r:gives {2000 log:repeat 580}] [ a r:Fact; r:gives {(580 2000) math:sum 2580}] - skolem:lemma1580 + skolem:lemma2579 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 580]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2580]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma581 a r:Inference; r:gives { 2581 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 581}] + [ a r:Fact; r:gives {2000 log:repeat 581}] [ a r:Fact; r:gives {(581 2000) math:sum 2581}] - skolem:lemma1581 + skolem:lemma2580 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 581]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2581]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma582 a r:Inference; r:gives { 2582 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 582}] + [ a r:Fact; r:gives {2000 log:repeat 582}] [ a r:Fact; r:gives {(582 2000) math:sum 2582}] - skolem:lemma1582 + skolem:lemma2581 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 582]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2582]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma583 a r:Inference; r:gives { 2583 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 583}] + [ a r:Fact; r:gives {2000 log:repeat 583}] [ a r:Fact; r:gives {(583 2000) math:sum 2583}] - skolem:lemma1583 + skolem:lemma2582 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 583]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2583]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma584 a r:Inference; r:gives { 2584 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 584}] + [ a r:Fact; r:gives {2000 log:repeat 584}] [ a r:Fact; r:gives {(584 2000) math:sum 2584}] - skolem:lemma1584 + skolem:lemma2583 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 584]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2584]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma585 a r:Inference; r:gives { 2585 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 585}] + [ a r:Fact; r:gives {2000 log:repeat 585}] [ a r:Fact; r:gives {(585 2000) math:sum 2585}] - skolem:lemma1585 + skolem:lemma2584 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 585]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2585]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma586 a r:Inference; r:gives { 2586 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 586}] + [ a r:Fact; r:gives {2000 log:repeat 586}] [ a r:Fact; r:gives {(586 2000) math:sum 2586}] - skolem:lemma1586 + skolem:lemma2585 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 586]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2586]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma587 a r:Inference; r:gives { 2587 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 587}] + [ a r:Fact; r:gives {2000 log:repeat 587}] [ a r:Fact; r:gives {(587 2000) math:sum 2587}] - skolem:lemma1587 + skolem:lemma2586 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 587]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2587]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma588 a r:Inference; r:gives { 2588 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 588}] + [ a r:Fact; r:gives {2000 log:repeat 588}] [ a r:Fact; r:gives {(588 2000) math:sum 2588}] - skolem:lemma1588 + skolem:lemma2587 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 588]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2588]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma589 a r:Inference; r:gives { 2589 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 589}] + [ a r:Fact; r:gives {2000 log:repeat 589}] [ a r:Fact; r:gives {(589 2000) math:sum 2589}] - skolem:lemma1589 + skolem:lemma2588 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 589]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2589]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma590 a r:Inference; r:gives { 2590 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 590}] + [ a r:Fact; r:gives {2000 log:repeat 590}] [ a r:Fact; r:gives {(590 2000) math:sum 2590}] - skolem:lemma1590 + skolem:lemma2589 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 590]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2590]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma591 a r:Inference; r:gives { 2591 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 591}] + [ a r:Fact; r:gives {2000 log:repeat 591}] [ a r:Fact; r:gives {(591 2000) math:sum 2591}] - skolem:lemma1591 + skolem:lemma2590 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 591]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2591]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma592 a r:Inference; r:gives { 2592 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 592}] + [ a r:Fact; r:gives {2000 log:repeat 592}] [ a r:Fact; r:gives {(592 2000) math:sum 2592}] - skolem:lemma1592 + skolem:lemma2591 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 592]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2592]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma593 a r:Inference; r:gives { 2593 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 593}] + [ a r:Fact; r:gives {2000 log:repeat 593}] [ a r:Fact; r:gives {(593 2000) math:sum 2593}] - skolem:lemma1593 + skolem:lemma2592 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 593]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2593]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma594 a r:Inference; r:gives { 2594 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 594}] + [ a r:Fact; r:gives {2000 log:repeat 594}] [ a r:Fact; r:gives {(594 2000) math:sum 2594}] - skolem:lemma1594 + skolem:lemma2593 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 594]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2594]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma595 a r:Inference; r:gives { 2595 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 595}] + [ a r:Fact; r:gives {2000 log:repeat 595}] [ a r:Fact; r:gives {(595 2000) math:sum 2595}] - skolem:lemma1595 + skolem:lemma2594 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 595]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2595]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma596 a r:Inference; r:gives { 2596 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 596}] + [ a r:Fact; r:gives {2000 log:repeat 596}] [ a r:Fact; r:gives {(596 2000) math:sum 2596}] - skolem:lemma1596 + skolem:lemma2595 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 596]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2596]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma597 a r:Inference; r:gives { 2597 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 597}] + [ a r:Fact; r:gives {2000 log:repeat 597}] [ a r:Fact; r:gives {(597 2000) math:sum 2597}] - skolem:lemma1597 + skolem:lemma2596 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 597]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2597]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma598 a r:Inference; r:gives { 2598 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 598}] + [ a r:Fact; r:gives {2000 log:repeat 598}] [ a r:Fact; r:gives {(598 2000) math:sum 2598}] - skolem:lemma1598 + skolem:lemma2597 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 598]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2598]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma599 a r:Inference; r:gives { 2599 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 599}] + [ a r:Fact; r:gives {2000 log:repeat 599}] [ a r:Fact; r:gives {(599 2000) math:sum 2599}] - skolem:lemma1599 + skolem:lemma2598 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 599]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2599]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma600 a r:Inference; r:gives { 2600 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 600}] + [ a r:Fact; r:gives {2000 log:repeat 600}] [ a r:Fact; r:gives {(600 2000) math:sum 2600}] - skolem:lemma1600 + skolem:lemma2599 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 600]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2600]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma601 a r:Inference; r:gives { 2601 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 601}] + [ a r:Fact; r:gives {2000 log:repeat 601}] [ a r:Fact; r:gives {(601 2000) math:sum 2601}] - skolem:lemma1601 + skolem:lemma2600 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 601]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2601]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma602 a r:Inference; r:gives { 2602 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 602}] + [ a r:Fact; r:gives {2000 log:repeat 602}] [ a r:Fact; r:gives {(602 2000) math:sum 2602}] - skolem:lemma1602 + skolem:lemma2601 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 602]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2602]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma603 a r:Inference; r:gives { 2603 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 603}] + [ a r:Fact; r:gives {2000 log:repeat 603}] [ a r:Fact; r:gives {(603 2000) math:sum 2603}] - skolem:lemma1603 + skolem:lemma2602 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 603]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2603]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma604 a r:Inference; r:gives { 2604 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 604}] + [ a r:Fact; r:gives {2000 log:repeat 604}] [ a r:Fact; r:gives {(604 2000) math:sum 2604}] - skolem:lemma1604 + skolem:lemma2603 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 604]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2604]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma605 a r:Inference; r:gives { 2605 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 605}] + [ a r:Fact; r:gives {2000 log:repeat 605}] [ a r:Fact; r:gives {(605 2000) math:sum 2605}] - skolem:lemma1605 + skolem:lemma2604 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 605]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2605]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma606 a r:Inference; r:gives { 2606 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 606}] + [ a r:Fact; r:gives {2000 log:repeat 606}] [ a r:Fact; r:gives {(606 2000) math:sum 2606}] - skolem:lemma1606 + skolem:lemma2605 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 606]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2606]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma607 a r:Inference; r:gives { 2607 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 607}] + [ a r:Fact; r:gives {2000 log:repeat 607}] [ a r:Fact; r:gives {(607 2000) math:sum 2607}] - skolem:lemma1607 + skolem:lemma2606 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 607]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2607]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma608 a r:Inference; r:gives { 2608 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 608}] + [ a r:Fact; r:gives {2000 log:repeat 608}] [ a r:Fact; r:gives {(608 2000) math:sum 2608}] - skolem:lemma1608 + skolem:lemma2607 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 608]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2608]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma609 a r:Inference; r:gives { 2609 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 609}] + [ a r:Fact; r:gives {2000 log:repeat 609}] [ a r:Fact; r:gives {(609 2000) math:sum 2609}] - skolem:lemma1609 + skolem:lemma2608 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 609]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2609]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma610 a r:Inference; r:gives { 2610 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 610}] + [ a r:Fact; r:gives {2000 log:repeat 610}] [ a r:Fact; r:gives {(610 2000) math:sum 2610}] - skolem:lemma1610 + skolem:lemma2609 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 610]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2610]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma611 a r:Inference; r:gives { 2611 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 611}] + [ a r:Fact; r:gives {2000 log:repeat 611}] [ a r:Fact; r:gives {(611 2000) math:sum 2611}] - skolem:lemma1611 + skolem:lemma2610 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 611]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2611]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma612 a r:Inference; r:gives { 2612 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 612}] + [ a r:Fact; r:gives {2000 log:repeat 612}] [ a r:Fact; r:gives {(612 2000) math:sum 2612}] - skolem:lemma1612 + skolem:lemma2611 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 612]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2612]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma613 a r:Inference; r:gives { 2613 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 613}] + [ a r:Fact; r:gives {2000 log:repeat 613}] [ a r:Fact; r:gives {(613 2000) math:sum 2613}] - skolem:lemma1613 + skolem:lemma2612 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 613]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2613]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma614 a r:Inference; r:gives { 2614 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 614}] + [ a r:Fact; r:gives {2000 log:repeat 614}] [ a r:Fact; r:gives {(614 2000) math:sum 2614}] - skolem:lemma1614 + skolem:lemma2613 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 614]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2614]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma615 a r:Inference; r:gives { 2615 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 615}] + [ a r:Fact; r:gives {2000 log:repeat 615}] [ a r:Fact; r:gives {(615 2000) math:sum 2615}] - skolem:lemma1615 + skolem:lemma2614 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 615]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2615]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma616 a r:Inference; r:gives { 2616 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 616}] + [ a r:Fact; r:gives {2000 log:repeat 616}] [ a r:Fact; r:gives {(616 2000) math:sum 2616}] - skolem:lemma1616 + skolem:lemma2615 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 616]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2616]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma617 a r:Inference; r:gives { 2617 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 617}] + [ a r:Fact; r:gives {2000 log:repeat 617}] [ a r:Fact; r:gives {(617 2000) math:sum 2617}] - skolem:lemma1617 + skolem:lemma2616 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 617]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2617]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma618 a r:Inference; r:gives { 2618 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 618}] + [ a r:Fact; r:gives {2000 log:repeat 618}] [ a r:Fact; r:gives {(618 2000) math:sum 2618}] - skolem:lemma1618 + skolem:lemma2617 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 618]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2618]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma619 a r:Inference; r:gives { 2619 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 619}] + [ a r:Fact; r:gives {2000 log:repeat 619}] [ a r:Fact; r:gives {(619 2000) math:sum 2619}] - skolem:lemma1619 + skolem:lemma2618 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 619]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2619]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma620 a r:Inference; r:gives { 2620 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 620}] + [ a r:Fact; r:gives {2000 log:repeat 620}] [ a r:Fact; r:gives {(620 2000) math:sum 2620}] - skolem:lemma1620 + skolem:lemma2619 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 620]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2620]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma621 a r:Inference; r:gives { 2621 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 621}] + [ a r:Fact; r:gives {2000 log:repeat 621}] [ a r:Fact; r:gives {(621 2000) math:sum 2621}] - skolem:lemma1621 + skolem:lemma2620 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 621]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2621]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma622 a r:Inference; r:gives { 2622 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 622}] + [ a r:Fact; r:gives {2000 log:repeat 622}] [ a r:Fact; r:gives {(622 2000) math:sum 2622}] - skolem:lemma1622 + skolem:lemma2621 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 622]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2622]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma623 a r:Inference; r:gives { 2623 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 623}] + [ a r:Fact; r:gives {2000 log:repeat 623}] [ a r:Fact; r:gives {(623 2000) math:sum 2623}] - skolem:lemma1623 + skolem:lemma2622 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 623]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2623]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma624 a r:Inference; r:gives { 2624 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 624}] + [ a r:Fact; r:gives {2000 log:repeat 624}] [ a r:Fact; r:gives {(624 2000) math:sum 2624}] - skolem:lemma1624 + skolem:lemma2623 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 624]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2624]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma625 a r:Inference; r:gives { 2625 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 625}] + [ a r:Fact; r:gives {2000 log:repeat 625}] [ a r:Fact; r:gives {(625 2000) math:sum 2625}] - skolem:lemma1625 + skolem:lemma2624 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 625]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2625]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma626 a r:Inference; r:gives { 2626 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 626}] + [ a r:Fact; r:gives {2000 log:repeat 626}] [ a r:Fact; r:gives {(626 2000) math:sum 2626}] - skolem:lemma1626 + skolem:lemma2625 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 626]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2626]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma627 a r:Inference; r:gives { 2627 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 627}] + [ a r:Fact; r:gives {2000 log:repeat 627}] [ a r:Fact; r:gives {(627 2000) math:sum 2627}] - skolem:lemma1627 + skolem:lemma2626 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 627]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2627]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma628 a r:Inference; r:gives { 2628 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 628}] + [ a r:Fact; r:gives {2000 log:repeat 628}] [ a r:Fact; r:gives {(628 2000) math:sum 2628}] - skolem:lemma1628 + skolem:lemma2627 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 628]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2628]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma629 a r:Inference; r:gives { 2629 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 629}] + [ a r:Fact; r:gives {2000 log:repeat 629}] [ a r:Fact; r:gives {(629 2000) math:sum 2629}] - skolem:lemma1629 + skolem:lemma2628 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 629]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2629]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma630 a r:Inference; r:gives { 2630 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 630}] + [ a r:Fact; r:gives {2000 log:repeat 630}] [ a r:Fact; r:gives {(630 2000) math:sum 2630}] - skolem:lemma1630 + skolem:lemma2629 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 630]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2630]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma631 a r:Inference; r:gives { 2631 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 631}] + [ a r:Fact; r:gives {2000 log:repeat 631}] [ a r:Fact; r:gives {(631 2000) math:sum 2631}] - skolem:lemma1631 + skolem:lemma2630 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 631]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2631]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma632 a r:Inference; r:gives { 2632 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 632}] + [ a r:Fact; r:gives {2000 log:repeat 632}] [ a r:Fact; r:gives {(632 2000) math:sum 2632}] - skolem:lemma1632 + skolem:lemma2631 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 632]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2632]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma633 a r:Inference; r:gives { 2633 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 633}] + [ a r:Fact; r:gives {2000 log:repeat 633}] [ a r:Fact; r:gives {(633 2000) math:sum 2633}] - skolem:lemma1633 + skolem:lemma2632 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 633]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2633]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma634 a r:Inference; r:gives { 2634 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 634}] + [ a r:Fact; r:gives {2000 log:repeat 634}] [ a r:Fact; r:gives {(634 2000) math:sum 2634}] - skolem:lemma1634 + skolem:lemma2633 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 634]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2634]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma635 a r:Inference; r:gives { 2635 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 635}] + [ a r:Fact; r:gives {2000 log:repeat 635}] [ a r:Fact; r:gives {(635 2000) math:sum 2635}] - skolem:lemma1635 + skolem:lemma2634 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 635]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2635]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma636 a r:Inference; r:gives { 2636 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 636}] + [ a r:Fact; r:gives {2000 log:repeat 636}] [ a r:Fact; r:gives {(636 2000) math:sum 2636}] - skolem:lemma1636 + skolem:lemma2635 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 636]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2636]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma637 a r:Inference; r:gives { 2637 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 637}] + [ a r:Fact; r:gives {2000 log:repeat 637}] [ a r:Fact; r:gives {(637 2000) math:sum 2637}] - skolem:lemma1637 + skolem:lemma2636 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 637]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2637]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma638 a r:Inference; r:gives { 2638 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 638}] + [ a r:Fact; r:gives {2000 log:repeat 638}] [ a r:Fact; r:gives {(638 2000) math:sum 2638}] - skolem:lemma1638 + skolem:lemma2637 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 638]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2638]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma639 a r:Inference; r:gives { 2639 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 639}] + [ a r:Fact; r:gives {2000 log:repeat 639}] [ a r:Fact; r:gives {(639 2000) math:sum 2639}] - skolem:lemma1639 + skolem:lemma2638 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 639]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2639]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma640 a r:Inference; r:gives { 2640 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 640}] + [ a r:Fact; r:gives {2000 log:repeat 640}] [ a r:Fact; r:gives {(640 2000) math:sum 2640}] - skolem:lemma1640 + skolem:lemma2639 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 640]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2640]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma641 a r:Inference; r:gives { 2641 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 641}] + [ a r:Fact; r:gives {2000 log:repeat 641}] [ a r:Fact; r:gives {(641 2000) math:sum 2641}] - skolem:lemma1641 + skolem:lemma2640 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 641]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2641]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma642 a r:Inference; r:gives { 2642 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 642}] + [ a r:Fact; r:gives {2000 log:repeat 642}] [ a r:Fact; r:gives {(642 2000) math:sum 2642}] - skolem:lemma1642 + skolem:lemma2641 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 642]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2642]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma643 a r:Inference; r:gives { 2643 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 643}] + [ a r:Fact; r:gives {2000 log:repeat 643}] [ a r:Fact; r:gives {(643 2000) math:sum 2643}] - skolem:lemma1643 + skolem:lemma2642 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 643]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2643]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma644 a r:Inference; r:gives { 2644 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 644}] + [ a r:Fact; r:gives {2000 log:repeat 644}] [ a r:Fact; r:gives {(644 2000) math:sum 2644}] - skolem:lemma1644 + skolem:lemma2643 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 644]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2644]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma645 a r:Inference; r:gives { 2645 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 645}] + [ a r:Fact; r:gives {2000 log:repeat 645}] [ a r:Fact; r:gives {(645 2000) math:sum 2645}] - skolem:lemma1645 + skolem:lemma2644 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 645]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2645]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma646 a r:Inference; r:gives { 2646 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 646}] + [ a r:Fact; r:gives {2000 log:repeat 646}] [ a r:Fact; r:gives {(646 2000) math:sum 2646}] - skolem:lemma1646 + skolem:lemma2645 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 646]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2646]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma647 a r:Inference; r:gives { 2647 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 647}] + [ a r:Fact; r:gives {2000 log:repeat 647}] [ a r:Fact; r:gives {(647 2000) math:sum 2647}] - skolem:lemma1647 + skolem:lemma2646 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 647]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2647]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma648 a r:Inference; r:gives { 2648 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 648}] + [ a r:Fact; r:gives {2000 log:repeat 648}] [ a r:Fact; r:gives {(648 2000) math:sum 2648}] - skolem:lemma1648 + skolem:lemma2647 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 648]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2648]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma649 a r:Inference; r:gives { 2649 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 649}] + [ a r:Fact; r:gives {2000 log:repeat 649}] [ a r:Fact; r:gives {(649 2000) math:sum 2649}] - skolem:lemma1649 + skolem:lemma2648 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 649]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2649]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma650 a r:Inference; r:gives { 2650 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 650}] + [ a r:Fact; r:gives {2000 log:repeat 650}] [ a r:Fact; r:gives {(650 2000) math:sum 2650}] - skolem:lemma1650 + skolem:lemma2649 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 650]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2650]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma651 a r:Inference; r:gives { 2651 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 651}] + [ a r:Fact; r:gives {2000 log:repeat 651}] [ a r:Fact; r:gives {(651 2000) math:sum 2651}] - skolem:lemma1651 + skolem:lemma2650 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 651]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2651]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma652 a r:Inference; r:gives { 2652 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 652}] + [ a r:Fact; r:gives {2000 log:repeat 652}] [ a r:Fact; r:gives {(652 2000) math:sum 2652}] - skolem:lemma1652 + skolem:lemma2651 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 652]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2652]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma653 a r:Inference; r:gives { 2653 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 653}] + [ a r:Fact; r:gives {2000 log:repeat 653}] [ a r:Fact; r:gives {(653 2000) math:sum 2653}] - skolem:lemma1653 + skolem:lemma2652 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 653]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2653]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma654 a r:Inference; r:gives { 2654 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 654}] + [ a r:Fact; r:gives {2000 log:repeat 654}] [ a r:Fact; r:gives {(654 2000) math:sum 2654}] - skolem:lemma1654 + skolem:lemma2653 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 654]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2654]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma655 a r:Inference; r:gives { 2655 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 655}] + [ a r:Fact; r:gives {2000 log:repeat 655}] [ a r:Fact; r:gives {(655 2000) math:sum 2655}] - skolem:lemma1655 + skolem:lemma2654 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 655]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2655]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma656 a r:Inference; r:gives { 2656 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 656}] + [ a r:Fact; r:gives {2000 log:repeat 656}] [ a r:Fact; r:gives {(656 2000) math:sum 2656}] - skolem:lemma1656 + skolem:lemma2655 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 656]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2656]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma657 a r:Inference; r:gives { 2657 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 657}] + [ a r:Fact; r:gives {2000 log:repeat 657}] [ a r:Fact; r:gives {(657 2000) math:sum 2657}] - skolem:lemma1657 + skolem:lemma2656 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 657]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2657]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma658 a r:Inference; r:gives { 2658 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 658}] + [ a r:Fact; r:gives {2000 log:repeat 658}] [ a r:Fact; r:gives {(658 2000) math:sum 2658}] - skolem:lemma1658 + skolem:lemma2657 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 658]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2658]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma659 a r:Inference; r:gives { 2659 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 659}] + [ a r:Fact; r:gives {2000 log:repeat 659}] [ a r:Fact; r:gives {(659 2000) math:sum 2659}] - skolem:lemma1659 + skolem:lemma2658 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 659]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2659]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma660 a r:Inference; r:gives { 2660 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 660}] + [ a r:Fact; r:gives {2000 log:repeat 660}] [ a r:Fact; r:gives {(660 2000) math:sum 2660}] - skolem:lemma1660 + skolem:lemma2659 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 660]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2660]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma661 a r:Inference; r:gives { 2661 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 661}] + [ a r:Fact; r:gives {2000 log:repeat 661}] [ a r:Fact; r:gives {(661 2000) math:sum 2661}] - skolem:lemma1661 + skolem:lemma2660 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 661]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2661]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma662 a r:Inference; r:gives { 2662 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 662}] + [ a r:Fact; r:gives {2000 log:repeat 662}] [ a r:Fact; r:gives {(662 2000) math:sum 2662}] - skolem:lemma1662 + skolem:lemma2661 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 662]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2662]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma663 a r:Inference; r:gives { 2663 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 663}] + [ a r:Fact; r:gives {2000 log:repeat 663}] [ a r:Fact; r:gives {(663 2000) math:sum 2663}] - skolem:lemma1663 + skolem:lemma2662 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 663]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2663]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma664 a r:Inference; r:gives { 2664 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 664}] + [ a r:Fact; r:gives {2000 log:repeat 664}] [ a r:Fact; r:gives {(664 2000) math:sum 2664}] - skolem:lemma1664 + skolem:lemma2663 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 664]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2664]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma665 a r:Inference; r:gives { 2665 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 665}] + [ a r:Fact; r:gives {2000 log:repeat 665}] [ a r:Fact; r:gives {(665 2000) math:sum 2665}] - skolem:lemma1665 + skolem:lemma2664 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 665]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2665]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma666 a r:Inference; r:gives { 2666 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 666}] + [ a r:Fact; r:gives {2000 log:repeat 666}] [ a r:Fact; r:gives {(666 2000) math:sum 2666}] - skolem:lemma1666 + skolem:lemma2665 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 666]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2666]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma667 a r:Inference; r:gives { 2667 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 667}] + [ a r:Fact; r:gives {2000 log:repeat 667}] [ a r:Fact; r:gives {(667 2000) math:sum 2667}] - skolem:lemma1667 + skolem:lemma2666 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 667]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2667]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma668 a r:Inference; r:gives { 2668 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 668}] + [ a r:Fact; r:gives {2000 log:repeat 668}] [ a r:Fact; r:gives {(668 2000) math:sum 2668}] - skolem:lemma1668 + skolem:lemma2667 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 668]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2668]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma669 a r:Inference; r:gives { 2669 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 669}] + [ a r:Fact; r:gives {2000 log:repeat 669}] [ a r:Fact; r:gives {(669 2000) math:sum 2669}] - skolem:lemma1669 + skolem:lemma2668 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 669]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2669]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma670 a r:Inference; r:gives { 2670 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 670}] + [ a r:Fact; r:gives {2000 log:repeat 670}] [ a r:Fact; r:gives {(670 2000) math:sum 2670}] - skolem:lemma1670 + skolem:lemma2669 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 670]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2670]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma671 a r:Inference; r:gives { 2671 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 671}] + [ a r:Fact; r:gives {2000 log:repeat 671}] [ a r:Fact; r:gives {(671 2000) math:sum 2671}] - skolem:lemma1671 + skolem:lemma2670 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 671]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2671]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma672 a r:Inference; r:gives { 2672 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 672}] + [ a r:Fact; r:gives {2000 log:repeat 672}] [ a r:Fact; r:gives {(672 2000) math:sum 2672}] - skolem:lemma1672 + skolem:lemma2671 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 672]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2672]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma673 a r:Inference; r:gives { 2673 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 673}] + [ a r:Fact; r:gives {2000 log:repeat 673}] [ a r:Fact; r:gives {(673 2000) math:sum 2673}] - skolem:lemma1673 + skolem:lemma2672 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 673]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2673]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma674 a r:Inference; r:gives { 2674 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 674}] + [ a r:Fact; r:gives {2000 log:repeat 674}] [ a r:Fact; r:gives {(674 2000) math:sum 2674}] - skolem:lemma1674 + skolem:lemma2673 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 674]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2674]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma675 a r:Inference; r:gives { 2675 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 675}] + [ a r:Fact; r:gives {2000 log:repeat 675}] [ a r:Fact; r:gives {(675 2000) math:sum 2675}] - skolem:lemma1675 + skolem:lemma2674 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 675]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2675]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma676 a r:Inference; r:gives { 2676 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 676}] + [ a r:Fact; r:gives {2000 log:repeat 676}] [ a r:Fact; r:gives {(676 2000) math:sum 2676}] - skolem:lemma1676 + skolem:lemma2675 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 676]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2676]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma677 a r:Inference; r:gives { 2677 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 677}] + [ a r:Fact; r:gives {2000 log:repeat 677}] [ a r:Fact; r:gives {(677 2000) math:sum 2677}] - skolem:lemma1677 + skolem:lemma2676 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 677]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2677]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma678 a r:Inference; r:gives { 2678 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 678}] + [ a r:Fact; r:gives {2000 log:repeat 678}] [ a r:Fact; r:gives {(678 2000) math:sum 2678}] - skolem:lemma1678 + skolem:lemma2677 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 678]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2678]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma679 a r:Inference; r:gives { 2679 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 679}] + [ a r:Fact; r:gives {2000 log:repeat 679}] [ a r:Fact; r:gives {(679 2000) math:sum 2679}] - skolem:lemma1679 + skolem:lemma2678 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 679]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2679]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma680 a r:Inference; r:gives { 2680 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 680}] + [ a r:Fact; r:gives {2000 log:repeat 680}] [ a r:Fact; r:gives {(680 2000) math:sum 2680}] - skolem:lemma1680 + skolem:lemma2679 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 680]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2680]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma681 a r:Inference; r:gives { 2681 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 681}] + [ a r:Fact; r:gives {2000 log:repeat 681}] [ a r:Fact; r:gives {(681 2000) math:sum 2681}] - skolem:lemma1681 + skolem:lemma2680 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 681]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2681]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma682 a r:Inference; r:gives { 2682 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 682}] + [ a r:Fact; r:gives {2000 log:repeat 682}] [ a r:Fact; r:gives {(682 2000) math:sum 2682}] - skolem:lemma1682 + skolem:lemma2681 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 682]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2682]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma683 a r:Inference; r:gives { 2683 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 683}] + [ a r:Fact; r:gives {2000 log:repeat 683}] [ a r:Fact; r:gives {(683 2000) math:sum 2683}] - skolem:lemma1683 + skolem:lemma2682 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 683]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2683]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma684 a r:Inference; r:gives { 2684 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 684}] + [ a r:Fact; r:gives {2000 log:repeat 684}] [ a r:Fact; r:gives {(684 2000) math:sum 2684}] - skolem:lemma1684 + skolem:lemma2683 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 684]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2684]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma685 a r:Inference; r:gives { 2685 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 685}] + [ a r:Fact; r:gives {2000 log:repeat 685}] [ a r:Fact; r:gives {(685 2000) math:sum 2685}] - skolem:lemma1685 + skolem:lemma2684 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 685]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2685]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma686 a r:Inference; r:gives { 2686 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 686}] + [ a r:Fact; r:gives {2000 log:repeat 686}] [ a r:Fact; r:gives {(686 2000) math:sum 2686}] - skolem:lemma1686 + skolem:lemma2685 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 686]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2686]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma687 a r:Inference; r:gives { 2687 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 687}] + [ a r:Fact; r:gives {2000 log:repeat 687}] [ a r:Fact; r:gives {(687 2000) math:sum 2687}] - skolem:lemma1687 + skolem:lemma2686 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 687]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2687]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma688 a r:Inference; r:gives { 2688 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 688}] + [ a r:Fact; r:gives {2000 log:repeat 688}] [ a r:Fact; r:gives {(688 2000) math:sum 2688}] - skolem:lemma1688 + skolem:lemma2687 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 688]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2688]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma689 a r:Inference; r:gives { 2689 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 689}] + [ a r:Fact; r:gives {2000 log:repeat 689}] [ a r:Fact; r:gives {(689 2000) math:sum 2689}] - skolem:lemma1689 + skolem:lemma2688 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 689]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2689]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma690 a r:Inference; r:gives { 2690 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 690}] + [ a r:Fact; r:gives {2000 log:repeat 690}] [ a r:Fact; r:gives {(690 2000) math:sum 2690}] - skolem:lemma1690 + skolem:lemma2689 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 690]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2690]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma691 a r:Inference; r:gives { 2691 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 691}] + [ a r:Fact; r:gives {2000 log:repeat 691}] [ a r:Fact; r:gives {(691 2000) math:sum 2691}] - skolem:lemma1691 + skolem:lemma2690 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 691]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2691]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma692 a r:Inference; r:gives { 2692 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 692}] + [ a r:Fact; r:gives {2000 log:repeat 692}] [ a r:Fact; r:gives {(692 2000) math:sum 2692}] - skolem:lemma1692 + skolem:lemma2691 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 692]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2692]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma693 a r:Inference; r:gives { 2693 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 693}] + [ a r:Fact; r:gives {2000 log:repeat 693}] [ a r:Fact; r:gives {(693 2000) math:sum 2693}] - skolem:lemma1693 + skolem:lemma2692 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 693]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2693]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma694 a r:Inference; r:gives { 2694 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 694}] + [ a r:Fact; r:gives {2000 log:repeat 694}] [ a r:Fact; r:gives {(694 2000) math:sum 2694}] - skolem:lemma1694 + skolem:lemma2693 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 694]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2694]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma695 a r:Inference; r:gives { 2695 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 695}] + [ a r:Fact; r:gives {2000 log:repeat 695}] [ a r:Fact; r:gives {(695 2000) math:sum 2695}] - skolem:lemma1695 + skolem:lemma2694 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 695]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2695]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma696 a r:Inference; r:gives { 2696 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 696}] + [ a r:Fact; r:gives {2000 log:repeat 696}] [ a r:Fact; r:gives {(696 2000) math:sum 2696}] - skolem:lemma1696 + skolem:lemma2695 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 696]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2696]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma697 a r:Inference; r:gives { 2697 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 697}] + [ a r:Fact; r:gives {2000 log:repeat 697}] [ a r:Fact; r:gives {(697 2000) math:sum 2697}] - skolem:lemma1697 + skolem:lemma2696 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 697]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2697]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma698 a r:Inference; r:gives { 2698 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 698}] + [ a r:Fact; r:gives {2000 log:repeat 698}] [ a r:Fact; r:gives {(698 2000) math:sum 2698}] - skolem:lemma1698 + skolem:lemma2697 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 698]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2698]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma699 a r:Inference; r:gives { 2699 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 699}] + [ a r:Fact; r:gives {2000 log:repeat 699}] [ a r:Fact; r:gives {(699 2000) math:sum 2699}] - skolem:lemma1699 + skolem:lemma2698 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 699]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2699]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma700 a r:Inference; r:gives { 2700 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 700}] + [ a r:Fact; r:gives {2000 log:repeat 700}] [ a r:Fact; r:gives {(700 2000) math:sum 2700}] - skolem:lemma1700 + skolem:lemma2699 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 700]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2700]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma701 a r:Inference; r:gives { 2701 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 701}] + [ a r:Fact; r:gives {2000 log:repeat 701}] [ a r:Fact; r:gives {(701 2000) math:sum 2701}] - skolem:lemma1701 + skolem:lemma2700 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 701]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2701]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma702 a r:Inference; r:gives { 2702 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 702}] + [ a r:Fact; r:gives {2000 log:repeat 702}] [ a r:Fact; r:gives {(702 2000) math:sum 2702}] - skolem:lemma1702 + skolem:lemma2701 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 702]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2702]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma703 a r:Inference; r:gives { 2703 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 703}] + [ a r:Fact; r:gives {2000 log:repeat 703}] [ a r:Fact; r:gives {(703 2000) math:sum 2703}] - skolem:lemma1703 + skolem:lemma2702 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 703]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2703]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma704 a r:Inference; r:gives { 2704 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 704}] + [ a r:Fact; r:gives {2000 log:repeat 704}] [ a r:Fact; r:gives {(704 2000) math:sum 2704}] - skolem:lemma1704 + skolem:lemma2703 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 704]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2704]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma705 a r:Inference; r:gives { 2705 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 705}] + [ a r:Fact; r:gives {2000 log:repeat 705}] [ a r:Fact; r:gives {(705 2000) math:sum 2705}] - skolem:lemma1705 + skolem:lemma2704 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 705]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2705]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma706 a r:Inference; r:gives { 2706 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 706}] + [ a r:Fact; r:gives {2000 log:repeat 706}] [ a r:Fact; r:gives {(706 2000) math:sum 2706}] - skolem:lemma1706 + skolem:lemma2705 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 706]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2706]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma707 a r:Inference; r:gives { 2707 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 707}] + [ a r:Fact; r:gives {2000 log:repeat 707}] [ a r:Fact; r:gives {(707 2000) math:sum 2707}] - skolem:lemma1707 + skolem:lemma2706 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 707]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2707]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma708 a r:Inference; r:gives { 2708 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 708}] + [ a r:Fact; r:gives {2000 log:repeat 708}] [ a r:Fact; r:gives {(708 2000) math:sum 2708}] - skolem:lemma1708 + skolem:lemma2707 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 708]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2708]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma709 a r:Inference; r:gives { 2709 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 709}] + [ a r:Fact; r:gives {2000 log:repeat 709}] [ a r:Fact; r:gives {(709 2000) math:sum 2709}] - skolem:lemma1709 + skolem:lemma2708 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 709]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2709]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma710 a r:Inference; r:gives { 2710 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 710}] + [ a r:Fact; r:gives {2000 log:repeat 710}] [ a r:Fact; r:gives {(710 2000) math:sum 2710}] - skolem:lemma1710 + skolem:lemma2709 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 710]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2710]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma711 a r:Inference; r:gives { 2711 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 711}] + [ a r:Fact; r:gives {2000 log:repeat 711}] [ a r:Fact; r:gives {(711 2000) math:sum 2711}] - skolem:lemma1711 + skolem:lemma2710 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 711]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2711]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma712 a r:Inference; r:gives { 2712 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 712}] + [ a r:Fact; r:gives {2000 log:repeat 712}] [ a r:Fact; r:gives {(712 2000) math:sum 2712}] - skolem:lemma1712 + skolem:lemma2711 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 712]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2712]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma713 a r:Inference; r:gives { 2713 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 713}] + [ a r:Fact; r:gives {2000 log:repeat 713}] [ a r:Fact; r:gives {(713 2000) math:sum 2713}] - skolem:lemma1713 + skolem:lemma2712 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 713]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2713]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma714 a r:Inference; r:gives { 2714 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 714}] + [ a r:Fact; r:gives {2000 log:repeat 714}] [ a r:Fact; r:gives {(714 2000) math:sum 2714}] - skolem:lemma1714 + skolem:lemma2713 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 714]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2714]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma715 a r:Inference; r:gives { 2715 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 715}] + [ a r:Fact; r:gives {2000 log:repeat 715}] [ a r:Fact; r:gives {(715 2000) math:sum 2715}] - skolem:lemma1715 + skolem:lemma2714 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 715]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2715]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma716 a r:Inference; r:gives { 2716 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 716}] + [ a r:Fact; r:gives {2000 log:repeat 716}] [ a r:Fact; r:gives {(716 2000) math:sum 2716}] - skolem:lemma1716 + skolem:lemma2715 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 716]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2716]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma717 a r:Inference; r:gives { 2717 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 717}] + [ a r:Fact; r:gives {2000 log:repeat 717}] [ a r:Fact; r:gives {(717 2000) math:sum 2717}] - skolem:lemma1717 + skolem:lemma2716 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 717]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2717]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma718 a r:Inference; r:gives { 2718 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 718}] + [ a r:Fact; r:gives {2000 log:repeat 718}] [ a r:Fact; r:gives {(718 2000) math:sum 2718}] - skolem:lemma1718 + skolem:lemma2717 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 718]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2718]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma719 a r:Inference; r:gives { 2719 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 719}] + [ a r:Fact; r:gives {2000 log:repeat 719}] [ a r:Fact; r:gives {(719 2000) math:sum 2719}] - skolem:lemma1719 + skolem:lemma2718 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 719]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2719]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma720 a r:Inference; r:gives { 2720 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 720}] + [ a r:Fact; r:gives {2000 log:repeat 720}] [ a r:Fact; r:gives {(720 2000) math:sum 2720}] - skolem:lemma1720 + skolem:lemma2719 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 720]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2720]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma721 a r:Inference; r:gives { 2721 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 721}] + [ a r:Fact; r:gives {2000 log:repeat 721}] [ a r:Fact; r:gives {(721 2000) math:sum 2721}] - skolem:lemma1721 + skolem:lemma2720 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 721]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2721]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma722 a r:Inference; r:gives { 2722 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 722}] + [ a r:Fact; r:gives {2000 log:repeat 722}] [ a r:Fact; r:gives {(722 2000) math:sum 2722}] - skolem:lemma1722 + skolem:lemma2721 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 722]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2722]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma723 a r:Inference; r:gives { 2723 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 723}] + [ a r:Fact; r:gives {2000 log:repeat 723}] [ a r:Fact; r:gives {(723 2000) math:sum 2723}] - skolem:lemma1723 + skolem:lemma2722 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 723]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2723]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma724 a r:Inference; r:gives { 2724 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 724}] + [ a r:Fact; r:gives {2000 log:repeat 724}] [ a r:Fact; r:gives {(724 2000) math:sum 2724}] - skolem:lemma1724 + skolem:lemma2723 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 724]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2724]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma725 a r:Inference; r:gives { 2725 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 725}] + [ a r:Fact; r:gives {2000 log:repeat 725}] [ a r:Fact; r:gives {(725 2000) math:sum 2725}] - skolem:lemma1725 + skolem:lemma2724 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 725]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2725]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma726 a r:Inference; r:gives { 2726 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 726}] + [ a r:Fact; r:gives {2000 log:repeat 726}] [ a r:Fact; r:gives {(726 2000) math:sum 2726}] - skolem:lemma1726 + skolem:lemma2725 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 726]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2726]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma727 a r:Inference; r:gives { 2727 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 727}] + [ a r:Fact; r:gives {2000 log:repeat 727}] [ a r:Fact; r:gives {(727 2000) math:sum 2727}] - skolem:lemma1727 + skolem:lemma2726 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 727]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2727]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma728 a r:Inference; r:gives { 2728 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 728}] + [ a r:Fact; r:gives {2000 log:repeat 728}] [ a r:Fact; r:gives {(728 2000) math:sum 2728}] - skolem:lemma1728 + skolem:lemma2727 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 728]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2728]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma729 a r:Inference; r:gives { 2729 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 729}] + [ a r:Fact; r:gives {2000 log:repeat 729}] [ a r:Fact; r:gives {(729 2000) math:sum 2729}] - skolem:lemma1729 + skolem:lemma2728 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 729]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2729]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma730 a r:Inference; r:gives { 2730 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 730}] + [ a r:Fact; r:gives {2000 log:repeat 730}] [ a r:Fact; r:gives {(730 2000) math:sum 2730}] - skolem:lemma1730 + skolem:lemma2729 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 730]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2730]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma731 a r:Inference; r:gives { 2731 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 731}] + [ a r:Fact; r:gives {2000 log:repeat 731}] [ a r:Fact; r:gives {(731 2000) math:sum 2731}] - skolem:lemma1731 + skolem:lemma2730 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 731]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2731]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma732 a r:Inference; r:gives { 2732 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 732}] + [ a r:Fact; r:gives {2000 log:repeat 732}] [ a r:Fact; r:gives {(732 2000) math:sum 2732}] - skolem:lemma1732 + skolem:lemma2731 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 732]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2732]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma733 a r:Inference; r:gives { 2733 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 733}] + [ a r:Fact; r:gives {2000 log:repeat 733}] [ a r:Fact; r:gives {(733 2000) math:sum 2733}] - skolem:lemma1733 + skolem:lemma2732 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 733]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2733]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma734 a r:Inference; r:gives { 2734 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 734}] + [ a r:Fact; r:gives {2000 log:repeat 734}] [ a r:Fact; r:gives {(734 2000) math:sum 2734}] - skolem:lemma1734 + skolem:lemma2733 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 734]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2734]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma735 a r:Inference; r:gives { 2735 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 735}] + [ a r:Fact; r:gives {2000 log:repeat 735}] [ a r:Fact; r:gives {(735 2000) math:sum 2735}] - skolem:lemma1735 + skolem:lemma2734 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 735]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2735]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma736 a r:Inference; r:gives { 2736 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 736}] + [ a r:Fact; r:gives {2000 log:repeat 736}] [ a r:Fact; r:gives {(736 2000) math:sum 2736}] - skolem:lemma1736 + skolem:lemma2735 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 736]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2736]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma737 a r:Inference; r:gives { 2737 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 737}] + [ a r:Fact; r:gives {2000 log:repeat 737}] [ a r:Fact; r:gives {(737 2000) math:sum 2737}] - skolem:lemma1737 + skolem:lemma2736 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 737]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2737]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma738 a r:Inference; r:gives { 2738 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 738}] + [ a r:Fact; r:gives {2000 log:repeat 738}] [ a r:Fact; r:gives {(738 2000) math:sum 2738}] - skolem:lemma1738 + skolem:lemma2737 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 738]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2738]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma739 a r:Inference; r:gives { 2739 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 739}] + [ a r:Fact; r:gives {2000 log:repeat 739}] [ a r:Fact; r:gives {(739 2000) math:sum 2739}] - skolem:lemma1739 + skolem:lemma2738 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 739]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2739]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma740 a r:Inference; r:gives { 2740 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 740}] + [ a r:Fact; r:gives {2000 log:repeat 740}] [ a r:Fact; r:gives {(740 2000) math:sum 2740}] - skolem:lemma1740 + skolem:lemma2739 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 740]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2740]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma741 a r:Inference; r:gives { 2741 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 741}] + [ a r:Fact; r:gives {2000 log:repeat 741}] [ a r:Fact; r:gives {(741 2000) math:sum 2741}] - skolem:lemma1741 + skolem:lemma2740 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 741]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2741]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma742 a r:Inference; r:gives { 2742 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 742}] + [ a r:Fact; r:gives {2000 log:repeat 742}] [ a r:Fact; r:gives {(742 2000) math:sum 2742}] - skolem:lemma1742 + skolem:lemma2741 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 742]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2742]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma743 a r:Inference; r:gives { 2743 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 743}] + [ a r:Fact; r:gives {2000 log:repeat 743}] [ a r:Fact; r:gives {(743 2000) math:sum 2743}] - skolem:lemma1743 + skolem:lemma2742 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 743]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2743]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma744 a r:Inference; r:gives { 2744 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 744}] + [ a r:Fact; r:gives {2000 log:repeat 744}] [ a r:Fact; r:gives {(744 2000) math:sum 2744}] - skolem:lemma1744 + skolem:lemma2743 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 744]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2744]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma745 a r:Inference; r:gives { 2745 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 745}] + [ a r:Fact; r:gives {2000 log:repeat 745}] [ a r:Fact; r:gives {(745 2000) math:sum 2745}] - skolem:lemma1745 + skolem:lemma2744 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 745]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2745]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma746 a r:Inference; r:gives { 2746 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 746}] + [ a r:Fact; r:gives {2000 log:repeat 746}] [ a r:Fact; r:gives {(746 2000) math:sum 2746}] - skolem:lemma1746 + skolem:lemma2745 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 746]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2746]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma747 a r:Inference; r:gives { 2747 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 747}] + [ a r:Fact; r:gives {2000 log:repeat 747}] [ a r:Fact; r:gives {(747 2000) math:sum 2747}] - skolem:lemma1747 + skolem:lemma2746 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 747]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2747]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma748 a r:Inference; r:gives { 2748 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 748}] + [ a r:Fact; r:gives {2000 log:repeat 748}] [ a r:Fact; r:gives {(748 2000) math:sum 2748}] - skolem:lemma1748 + skolem:lemma2747 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 748]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2748]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma749 a r:Inference; r:gives { 2749 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 749}] + [ a r:Fact; r:gives {2000 log:repeat 749}] [ a r:Fact; r:gives {(749 2000) math:sum 2749}] - skolem:lemma1749 + skolem:lemma2748 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 749]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2749]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma750 a r:Inference; r:gives { 2750 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 750}] + [ a r:Fact; r:gives {2000 log:repeat 750}] [ a r:Fact; r:gives {(750 2000) math:sum 2750}] - skolem:lemma1750 + skolem:lemma2749 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 750]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2750]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma751 a r:Inference; r:gives { 2751 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 751}] + [ a r:Fact; r:gives {2000 log:repeat 751}] [ a r:Fact; r:gives {(751 2000) math:sum 2751}] - skolem:lemma1751 + skolem:lemma2750 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 751]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2751]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma752 a r:Inference; r:gives { 2752 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 752}] + [ a r:Fact; r:gives {2000 log:repeat 752}] [ a r:Fact; r:gives {(752 2000) math:sum 2752}] - skolem:lemma1752 + skolem:lemma2751 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 752]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2752]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma753 a r:Inference; r:gives { 2753 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 753}] + [ a r:Fact; r:gives {2000 log:repeat 753}] [ a r:Fact; r:gives {(753 2000) math:sum 2753}] - skolem:lemma1753 + skolem:lemma2752 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 753]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2753]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma754 a r:Inference; r:gives { 2754 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 754}] + [ a r:Fact; r:gives {2000 log:repeat 754}] [ a r:Fact; r:gives {(754 2000) math:sum 2754}] - skolem:lemma1754 + skolem:lemma2753 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 754]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2754]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma755 a r:Inference; r:gives { 2755 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 755}] + [ a r:Fact; r:gives {2000 log:repeat 755}] [ a r:Fact; r:gives {(755 2000) math:sum 2755}] - skolem:lemma1755 + skolem:lemma2754 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 755]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2755]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma756 a r:Inference; r:gives { 2756 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 756}] + [ a r:Fact; r:gives {2000 log:repeat 756}] [ a r:Fact; r:gives {(756 2000) math:sum 2756}] - skolem:lemma1756 + skolem:lemma2755 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 756]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2756]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma757 a r:Inference; r:gives { 2757 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 757}] + [ a r:Fact; r:gives {2000 log:repeat 757}] [ a r:Fact; r:gives {(757 2000) math:sum 2757}] - skolem:lemma1757 + skolem:lemma2756 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 757]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2757]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma758 a r:Inference; r:gives { 2758 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 758}] + [ a r:Fact; r:gives {2000 log:repeat 758}] [ a r:Fact; r:gives {(758 2000) math:sum 2758}] - skolem:lemma1758 + skolem:lemma2757 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 758]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2758]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma759 a r:Inference; r:gives { 2759 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 759}] + [ a r:Fact; r:gives {2000 log:repeat 759}] [ a r:Fact; r:gives {(759 2000) math:sum 2759}] - skolem:lemma1759 + skolem:lemma2758 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 759]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2759]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma760 a r:Inference; r:gives { 2760 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 760}] + [ a r:Fact; r:gives {2000 log:repeat 760}] [ a r:Fact; r:gives {(760 2000) math:sum 2760}] - skolem:lemma1760 + skolem:lemma2759 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 760]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2760]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma761 a r:Inference; r:gives { 2761 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 761}] + [ a r:Fact; r:gives {2000 log:repeat 761}] [ a r:Fact; r:gives {(761 2000) math:sum 2761}] - skolem:lemma1761 + skolem:lemma2760 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 761]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2761]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma762 a r:Inference; r:gives { 2762 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 762}] + [ a r:Fact; r:gives {2000 log:repeat 762}] [ a r:Fact; r:gives {(762 2000) math:sum 2762}] - skolem:lemma1762 + skolem:lemma2761 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 762]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2762]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma763 a r:Inference; r:gives { 2763 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 763}] + [ a r:Fact; r:gives {2000 log:repeat 763}] [ a r:Fact; r:gives {(763 2000) math:sum 2763}] - skolem:lemma1763 + skolem:lemma2762 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 763]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2763]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma764 a r:Inference; r:gives { 2764 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 764}] + [ a r:Fact; r:gives {2000 log:repeat 764}] [ a r:Fact; r:gives {(764 2000) math:sum 2764}] - skolem:lemma1764 + skolem:lemma2763 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 764]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2764]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma765 a r:Inference; r:gives { 2765 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 765}] + [ a r:Fact; r:gives {2000 log:repeat 765}] [ a r:Fact; r:gives {(765 2000) math:sum 2765}] - skolem:lemma1765 + skolem:lemma2764 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 765]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2765]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma766 a r:Inference; r:gives { 2766 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 766}] + [ a r:Fact; r:gives {2000 log:repeat 766}] [ a r:Fact; r:gives {(766 2000) math:sum 2766}] - skolem:lemma1766 + skolem:lemma2765 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 766]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2766]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma767 a r:Inference; r:gives { 2767 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 767}] + [ a r:Fact; r:gives {2000 log:repeat 767}] [ a r:Fact; r:gives {(767 2000) math:sum 2767}] - skolem:lemma1767 + skolem:lemma2766 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 767]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2767]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma768 a r:Inference; r:gives { 2768 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 768}] + [ a r:Fact; r:gives {2000 log:repeat 768}] [ a r:Fact; r:gives {(768 2000) math:sum 2768}] - skolem:lemma1768 + skolem:lemma2767 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 768]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2768]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma769 a r:Inference; r:gives { 2769 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 769}] + [ a r:Fact; r:gives {2000 log:repeat 769}] [ a r:Fact; r:gives {(769 2000) math:sum 2769}] - skolem:lemma1769 + skolem:lemma2768 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 769]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2769]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma770 a r:Inference; r:gives { 2770 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 770}] + [ a r:Fact; r:gives {2000 log:repeat 770}] [ a r:Fact; r:gives {(770 2000) math:sum 2770}] - skolem:lemma1770 + skolem:lemma2769 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 770]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2770]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma771 a r:Inference; r:gives { 2771 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 771}] + [ a r:Fact; r:gives {2000 log:repeat 771}] [ a r:Fact; r:gives {(771 2000) math:sum 2771}] - skolem:lemma1771 + skolem:lemma2770 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 771]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2771]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma772 a r:Inference; r:gives { 2772 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 772}] + [ a r:Fact; r:gives {2000 log:repeat 772}] [ a r:Fact; r:gives {(772 2000) math:sum 2772}] - skolem:lemma1772 + skolem:lemma2771 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 772]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2772]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma773 a r:Inference; r:gives { 2773 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 773}] + [ a r:Fact; r:gives {2000 log:repeat 773}] [ a r:Fact; r:gives {(773 2000) math:sum 2773}] - skolem:lemma1773 + skolem:lemma2772 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 773]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2773]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma774 a r:Inference; r:gives { 2774 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 774}] + [ a r:Fact; r:gives {2000 log:repeat 774}] [ a r:Fact; r:gives {(774 2000) math:sum 2774}] - skolem:lemma1774 + skolem:lemma2773 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 774]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2774]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma775 a r:Inference; r:gives { 2775 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 775}] + [ a r:Fact; r:gives {2000 log:repeat 775}] [ a r:Fact; r:gives {(775 2000) math:sum 2775}] - skolem:lemma1775 + skolem:lemma2774 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 775]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2775]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma776 a r:Inference; r:gives { 2776 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 776}] + [ a r:Fact; r:gives {2000 log:repeat 776}] [ a r:Fact; r:gives {(776 2000) math:sum 2776}] - skolem:lemma1776 + skolem:lemma2775 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 776]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2776]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma777 a r:Inference; r:gives { 2777 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 777}] + [ a r:Fact; r:gives {2000 log:repeat 777}] [ a r:Fact; r:gives {(777 2000) math:sum 2777}] - skolem:lemma1777 + skolem:lemma2776 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 777]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2777]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma778 a r:Inference; r:gives { 2778 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 778}] + [ a r:Fact; r:gives {2000 log:repeat 778}] [ a r:Fact; r:gives {(778 2000) math:sum 2778}] - skolem:lemma1778 + skolem:lemma2777 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 778]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2778]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma779 a r:Inference; r:gives { 2779 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 779}] + [ a r:Fact; r:gives {2000 log:repeat 779}] [ a r:Fact; r:gives {(779 2000) math:sum 2779}] - skolem:lemma1779 + skolem:lemma2778 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 779]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2779]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma780 a r:Inference; r:gives { 2780 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 780}] + [ a r:Fact; r:gives {2000 log:repeat 780}] [ a r:Fact; r:gives {(780 2000) math:sum 2780}] - skolem:lemma1780 + skolem:lemma2779 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 780]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2780]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma781 a r:Inference; r:gives { 2781 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 781}] + [ a r:Fact; r:gives {2000 log:repeat 781}] [ a r:Fact; r:gives {(781 2000) math:sum 2781}] - skolem:lemma1781 + skolem:lemma2780 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 781]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2781]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma782 a r:Inference; r:gives { 2782 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 782}] + [ a r:Fact; r:gives {2000 log:repeat 782}] [ a r:Fact; r:gives {(782 2000) math:sum 2782}] - skolem:lemma1782 + skolem:lemma2781 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 782]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2782]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma783 a r:Inference; r:gives { 2783 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 783}] + [ a r:Fact; r:gives {2000 log:repeat 783}] [ a r:Fact; r:gives {(783 2000) math:sum 2783}] - skolem:lemma1783 + skolem:lemma2782 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 783]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2783]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma784 a r:Inference; r:gives { 2784 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 784}] + [ a r:Fact; r:gives {2000 log:repeat 784}] [ a r:Fact; r:gives {(784 2000) math:sum 2784}] - skolem:lemma1784 + skolem:lemma2783 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 784]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2784]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma785 a r:Inference; r:gives { 2785 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 785}] + [ a r:Fact; r:gives {2000 log:repeat 785}] [ a r:Fact; r:gives {(785 2000) math:sum 2785}] - skolem:lemma1785 + skolem:lemma2784 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 785]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2785]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma786 a r:Inference; r:gives { 2786 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 786}] + [ a r:Fact; r:gives {2000 log:repeat 786}] [ a r:Fact; r:gives {(786 2000) math:sum 2786}] - skolem:lemma1786 + skolem:lemma2785 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 786]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2786]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma787 a r:Inference; r:gives { 2787 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 787}] + [ a r:Fact; r:gives {2000 log:repeat 787}] [ a r:Fact; r:gives {(787 2000) math:sum 2787}] - skolem:lemma1787 + skolem:lemma2786 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 787]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2787]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma788 a r:Inference; r:gives { 2788 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 788}] + [ a r:Fact; r:gives {2000 log:repeat 788}] [ a r:Fact; r:gives {(788 2000) math:sum 2788}] - skolem:lemma1788 + skolem:lemma2787 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 788]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2788]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma789 a r:Inference; r:gives { 2789 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 789}] + [ a r:Fact; r:gives {2000 log:repeat 789}] [ a r:Fact; r:gives {(789 2000) math:sum 2789}] - skolem:lemma1789 + skolem:lemma2788 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 789]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2789]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma790 a r:Inference; r:gives { 2790 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 790}] + [ a r:Fact; r:gives {2000 log:repeat 790}] [ a r:Fact; r:gives {(790 2000) math:sum 2790}] - skolem:lemma1790 + skolem:lemma2789 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 790]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2790]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma791 a r:Inference; r:gives { 2791 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 791}] + [ a r:Fact; r:gives {2000 log:repeat 791}] [ a r:Fact; r:gives {(791 2000) math:sum 2791}] - skolem:lemma1791 + skolem:lemma2790 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 791]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2791]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma792 a r:Inference; r:gives { 2792 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 792}] + [ a r:Fact; r:gives {2000 log:repeat 792}] [ a r:Fact; r:gives {(792 2000) math:sum 2792}] - skolem:lemma1792 + skolem:lemma2791 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 792]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2792]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma793 a r:Inference; r:gives { 2793 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 793}] + [ a r:Fact; r:gives {2000 log:repeat 793}] [ a r:Fact; r:gives {(793 2000) math:sum 2793}] - skolem:lemma1793 + skolem:lemma2792 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 793]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2793]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma794 a r:Inference; r:gives { 2794 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 794}] + [ a r:Fact; r:gives {2000 log:repeat 794}] [ a r:Fact; r:gives {(794 2000) math:sum 2794}] - skolem:lemma1794 + skolem:lemma2793 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 794]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2794]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma795 a r:Inference; r:gives { 2795 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 795}] + [ a r:Fact; r:gives {2000 log:repeat 795}] [ a r:Fact; r:gives {(795 2000) math:sum 2795}] - skolem:lemma1795 + skolem:lemma2794 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 795]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2795]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma796 a r:Inference; r:gives { 2796 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 796}] + [ a r:Fact; r:gives {2000 log:repeat 796}] [ a r:Fact; r:gives {(796 2000) math:sum 2796}] - skolem:lemma1796 + skolem:lemma2795 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 796]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2796]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma797 a r:Inference; r:gives { 2797 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 797}] + [ a r:Fact; r:gives {2000 log:repeat 797}] [ a r:Fact; r:gives {(797 2000) math:sum 2797}] - skolem:lemma1797 + skolem:lemma2796 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 797]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2797]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma798 a r:Inference; r:gives { 2798 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 798}] + [ a r:Fact; r:gives {2000 log:repeat 798}] [ a r:Fact; r:gives {(798 2000) math:sum 2798}] - skolem:lemma1798 + skolem:lemma2797 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 798]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2798]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma799 a r:Inference; r:gives { 2799 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 799}] + [ a r:Fact; r:gives {2000 log:repeat 799}] [ a r:Fact; r:gives {(799 2000) math:sum 2799}] - skolem:lemma1799 + skolem:lemma2798 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 799]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2799]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma800 a r:Inference; r:gives { 2800 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 800}] + [ a r:Fact; r:gives {2000 log:repeat 800}] [ a r:Fact; r:gives {(800 2000) math:sum 2800}] - skolem:lemma1800 + skolem:lemma2799 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 800]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2800]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma801 a r:Inference; r:gives { 2801 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 801}] + [ a r:Fact; r:gives {2000 log:repeat 801}] [ a r:Fact; r:gives {(801 2000) math:sum 2801}] - skolem:lemma1801 + skolem:lemma2800 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 801]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2801]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma802 a r:Inference; r:gives { 2802 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 802}] + [ a r:Fact; r:gives {2000 log:repeat 802}] [ a r:Fact; r:gives {(802 2000) math:sum 2802}] - skolem:lemma1802 + skolem:lemma2801 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 802]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2802]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma803 a r:Inference; r:gives { 2803 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 803}] + [ a r:Fact; r:gives {2000 log:repeat 803}] [ a r:Fact; r:gives {(803 2000) math:sum 2803}] - skolem:lemma1803 + skolem:lemma2802 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 803]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2803]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma804 a r:Inference; r:gives { 2804 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 804}] + [ a r:Fact; r:gives {2000 log:repeat 804}] [ a r:Fact; r:gives {(804 2000) math:sum 2804}] - skolem:lemma1804 + skolem:lemma2803 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 804]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2804]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma805 a r:Inference; r:gives { 2805 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 805}] + [ a r:Fact; r:gives {2000 log:repeat 805}] [ a r:Fact; r:gives {(805 2000) math:sum 2805}] - skolem:lemma1805 + skolem:lemma2804 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 805]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2805]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma806 a r:Inference; r:gives { 2806 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 806}] + [ a r:Fact; r:gives {2000 log:repeat 806}] [ a r:Fact; r:gives {(806 2000) math:sum 2806}] - skolem:lemma1806 + skolem:lemma2805 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 806]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2806]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma807 a r:Inference; r:gives { 2807 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 807}] + [ a r:Fact; r:gives {2000 log:repeat 807}] [ a r:Fact; r:gives {(807 2000) math:sum 2807}] - skolem:lemma1807 + skolem:lemma2806 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 807]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2807]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma808 a r:Inference; r:gives { 2808 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 808}] + [ a r:Fact; r:gives {2000 log:repeat 808}] [ a r:Fact; r:gives {(808 2000) math:sum 2808}] - skolem:lemma1808 + skolem:lemma2807 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 808]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2808]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma809 a r:Inference; r:gives { 2809 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 809}] + [ a r:Fact; r:gives {2000 log:repeat 809}] [ a r:Fact; r:gives {(809 2000) math:sum 2809}] - skolem:lemma1809 + skolem:lemma2808 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 809]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2809]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma810 a r:Inference; r:gives { 2810 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 810}] + [ a r:Fact; r:gives {2000 log:repeat 810}] [ a r:Fact; r:gives {(810 2000) math:sum 2810}] - skolem:lemma1810 + skolem:lemma2809 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 810]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2810]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma811 a r:Inference; r:gives { 2811 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 811}] + [ a r:Fact; r:gives {2000 log:repeat 811}] [ a r:Fact; r:gives {(811 2000) math:sum 2811}] - skolem:lemma1811 + skolem:lemma2810 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 811]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2811]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma812 a r:Inference; r:gives { 2812 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 812}] + [ a r:Fact; r:gives {2000 log:repeat 812}] [ a r:Fact; r:gives {(812 2000) math:sum 2812}] - skolem:lemma1812 + skolem:lemma2811 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 812]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2812]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma813 a r:Inference; r:gives { 2813 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 813}] + [ a r:Fact; r:gives {2000 log:repeat 813}] [ a r:Fact; r:gives {(813 2000) math:sum 2813}] - skolem:lemma1813 + skolem:lemma2812 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 813]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2813]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma814 a r:Inference; r:gives { 2814 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 814}] + [ a r:Fact; r:gives {2000 log:repeat 814}] [ a r:Fact; r:gives {(814 2000) math:sum 2814}] - skolem:lemma1814 + skolem:lemma2813 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 814]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2814]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma815 a r:Inference; r:gives { 2815 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 815}] + [ a r:Fact; r:gives {2000 log:repeat 815}] [ a r:Fact; r:gives {(815 2000) math:sum 2815}] - skolem:lemma1815 + skolem:lemma2814 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 815]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2815]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma816 a r:Inference; r:gives { 2816 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 816}] + [ a r:Fact; r:gives {2000 log:repeat 816}] [ a r:Fact; r:gives {(816 2000) math:sum 2816}] - skolem:lemma1816 + skolem:lemma2815 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 816]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2816]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma817 a r:Inference; r:gives { 2817 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 817}] + [ a r:Fact; r:gives {2000 log:repeat 817}] [ a r:Fact; r:gives {(817 2000) math:sum 2817}] - skolem:lemma1817 + skolem:lemma2816 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 817]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2817]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma818 a r:Inference; r:gives { 2818 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 818}] + [ a r:Fact; r:gives {2000 log:repeat 818}] [ a r:Fact; r:gives {(818 2000) math:sum 2818}] - skolem:lemma1818 + skolem:lemma2817 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 818]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2818]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma819 a r:Inference; r:gives { 2819 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 819}] + [ a r:Fact; r:gives {2000 log:repeat 819}] [ a r:Fact; r:gives {(819 2000) math:sum 2819}] - skolem:lemma1819 + skolem:lemma2818 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 819]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2819]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma820 a r:Inference; r:gives { 2820 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 820}] + [ a r:Fact; r:gives {2000 log:repeat 820}] [ a r:Fact; r:gives {(820 2000) math:sum 2820}] - skolem:lemma1820 + skolem:lemma2819 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 820]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2820]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma821 a r:Inference; r:gives { 2821 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 821}] + [ a r:Fact; r:gives {2000 log:repeat 821}] [ a r:Fact; r:gives {(821 2000) math:sum 2821}] - skolem:lemma1821 + skolem:lemma2820 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 821]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2821]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma822 a r:Inference; r:gives { 2822 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 822}] + [ a r:Fact; r:gives {2000 log:repeat 822}] [ a r:Fact; r:gives {(822 2000) math:sum 2822}] - skolem:lemma1822 + skolem:lemma2821 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 822]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2822]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma823 a r:Inference; r:gives { 2823 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 823}] + [ a r:Fact; r:gives {2000 log:repeat 823}] [ a r:Fact; r:gives {(823 2000) math:sum 2823}] - skolem:lemma1823 + skolem:lemma2822 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 823]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2823]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma824 a r:Inference; r:gives { 2824 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 824}] + [ a r:Fact; r:gives {2000 log:repeat 824}] [ a r:Fact; r:gives {(824 2000) math:sum 2824}] - skolem:lemma1824 + skolem:lemma2823 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 824]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2824]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma825 a r:Inference; r:gives { 2825 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 825}] + [ a r:Fact; r:gives {2000 log:repeat 825}] [ a r:Fact; r:gives {(825 2000) math:sum 2825}] - skolem:lemma1825 + skolem:lemma2824 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 825]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2825]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma826 a r:Inference; r:gives { 2826 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 826}] + [ a r:Fact; r:gives {2000 log:repeat 826}] [ a r:Fact; r:gives {(826 2000) math:sum 2826}] - skolem:lemma1826 + skolem:lemma2825 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 826]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2826]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma827 a r:Inference; r:gives { 2827 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 827}] + [ a r:Fact; r:gives {2000 log:repeat 827}] [ a r:Fact; r:gives {(827 2000) math:sum 2827}] - skolem:lemma1827 + skolem:lemma2826 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 827]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2827]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma828 a r:Inference; r:gives { 2828 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 828}] + [ a r:Fact; r:gives {2000 log:repeat 828}] [ a r:Fact; r:gives {(828 2000) math:sum 2828}] - skolem:lemma1828 + skolem:lemma2827 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 828]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2828]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma829 a r:Inference; r:gives { 2829 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 829}] + [ a r:Fact; r:gives {2000 log:repeat 829}] [ a r:Fact; r:gives {(829 2000) math:sum 2829}] - skolem:lemma1829 + skolem:lemma2828 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 829]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2829]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma830 a r:Inference; r:gives { 2830 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 830}] + [ a r:Fact; r:gives {2000 log:repeat 830}] [ a r:Fact; r:gives {(830 2000) math:sum 2830}] - skolem:lemma1830 + skolem:lemma2829 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 830]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2830]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma831 a r:Inference; r:gives { 2831 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 831}] + [ a r:Fact; r:gives {2000 log:repeat 831}] [ a r:Fact; r:gives {(831 2000) math:sum 2831}] - skolem:lemma1831 + skolem:lemma2830 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 831]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2831]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma832 a r:Inference; r:gives { 2832 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 832}] + [ a r:Fact; r:gives {2000 log:repeat 832}] [ a r:Fact; r:gives {(832 2000) math:sum 2832}] - skolem:lemma1832 + skolem:lemma2831 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 832]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2832]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma833 a r:Inference; r:gives { 2833 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 833}] + [ a r:Fact; r:gives {2000 log:repeat 833}] [ a r:Fact; r:gives {(833 2000) math:sum 2833}] - skolem:lemma1833 + skolem:lemma2832 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 833]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2833]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma834 a r:Inference; r:gives { 2834 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 834}] + [ a r:Fact; r:gives {2000 log:repeat 834}] [ a r:Fact; r:gives {(834 2000) math:sum 2834}] - skolem:lemma1834 + skolem:lemma2833 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 834]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2834]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma835 a r:Inference; r:gives { 2835 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 835}] + [ a r:Fact; r:gives {2000 log:repeat 835}] [ a r:Fact; r:gives {(835 2000) math:sum 2835}] - skolem:lemma1835 + skolem:lemma2834 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 835]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2835]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma836 a r:Inference; r:gives { 2836 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 836}] + [ a r:Fact; r:gives {2000 log:repeat 836}] [ a r:Fact; r:gives {(836 2000) math:sum 2836}] - skolem:lemma1836 + skolem:lemma2835 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 836]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2836]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma837 a r:Inference; r:gives { 2837 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 837}] + [ a r:Fact; r:gives {2000 log:repeat 837}] [ a r:Fact; r:gives {(837 2000) math:sum 2837}] - skolem:lemma1837 + skolem:lemma2836 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 837]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2837]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma838 a r:Inference; r:gives { 2838 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 838}] + [ a r:Fact; r:gives {2000 log:repeat 838}] [ a r:Fact; r:gives {(838 2000) math:sum 2838}] - skolem:lemma1838 + skolem:lemma2837 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 838]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2838]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma839 a r:Inference; r:gives { 2839 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 839}] + [ a r:Fact; r:gives {2000 log:repeat 839}] [ a r:Fact; r:gives {(839 2000) math:sum 2839}] - skolem:lemma1839 + skolem:lemma2838 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 839]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2839]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma840 a r:Inference; r:gives { 2840 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 840}] + [ a r:Fact; r:gives {2000 log:repeat 840}] [ a r:Fact; r:gives {(840 2000) math:sum 2840}] - skolem:lemma1840 + skolem:lemma2839 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 840]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2840]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma841 a r:Inference; r:gives { 2841 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 841}] + [ a r:Fact; r:gives {2000 log:repeat 841}] [ a r:Fact; r:gives {(841 2000) math:sum 2841}] - skolem:lemma1841 + skolem:lemma2840 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 841]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2841]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma842 a r:Inference; r:gives { 2842 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 842}] + [ a r:Fact; r:gives {2000 log:repeat 842}] [ a r:Fact; r:gives {(842 2000) math:sum 2842}] - skolem:lemma1842 + skolem:lemma2841 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 842]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2842]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma843 a r:Inference; r:gives { 2843 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 843}] + [ a r:Fact; r:gives {2000 log:repeat 843}] [ a r:Fact; r:gives {(843 2000) math:sum 2843}] - skolem:lemma1843 + skolem:lemma2842 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 843]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2843]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma844 a r:Inference; r:gives { 2844 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 844}] + [ a r:Fact; r:gives {2000 log:repeat 844}] [ a r:Fact; r:gives {(844 2000) math:sum 2844}] - skolem:lemma1844 + skolem:lemma2843 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 844]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2844]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma845 a r:Inference; r:gives { 2845 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 845}] + [ a r:Fact; r:gives {2000 log:repeat 845}] [ a r:Fact; r:gives {(845 2000) math:sum 2845}] - skolem:lemma1845 + skolem:lemma2844 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 845]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2845]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma846 a r:Inference; r:gives { 2846 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 846}] + [ a r:Fact; r:gives {2000 log:repeat 846}] [ a r:Fact; r:gives {(846 2000) math:sum 2846}] - skolem:lemma1846 + skolem:lemma2845 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 846]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2846]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma847 a r:Inference; r:gives { 2847 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 847}] + [ a r:Fact; r:gives {2000 log:repeat 847}] [ a r:Fact; r:gives {(847 2000) math:sum 2847}] - skolem:lemma1847 + skolem:lemma2846 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 847]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2847]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma848 a r:Inference; r:gives { 2848 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 848}] + [ a r:Fact; r:gives {2000 log:repeat 848}] [ a r:Fact; r:gives {(848 2000) math:sum 2848}] - skolem:lemma1848 + skolem:lemma2847 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 848]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2848]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma849 a r:Inference; r:gives { 2849 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 849}] + [ a r:Fact; r:gives {2000 log:repeat 849}] [ a r:Fact; r:gives {(849 2000) math:sum 2849}] - skolem:lemma1849 + skolem:lemma2848 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 849]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2849]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma850 a r:Inference; r:gives { 2850 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 850}] + [ a r:Fact; r:gives {2000 log:repeat 850}] [ a r:Fact; r:gives {(850 2000) math:sum 2850}] - skolem:lemma1850 + skolem:lemma2849 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 850]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2850]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma851 a r:Inference; r:gives { 2851 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 851}] + [ a r:Fact; r:gives {2000 log:repeat 851}] [ a r:Fact; r:gives {(851 2000) math:sum 2851}] - skolem:lemma1851 + skolem:lemma2850 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 851]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2851]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma852 a r:Inference; r:gives { 2852 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 852}] + [ a r:Fact; r:gives {2000 log:repeat 852}] [ a r:Fact; r:gives {(852 2000) math:sum 2852}] - skolem:lemma1852 + skolem:lemma2851 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 852]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2852]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma853 a r:Inference; r:gives { 2853 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 853}] + [ a r:Fact; r:gives {2000 log:repeat 853}] [ a r:Fact; r:gives {(853 2000) math:sum 2853}] - skolem:lemma1853 + skolem:lemma2852 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 853]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2853]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma854 a r:Inference; r:gives { 2854 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 854}] + [ a r:Fact; r:gives {2000 log:repeat 854}] [ a r:Fact; r:gives {(854 2000) math:sum 2854}] - skolem:lemma1854 + skolem:lemma2853 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 854]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2854]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma855 a r:Inference; r:gives { 2855 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 855}] + [ a r:Fact; r:gives {2000 log:repeat 855}] [ a r:Fact; r:gives {(855 2000) math:sum 2855}] - skolem:lemma1855 + skolem:lemma2854 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 855]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2855]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma856 a r:Inference; r:gives { 2856 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 856}] + [ a r:Fact; r:gives {2000 log:repeat 856}] [ a r:Fact; r:gives {(856 2000) math:sum 2856}] - skolem:lemma1856 + skolem:lemma2855 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 856]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2856]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma857 a r:Inference; r:gives { 2857 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 857}] + [ a r:Fact; r:gives {2000 log:repeat 857}] [ a r:Fact; r:gives {(857 2000) math:sum 2857}] - skolem:lemma1857 + skolem:lemma2856 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 857]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2857]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma858 a r:Inference; r:gives { 2858 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 858}] + [ a r:Fact; r:gives {2000 log:repeat 858}] [ a r:Fact; r:gives {(858 2000) math:sum 2858}] - skolem:lemma1858 + skolem:lemma2857 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 858]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2858]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma859 a r:Inference; r:gives { 2859 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 859}] + [ a r:Fact; r:gives {2000 log:repeat 859}] [ a r:Fact; r:gives {(859 2000) math:sum 2859}] - skolem:lemma1859 + skolem:lemma2858 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 859]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2859]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma860 a r:Inference; r:gives { 2860 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 860}] + [ a r:Fact; r:gives {2000 log:repeat 860}] [ a r:Fact; r:gives {(860 2000) math:sum 2860}] - skolem:lemma1860 + skolem:lemma2859 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 860]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2860]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma861 a r:Inference; r:gives { 2861 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 861}] + [ a r:Fact; r:gives {2000 log:repeat 861}] [ a r:Fact; r:gives {(861 2000) math:sum 2861}] - skolem:lemma1861 + skolem:lemma2860 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 861]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2861]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma862 a r:Inference; r:gives { 2862 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 862}] + [ a r:Fact; r:gives {2000 log:repeat 862}] [ a r:Fact; r:gives {(862 2000) math:sum 2862}] - skolem:lemma1862 + skolem:lemma2861 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 862]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2862]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma863 a r:Inference; r:gives { 2863 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 863}] + [ a r:Fact; r:gives {2000 log:repeat 863}] [ a r:Fact; r:gives {(863 2000) math:sum 2863}] - skolem:lemma1863 + skolem:lemma2862 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 863]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2863]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma864 a r:Inference; r:gives { 2864 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 864}] + [ a r:Fact; r:gives {2000 log:repeat 864}] [ a r:Fact; r:gives {(864 2000) math:sum 2864}] - skolem:lemma1864 + skolem:lemma2863 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 864]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2864]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma865 a r:Inference; r:gives { 2865 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 865}] + [ a r:Fact; r:gives {2000 log:repeat 865}] [ a r:Fact; r:gives {(865 2000) math:sum 2865}] - skolem:lemma1865 + skolem:lemma2864 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 865]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2865]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma866 a r:Inference; r:gives { 2866 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 866}] + [ a r:Fact; r:gives {2000 log:repeat 866}] [ a r:Fact; r:gives {(866 2000) math:sum 2866}] - skolem:lemma1866 + skolem:lemma2865 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 866]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2866]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma867 a r:Inference; r:gives { 2867 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 867}] + [ a r:Fact; r:gives {2000 log:repeat 867}] [ a r:Fact; r:gives {(867 2000) math:sum 2867}] - skolem:lemma1867 + skolem:lemma2866 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 867]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2867]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma868 a r:Inference; r:gives { 2868 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 868}] + [ a r:Fact; r:gives {2000 log:repeat 868}] [ a r:Fact; r:gives {(868 2000) math:sum 2868}] - skolem:lemma1868 + skolem:lemma2867 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 868]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2868]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma869 a r:Inference; r:gives { 2869 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 869}] + [ a r:Fact; r:gives {2000 log:repeat 869}] [ a r:Fact; r:gives {(869 2000) math:sum 2869}] - skolem:lemma1869 + skolem:lemma2868 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 869]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2869]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma870 a r:Inference; r:gives { 2870 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 870}] + [ a r:Fact; r:gives {2000 log:repeat 870}] [ a r:Fact; r:gives {(870 2000) math:sum 2870}] - skolem:lemma1870 + skolem:lemma2869 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 870]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2870]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma871 a r:Inference; r:gives { 2871 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 871}] + [ a r:Fact; r:gives {2000 log:repeat 871}] [ a r:Fact; r:gives {(871 2000) math:sum 2871}] - skolem:lemma1871 + skolem:lemma2870 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 871]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2871]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma872 a r:Inference; r:gives { 2872 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 872}] + [ a r:Fact; r:gives {2000 log:repeat 872}] [ a r:Fact; r:gives {(872 2000) math:sum 2872}] - skolem:lemma1872 + skolem:lemma2871 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 872]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2872]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma873 a r:Inference; r:gives { 2873 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 873}] + [ a r:Fact; r:gives {2000 log:repeat 873}] [ a r:Fact; r:gives {(873 2000) math:sum 2873}] - skolem:lemma1873 + skolem:lemma2872 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 873]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2873]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma874 a r:Inference; r:gives { 2874 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 874}] + [ a r:Fact; r:gives {2000 log:repeat 874}] [ a r:Fact; r:gives {(874 2000) math:sum 2874}] - skolem:lemma1874 + skolem:lemma2873 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 874]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2874]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma875 a r:Inference; r:gives { 2875 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 875}] + [ a r:Fact; r:gives {2000 log:repeat 875}] [ a r:Fact; r:gives {(875 2000) math:sum 2875}] - skolem:lemma1875 + skolem:lemma2874 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 875]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2875]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma876 a r:Inference; r:gives { 2876 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 876}] + [ a r:Fact; r:gives {2000 log:repeat 876}] [ a r:Fact; r:gives {(876 2000) math:sum 2876}] - skolem:lemma1876 + skolem:lemma2875 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 876]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2876]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma877 a r:Inference; r:gives { 2877 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 877}] + [ a r:Fact; r:gives {2000 log:repeat 877}] [ a r:Fact; r:gives {(877 2000) math:sum 2877}] - skolem:lemma1877 + skolem:lemma2876 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 877]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2877]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma878 a r:Inference; r:gives { 2878 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 878}] + [ a r:Fact; r:gives {2000 log:repeat 878}] [ a r:Fact; r:gives {(878 2000) math:sum 2878}] - skolem:lemma1878 + skolem:lemma2877 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 878]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2878]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma879 a r:Inference; r:gives { 2879 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 879}] + [ a r:Fact; r:gives {2000 log:repeat 879}] [ a r:Fact; r:gives {(879 2000) math:sum 2879}] - skolem:lemma1879 + skolem:lemma2878 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 879]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2879]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma880 a r:Inference; r:gives { 2880 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 880}] + [ a r:Fact; r:gives {2000 log:repeat 880}] [ a r:Fact; r:gives {(880 2000) math:sum 2880}] - skolem:lemma1880 + skolem:lemma2879 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 880]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2880]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma881 a r:Inference; r:gives { 2881 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 881}] + [ a r:Fact; r:gives {2000 log:repeat 881}] [ a r:Fact; r:gives {(881 2000) math:sum 2881}] - skolem:lemma1881 + skolem:lemma2880 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 881]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2881]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma882 a r:Inference; r:gives { 2882 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 882}] + [ a r:Fact; r:gives {2000 log:repeat 882}] [ a r:Fact; r:gives {(882 2000) math:sum 2882}] - skolem:lemma1882 + skolem:lemma2881 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 882]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2882]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma883 a r:Inference; r:gives { 2883 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 883}] + [ a r:Fact; r:gives {2000 log:repeat 883}] [ a r:Fact; r:gives {(883 2000) math:sum 2883}] - skolem:lemma1883 + skolem:lemma2882 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 883]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2883]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma884 a r:Inference; r:gives { 2884 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 884}] + [ a r:Fact; r:gives {2000 log:repeat 884}] [ a r:Fact; r:gives {(884 2000) math:sum 2884}] - skolem:lemma1884 + skolem:lemma2883 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 884]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2884]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma885 a r:Inference; r:gives { 2885 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 885}] + [ a r:Fact; r:gives {2000 log:repeat 885}] [ a r:Fact; r:gives {(885 2000) math:sum 2885}] - skolem:lemma1885 + skolem:lemma2884 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 885]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2885]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma886 a r:Inference; r:gives { 2886 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 886}] + [ a r:Fact; r:gives {2000 log:repeat 886}] [ a r:Fact; r:gives {(886 2000) math:sum 2886}] - skolem:lemma1886 + skolem:lemma2885 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 886]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2886]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma887 a r:Inference; r:gives { 2887 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 887}] + [ a r:Fact; r:gives {2000 log:repeat 887}] [ a r:Fact; r:gives {(887 2000) math:sum 2887}] - skolem:lemma1887 + skolem:lemma2886 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 887]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2887]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma888 a r:Inference; r:gives { 2888 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 888}] + [ a r:Fact; r:gives {2000 log:repeat 888}] [ a r:Fact; r:gives {(888 2000) math:sum 2888}] - skolem:lemma1888 + skolem:lemma2887 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 888]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2888]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma889 a r:Inference; r:gives { 2889 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 889}] + [ a r:Fact; r:gives {2000 log:repeat 889}] [ a r:Fact; r:gives {(889 2000) math:sum 2889}] - skolem:lemma1889 + skolem:lemma2888 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 889]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2889]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma890 a r:Inference; r:gives { 2890 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 890}] + [ a r:Fact; r:gives {2000 log:repeat 890}] [ a r:Fact; r:gives {(890 2000) math:sum 2890}] - skolem:lemma1890 + skolem:lemma2889 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 890]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2890]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma891 a r:Inference; r:gives { 2891 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 891}] + [ a r:Fact; r:gives {2000 log:repeat 891}] [ a r:Fact; r:gives {(891 2000) math:sum 2891}] - skolem:lemma1891 + skolem:lemma2890 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 891]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2891]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma892 a r:Inference; r:gives { 2892 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 892}] + [ a r:Fact; r:gives {2000 log:repeat 892}] [ a r:Fact; r:gives {(892 2000) math:sum 2892}] - skolem:lemma1892 + skolem:lemma2891 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 892]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2892]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma893 a r:Inference; r:gives { 2893 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 893}] + [ a r:Fact; r:gives {2000 log:repeat 893}] [ a r:Fact; r:gives {(893 2000) math:sum 2893}] - skolem:lemma1893 + skolem:lemma2892 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 893]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2893]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma894 a r:Inference; r:gives { 2894 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 894}] + [ a r:Fact; r:gives {2000 log:repeat 894}] [ a r:Fact; r:gives {(894 2000) math:sum 2894}] - skolem:lemma1894 + skolem:lemma2893 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 894]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2894]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma895 a r:Inference; r:gives { 2895 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 895}] + [ a r:Fact; r:gives {2000 log:repeat 895}] [ a r:Fact; r:gives {(895 2000) math:sum 2895}] - skolem:lemma1895 + skolem:lemma2894 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 895]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2895]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma896 a r:Inference; r:gives { 2896 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 896}] + [ a r:Fact; r:gives {2000 log:repeat 896}] [ a r:Fact; r:gives {(896 2000) math:sum 2896}] - skolem:lemma1896 + skolem:lemma2895 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 896]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2896]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma897 a r:Inference; r:gives { 2897 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 897}] + [ a r:Fact; r:gives {2000 log:repeat 897}] [ a r:Fact; r:gives {(897 2000) math:sum 2897}] - skolem:lemma1897 + skolem:lemma2896 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 897]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2897]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma898 a r:Inference; r:gives { 2898 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 898}] + [ a r:Fact; r:gives {2000 log:repeat 898}] [ a r:Fact; r:gives {(898 2000) math:sum 2898}] - skolem:lemma1898 + skolem:lemma2897 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 898]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2898]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma899 a r:Inference; r:gives { 2899 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 899}] + [ a r:Fact; r:gives {2000 log:repeat 899}] [ a r:Fact; r:gives {(899 2000) math:sum 2899}] - skolem:lemma1899 + skolem:lemma2898 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 899]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2899]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma900 a r:Inference; r:gives { 2900 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 900}] + [ a r:Fact; r:gives {2000 log:repeat 900}] [ a r:Fact; r:gives {(900 2000) math:sum 2900}] - skolem:lemma1900 + skolem:lemma2899 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 900]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2900]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma901 a r:Inference; r:gives { 2901 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 901}] + [ a r:Fact; r:gives {2000 log:repeat 901}] [ a r:Fact; r:gives {(901 2000) math:sum 2901}] - skolem:lemma1901 + skolem:lemma2900 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 901]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2901]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma902 a r:Inference; r:gives { 2902 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 902}] + [ a r:Fact; r:gives {2000 log:repeat 902}] [ a r:Fact; r:gives {(902 2000) math:sum 2902}] - skolem:lemma1902 + skolem:lemma2901 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 902]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2902]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma903 a r:Inference; r:gives { 2903 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 903}] + [ a r:Fact; r:gives {2000 log:repeat 903}] [ a r:Fact; r:gives {(903 2000) math:sum 2903}] - skolem:lemma1903 + skolem:lemma2902 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 903]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2903]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma904 a r:Inference; r:gives { 2904 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 904}] + [ a r:Fact; r:gives {2000 log:repeat 904}] [ a r:Fact; r:gives {(904 2000) math:sum 2904}] - skolem:lemma1904 + skolem:lemma2903 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 904]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2904]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma905 a r:Inference; r:gives { 2905 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 905}] + [ a r:Fact; r:gives {2000 log:repeat 905}] [ a r:Fact; r:gives {(905 2000) math:sum 2905}] - skolem:lemma1905 + skolem:lemma2904 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 905]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2905]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma906 a r:Inference; r:gives { 2906 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 906}] + [ a r:Fact; r:gives {2000 log:repeat 906}] [ a r:Fact; r:gives {(906 2000) math:sum 2906}] - skolem:lemma1906 + skolem:lemma2905 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 906]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2906]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma907 a r:Inference; r:gives { 2907 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 907}] + [ a r:Fact; r:gives {2000 log:repeat 907}] [ a r:Fact; r:gives {(907 2000) math:sum 2907}] - skolem:lemma1907 + skolem:lemma2906 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 907]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2907]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma908 a r:Inference; r:gives { 2908 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 908}] + [ a r:Fact; r:gives {2000 log:repeat 908}] [ a r:Fact; r:gives {(908 2000) math:sum 2908}] - skolem:lemma1908 + skolem:lemma2907 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 908]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2908]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma909 a r:Inference; r:gives { 2909 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 909}] + [ a r:Fact; r:gives {2000 log:repeat 909}] [ a r:Fact; r:gives {(909 2000) math:sum 2909}] - skolem:lemma1909 + skolem:lemma2908 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 909]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2909]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma910 a r:Inference; r:gives { 2910 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 910}] + [ a r:Fact; r:gives {2000 log:repeat 910}] [ a r:Fact; r:gives {(910 2000) math:sum 2910}] - skolem:lemma1910 + skolem:lemma2909 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 910]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2910]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma911 a r:Inference; r:gives { 2911 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 911}] + [ a r:Fact; r:gives {2000 log:repeat 911}] [ a r:Fact; r:gives {(911 2000) math:sum 2911}] - skolem:lemma1911 + skolem:lemma2910 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 911]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2911]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma912 a r:Inference; r:gives { 2912 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 912}] + [ a r:Fact; r:gives {2000 log:repeat 912}] [ a r:Fact; r:gives {(912 2000) math:sum 2912}] - skolem:lemma1912 + skolem:lemma2911 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 912]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2912]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma913 a r:Inference; r:gives { 2913 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 913}] + [ a r:Fact; r:gives {2000 log:repeat 913}] [ a r:Fact; r:gives {(913 2000) math:sum 2913}] - skolem:lemma1913 + skolem:lemma2912 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 913]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2913]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma914 a r:Inference; r:gives { 2914 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 914}] + [ a r:Fact; r:gives {2000 log:repeat 914}] [ a r:Fact; r:gives {(914 2000) math:sum 2914}] - skolem:lemma1914 + skolem:lemma2913 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 914]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2914]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma915 a r:Inference; r:gives { 2915 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 915}] + [ a r:Fact; r:gives {2000 log:repeat 915}] [ a r:Fact; r:gives {(915 2000) math:sum 2915}] - skolem:lemma1915 + skolem:lemma2914 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 915]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2915]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma916 a r:Inference; r:gives { 2916 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 916}] + [ a r:Fact; r:gives {2000 log:repeat 916}] [ a r:Fact; r:gives {(916 2000) math:sum 2916}] - skolem:lemma1916 + skolem:lemma2915 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 916]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2916]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma917 a r:Inference; r:gives { 2917 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 917}] + [ a r:Fact; r:gives {2000 log:repeat 917}] [ a r:Fact; r:gives {(917 2000) math:sum 2917}] - skolem:lemma1917 + skolem:lemma2916 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 917]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2917]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma918 a r:Inference; r:gives { 2918 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 918}] + [ a r:Fact; r:gives {2000 log:repeat 918}] [ a r:Fact; r:gives {(918 2000) math:sum 2918}] - skolem:lemma1918 + skolem:lemma2917 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 918]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2918]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma919 a r:Inference; r:gives { 2919 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 919}] + [ a r:Fact; r:gives {2000 log:repeat 919}] [ a r:Fact; r:gives {(919 2000) math:sum 2919}] - skolem:lemma1919 + skolem:lemma2918 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 919]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2919]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma920 a r:Inference; r:gives { 2920 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 920}] + [ a r:Fact; r:gives {2000 log:repeat 920}] [ a r:Fact; r:gives {(920 2000) math:sum 2920}] - skolem:lemma1920 + skolem:lemma2919 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 920]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2920]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma921 a r:Inference; r:gives { 2921 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 921}] + [ a r:Fact; r:gives {2000 log:repeat 921}] [ a r:Fact; r:gives {(921 2000) math:sum 2921}] - skolem:lemma1921 + skolem:lemma2920 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 921]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2921]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma922 a r:Inference; r:gives { 2922 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 922}] + [ a r:Fact; r:gives {2000 log:repeat 922}] [ a r:Fact; r:gives {(922 2000) math:sum 2922}] - skolem:lemma1922 + skolem:lemma2921 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 922]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2922]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma923 a r:Inference; r:gives { 2923 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 923}] + [ a r:Fact; r:gives {2000 log:repeat 923}] [ a r:Fact; r:gives {(923 2000) math:sum 2923}] - skolem:lemma1923 + skolem:lemma2922 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 923]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2923]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma924 a r:Inference; r:gives { 2924 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 924}] + [ a r:Fact; r:gives {2000 log:repeat 924}] [ a r:Fact; r:gives {(924 2000) math:sum 2924}] - skolem:lemma1924 + skolem:lemma2923 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 924]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2924]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma925 a r:Inference; r:gives { 2925 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 925}] + [ a r:Fact; r:gives {2000 log:repeat 925}] [ a r:Fact; r:gives {(925 2000) math:sum 2925}] - skolem:lemma1925 + skolem:lemma2924 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 925]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2925]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma926 a r:Inference; r:gives { 2926 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 926}] + [ a r:Fact; r:gives {2000 log:repeat 926}] [ a r:Fact; r:gives {(926 2000) math:sum 2926}] - skolem:lemma1926 + skolem:lemma2925 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 926]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2926]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma927 a r:Inference; r:gives { 2927 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 927}] + [ a r:Fact; r:gives {2000 log:repeat 927}] [ a r:Fact; r:gives {(927 2000) math:sum 2927}] - skolem:lemma1927 + skolem:lemma2926 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 927]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2927]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma928 a r:Inference; r:gives { 2928 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 928}] + [ a r:Fact; r:gives {2000 log:repeat 928}] [ a r:Fact; r:gives {(928 2000) math:sum 2928}] - skolem:lemma1928 + skolem:lemma2927 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 928]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2928]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma929 a r:Inference; r:gives { 2929 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 929}] + [ a r:Fact; r:gives {2000 log:repeat 929}] [ a r:Fact; r:gives {(929 2000) math:sum 2929}] - skolem:lemma1929 + skolem:lemma2928 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 929]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2929]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma930 a r:Inference; r:gives { 2930 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 930}] + [ a r:Fact; r:gives {2000 log:repeat 930}] [ a r:Fact; r:gives {(930 2000) math:sum 2930}] - skolem:lemma1930 + skolem:lemma2929 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 930]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2930]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma931 a r:Inference; r:gives { 2931 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 931}] + [ a r:Fact; r:gives {2000 log:repeat 931}] [ a r:Fact; r:gives {(931 2000) math:sum 2931}] - skolem:lemma1931 + skolem:lemma2930 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 931]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2931]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma932 a r:Inference; r:gives { 2932 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 932}] + [ a r:Fact; r:gives {2000 log:repeat 932}] [ a r:Fact; r:gives {(932 2000) math:sum 2932}] - skolem:lemma1932 + skolem:lemma2931 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 932]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2932]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma933 a r:Inference; r:gives { 2933 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 933}] + [ a r:Fact; r:gives {2000 log:repeat 933}] [ a r:Fact; r:gives {(933 2000) math:sum 2933}] - skolem:lemma1933 + skolem:lemma2932 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 933]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2933]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma934 a r:Inference; r:gives { 2934 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 934}] + [ a r:Fact; r:gives {2000 log:repeat 934}] [ a r:Fact; r:gives {(934 2000) math:sum 2934}] - skolem:lemma1934 + skolem:lemma2933 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 934]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2934]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma935 a r:Inference; r:gives { 2935 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 935}] + [ a r:Fact; r:gives {2000 log:repeat 935}] [ a r:Fact; r:gives {(935 2000) math:sum 2935}] - skolem:lemma1935 + skolem:lemma2934 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 935]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2935]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma936 a r:Inference; r:gives { 2936 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 936}] + [ a r:Fact; r:gives {2000 log:repeat 936}] [ a r:Fact; r:gives {(936 2000) math:sum 2936}] - skolem:lemma1936 + skolem:lemma2935 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 936]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2936]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma937 a r:Inference; r:gives { 2937 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 937}] + [ a r:Fact; r:gives {2000 log:repeat 937}] [ a r:Fact; r:gives {(937 2000) math:sum 2937}] - skolem:lemma1937 + skolem:lemma2936 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 937]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2937]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma938 a r:Inference; r:gives { 2938 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 938}] + [ a r:Fact; r:gives {2000 log:repeat 938}] [ a r:Fact; r:gives {(938 2000) math:sum 2938}] - skolem:lemma1938 + skolem:lemma2937 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 938]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2938]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma939 a r:Inference; r:gives { 2939 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 939}] + [ a r:Fact; r:gives {2000 log:repeat 939}] [ a r:Fact; r:gives {(939 2000) math:sum 2939}] - skolem:lemma1939 + skolem:lemma2938 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 939]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2939]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma940 a r:Inference; r:gives { 2940 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 940}] + [ a r:Fact; r:gives {2000 log:repeat 940}] [ a r:Fact; r:gives {(940 2000) math:sum 2940}] - skolem:lemma1940 + skolem:lemma2939 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 940]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2940]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma941 a r:Inference; r:gives { 2941 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 941}] + [ a r:Fact; r:gives {2000 log:repeat 941}] [ a r:Fact; r:gives {(941 2000) math:sum 2941}] - skolem:lemma1941 + skolem:lemma2940 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 941]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2941]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma942 a r:Inference; r:gives { 2942 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 942}] + [ a r:Fact; r:gives {2000 log:repeat 942}] [ a r:Fact; r:gives {(942 2000) math:sum 2942}] - skolem:lemma1942 + skolem:lemma2941 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 942]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2942]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma943 a r:Inference; r:gives { 2943 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 943}] + [ a r:Fact; r:gives {2000 log:repeat 943}] [ a r:Fact; r:gives {(943 2000) math:sum 2943}] - skolem:lemma1943 + skolem:lemma2942 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 943]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2943]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma944 a r:Inference; r:gives { 2944 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 944}] + [ a r:Fact; r:gives {2000 log:repeat 944}] [ a r:Fact; r:gives {(944 2000) math:sum 2944}] - skolem:lemma1944 + skolem:lemma2943 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 944]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2944]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma945 a r:Inference; r:gives { 2945 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 945}] + [ a r:Fact; r:gives {2000 log:repeat 945}] [ a r:Fact; r:gives {(945 2000) math:sum 2945}] - skolem:lemma1945 + skolem:lemma2944 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 945]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2945]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma946 a r:Inference; r:gives { 2946 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 946}] + [ a r:Fact; r:gives {2000 log:repeat 946}] [ a r:Fact; r:gives {(946 2000) math:sum 2946}] - skolem:lemma1946 + skolem:lemma2945 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 946]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2946]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma947 a r:Inference; r:gives { 2947 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 947}] + [ a r:Fact; r:gives {2000 log:repeat 947}] [ a r:Fact; r:gives {(947 2000) math:sum 2947}] - skolem:lemma1947 + skolem:lemma2946 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 947]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2947]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma948 a r:Inference; r:gives { 2948 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 948}] + [ a r:Fact; r:gives {2000 log:repeat 948}] [ a r:Fact; r:gives {(948 2000) math:sum 2948}] - skolem:lemma1948 + skolem:lemma2947 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 948]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2948]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma949 a r:Inference; r:gives { 2949 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 949}] + [ a r:Fact; r:gives {2000 log:repeat 949}] [ a r:Fact; r:gives {(949 2000) math:sum 2949}] - skolem:lemma1949 + skolem:lemma2948 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 949]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2949]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma950 a r:Inference; r:gives { 2950 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 950}] + [ a r:Fact; r:gives {2000 log:repeat 950}] [ a r:Fact; r:gives {(950 2000) math:sum 2950}] - skolem:lemma1950 + skolem:lemma2949 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 950]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2950]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma951 a r:Inference; r:gives { 2951 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 951}] + [ a r:Fact; r:gives {2000 log:repeat 951}] [ a r:Fact; r:gives {(951 2000) math:sum 2951}] - skolem:lemma1951 + skolem:lemma2950 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 951]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2951]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma952 a r:Inference; r:gives { 2952 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 952}] + [ a r:Fact; r:gives {2000 log:repeat 952}] [ a r:Fact; r:gives {(952 2000) math:sum 2952}] - skolem:lemma1952 + skolem:lemma2951 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 952]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2952]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma953 a r:Inference; r:gives { 2953 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 953}] + [ a r:Fact; r:gives {2000 log:repeat 953}] [ a r:Fact; r:gives {(953 2000) math:sum 2953}] - skolem:lemma1953 + skolem:lemma2952 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 953]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2953]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma954 a r:Inference; r:gives { 2954 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 954}] + [ a r:Fact; r:gives {2000 log:repeat 954}] [ a r:Fact; r:gives {(954 2000) math:sum 2954}] - skolem:lemma1954 + skolem:lemma2953 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 954]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2954]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma955 a r:Inference; r:gives { 2955 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 955}] + [ a r:Fact; r:gives {2000 log:repeat 955}] [ a r:Fact; r:gives {(955 2000) math:sum 2955}] - skolem:lemma1955 + skolem:lemma2954 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 955]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2955]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma956 a r:Inference; r:gives { 2956 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 956}] + [ a r:Fact; r:gives {2000 log:repeat 956}] [ a r:Fact; r:gives {(956 2000) math:sum 2956}] - skolem:lemma1956 + skolem:lemma2955 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 956]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2956]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma957 a r:Inference; r:gives { 2957 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 957}] + [ a r:Fact; r:gives {2000 log:repeat 957}] [ a r:Fact; r:gives {(957 2000) math:sum 2957}] - skolem:lemma1957 + skolem:lemma2956 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 957]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2957]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma958 a r:Inference; r:gives { 2958 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 958}] + [ a r:Fact; r:gives {2000 log:repeat 958}] [ a r:Fact; r:gives {(958 2000) math:sum 2958}] - skolem:lemma1958 + skolem:lemma2957 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 958]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2958]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma959 a r:Inference; r:gives { 2959 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 959}] + [ a r:Fact; r:gives {2000 log:repeat 959}] [ a r:Fact; r:gives {(959 2000) math:sum 2959}] - skolem:lemma1959 + skolem:lemma2958 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 959]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2959]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma960 a r:Inference; r:gives { 2960 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 960}] + [ a r:Fact; r:gives {2000 log:repeat 960}] [ a r:Fact; r:gives {(960 2000) math:sum 2960}] - skolem:lemma1960 + skolem:lemma2959 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 960]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2960]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma961 a r:Inference; r:gives { 2961 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 961}] + [ a r:Fact; r:gives {2000 log:repeat 961}] [ a r:Fact; r:gives {(961 2000) math:sum 2961}] - skolem:lemma1961 + skolem:lemma2960 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 961]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2961]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma962 a r:Inference; r:gives { 2962 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 962}] + [ a r:Fact; r:gives {2000 log:repeat 962}] [ a r:Fact; r:gives {(962 2000) math:sum 2962}] - skolem:lemma1962 + skolem:lemma2961 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 962]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2962]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma963 a r:Inference; r:gives { 2963 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 963}] + [ a r:Fact; r:gives {2000 log:repeat 963}] [ a r:Fact; r:gives {(963 2000) math:sum 2963}] - skolem:lemma1963 + skolem:lemma2962 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 963]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2963]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma964 a r:Inference; r:gives { 2964 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 964}] + [ a r:Fact; r:gives {2000 log:repeat 964}] [ a r:Fact; r:gives {(964 2000) math:sum 2964}] - skolem:lemma1964 + skolem:lemma2963 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 964]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2964]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma965 a r:Inference; r:gives { 2965 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 965}] + [ a r:Fact; r:gives {2000 log:repeat 965}] [ a r:Fact; r:gives {(965 2000) math:sum 2965}] - skolem:lemma1965 + skolem:lemma2964 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 965]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2965]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma966 a r:Inference; r:gives { 2966 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 966}] + [ a r:Fact; r:gives {2000 log:repeat 966}] [ a r:Fact; r:gives {(966 2000) math:sum 2966}] - skolem:lemma1966 + skolem:lemma2965 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 966]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2966]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma967 a r:Inference; r:gives { 2967 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 967}] + [ a r:Fact; r:gives {2000 log:repeat 967}] [ a r:Fact; r:gives {(967 2000) math:sum 2967}] - skolem:lemma1967 + skolem:lemma2966 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 967]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2967]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma968 a r:Inference; r:gives { 2968 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 968}] + [ a r:Fact; r:gives {2000 log:repeat 968}] [ a r:Fact; r:gives {(968 2000) math:sum 2968}] - skolem:lemma1968 + skolem:lemma2967 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 968]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2968]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma969 a r:Inference; r:gives { 2969 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 969}] + [ a r:Fact; r:gives {2000 log:repeat 969}] [ a r:Fact; r:gives {(969 2000) math:sum 2969}] - skolem:lemma1969 + skolem:lemma2968 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 969]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2969]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma970 a r:Inference; r:gives { 2970 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 970}] + [ a r:Fact; r:gives {2000 log:repeat 970}] [ a r:Fact; r:gives {(970 2000) math:sum 2970}] - skolem:lemma1970 + skolem:lemma2969 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 970]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2970]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma971 a r:Inference; r:gives { 2971 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 971}] + [ a r:Fact; r:gives {2000 log:repeat 971}] [ a r:Fact; r:gives {(971 2000) math:sum 2971}] - skolem:lemma1971 + skolem:lemma2970 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 971]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2971]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma972 a r:Inference; r:gives { 2972 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 972}] + [ a r:Fact; r:gives {2000 log:repeat 972}] [ a r:Fact; r:gives {(972 2000) math:sum 2972}] - skolem:lemma1972 + skolem:lemma2971 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 972]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2972]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma973 a r:Inference; r:gives { 2973 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 973}] + [ a r:Fact; r:gives {2000 log:repeat 973}] [ a r:Fact; r:gives {(973 2000) math:sum 2973}] - skolem:lemma1973 + skolem:lemma2972 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 973]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2973]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma974 a r:Inference; r:gives { 2974 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 974}] + [ a r:Fact; r:gives {2000 log:repeat 974}] [ a r:Fact; r:gives {(974 2000) math:sum 2974}] - skolem:lemma1974 + skolem:lemma2973 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 974]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2974]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma975 a r:Inference; r:gives { 2975 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 975}] + [ a r:Fact; r:gives {2000 log:repeat 975}] [ a r:Fact; r:gives {(975 2000) math:sum 2975}] - skolem:lemma1975 + skolem:lemma2974 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 975]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2975]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma976 a r:Inference; r:gives { 2976 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 976}] + [ a r:Fact; r:gives {2000 log:repeat 976}] [ a r:Fact; r:gives {(976 2000) math:sum 2976}] - skolem:lemma1976 + skolem:lemma2975 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 976]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2976]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma977 a r:Inference; r:gives { 2977 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 977}] + [ a r:Fact; r:gives {2000 log:repeat 977}] [ a r:Fact; r:gives {(977 2000) math:sum 2977}] - skolem:lemma1977 + skolem:lemma2976 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 977]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2977]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma978 a r:Inference; r:gives { 2978 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 978}] + [ a r:Fact; r:gives {2000 log:repeat 978}] [ a r:Fact; r:gives {(978 2000) math:sum 2978}] - skolem:lemma1978 + skolem:lemma2977 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 978]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2978]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma979 a r:Inference; r:gives { 2979 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 979}] + [ a r:Fact; r:gives {2000 log:repeat 979}] [ a r:Fact; r:gives {(979 2000) math:sum 2979}] - skolem:lemma1979 + skolem:lemma2978 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 979]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2979]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma980 a r:Inference; r:gives { 2980 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 980}] + [ a r:Fact; r:gives {2000 log:repeat 980}] [ a r:Fact; r:gives {(980 2000) math:sum 2980}] - skolem:lemma1980 + skolem:lemma2979 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 980]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2980]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma981 a r:Inference; r:gives { 2981 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 981}] + [ a r:Fact; r:gives {2000 log:repeat 981}] [ a r:Fact; r:gives {(981 2000) math:sum 2981}] - skolem:lemma1981 + skolem:lemma2980 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 981]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2981]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma982 a r:Inference; r:gives { 2982 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 982}] + [ a r:Fact; r:gives {2000 log:repeat 982}] [ a r:Fact; r:gives {(982 2000) math:sum 2982}] - skolem:lemma1982 + skolem:lemma2981 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 982]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2982]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma983 a r:Inference; r:gives { 2983 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 983}] + [ a r:Fact; r:gives {2000 log:repeat 983}] [ a r:Fact; r:gives {(983 2000) math:sum 2983}] - skolem:lemma1983 + skolem:lemma2982 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 983]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2983]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma984 a r:Inference; r:gives { 2984 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 984}] + [ a r:Fact; r:gives {2000 log:repeat 984}] [ a r:Fact; r:gives {(984 2000) math:sum 2984}] - skolem:lemma1984 + skolem:lemma2983 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 984]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2984]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma985 a r:Inference; r:gives { 2985 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 985}] + [ a r:Fact; r:gives {2000 log:repeat 985}] [ a r:Fact; r:gives {(985 2000) math:sum 2985}] - skolem:lemma1985 + skolem:lemma2984 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 985]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2985]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma986 a r:Inference; r:gives { 2986 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 986}] + [ a r:Fact; r:gives {2000 log:repeat 986}] [ a r:Fact; r:gives {(986 2000) math:sum 2986}] - skolem:lemma1986 + skolem:lemma2985 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 986]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2986]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma987 a r:Inference; r:gives { 2987 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 987}] + [ a r:Fact; r:gives {2000 log:repeat 987}] [ a r:Fact; r:gives {(987 2000) math:sum 2987}] - skolem:lemma1987 + skolem:lemma2986 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 987]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2987]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma988 a r:Inference; r:gives { 2988 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 988}] + [ a r:Fact; r:gives {2000 log:repeat 988}] [ a r:Fact; r:gives {(988 2000) math:sum 2988}] - skolem:lemma1988 + skolem:lemma2987 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 988]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2988]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma989 a r:Inference; r:gives { 2989 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 989}] + [ a r:Fact; r:gives {2000 log:repeat 989}] [ a r:Fact; r:gives {(989 2000) math:sum 2989}] - skolem:lemma1989 + skolem:lemma2988 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 989]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2989]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma990 a r:Inference; r:gives { 2990 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 990}] + [ a r:Fact; r:gives {2000 log:repeat 990}] [ a r:Fact; r:gives {(990 2000) math:sum 2990}] - skolem:lemma1990 + skolem:lemma2989 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 990]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2990]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma991 a r:Inference; r:gives { 2991 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 991}] + [ a r:Fact; r:gives {2000 log:repeat 991}] [ a r:Fact; r:gives {(991 2000) math:sum 2991}] - skolem:lemma1991 + skolem:lemma2990 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 991]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2991]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma992 a r:Inference; r:gives { 2992 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 992}] + [ a r:Fact; r:gives {2000 log:repeat 992}] [ a r:Fact; r:gives {(992 2000) math:sum 2992}] - skolem:lemma1992 + skolem:lemma2991 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 992]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2992]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma993 a r:Inference; r:gives { 2993 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 993}] + [ a r:Fact; r:gives {2000 log:repeat 993}] [ a r:Fact; r:gives {(993 2000) math:sum 2993}] - skolem:lemma1993 + skolem:lemma2992 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 993]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2993]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma994 a r:Inference; r:gives { 2994 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 994}] + [ a r:Fact; r:gives {2000 log:repeat 994}] [ a r:Fact; r:gives {(994 2000) math:sum 2994}] - skolem:lemma1994 + skolem:lemma2993 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 994]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2994]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma995 a r:Inference; r:gives { 2995 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 995}] + [ a r:Fact; r:gives {2000 log:repeat 995}] [ a r:Fact; r:gives {(995 2000) math:sum 2995}] - skolem:lemma1995 + skolem:lemma2994 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 995]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2995]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma996 a r:Inference; r:gives { 2996 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 996}] + [ a r:Fact; r:gives {2000 log:repeat 996}] [ a r:Fact; r:gives {(996 2000) math:sum 2996}] - skolem:lemma1996 + skolem:lemma2995 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 996]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2996]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma997 a r:Inference; r:gives { 2997 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 997}] + [ a r:Fact; r:gives {2000 log:repeat 997}] [ a r:Fact; r:gives {(997 2000) math:sum 2997}] - skolem:lemma1997 + skolem:lemma2996 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 997]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2997]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma998 a r:Inference; r:gives { 2998 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 998}] + [ a r:Fact; r:gives {2000 log:repeat 998}] [ a r:Fact; r:gives {(998 2000) math:sum 2998}] - skolem:lemma1998 + skolem:lemma2997 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 998]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2998]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma999 a r:Inference; r:gives { 2999 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {1000 log:repeat 999}] + [ a r:Fact; r:gives {2000 log:repeat 999}] [ a r:Fact; r:gives {(999 2000) math:sum 2999}] - skolem:lemma1999 + skolem:lemma2998 ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 999]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2999]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:rule skolem:lemma1001. + r:rule skolem:lemma2000. skolem:lemma1000 a r:Inference; r:gives { - 2000 :kaprekar (0 4). + 3000 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2000 math:notEqualTo 0}] - skolem:lemma2000 - [ a r:Fact; r:gives {((2 0 0 0) "=<") list:sort (0 0 0 2)}] - [ a r:Fact; r:gives {((2 0 0 0) ">=") list:sort (2 0 0 0)}] - skolem:lemma2001 - skolem:lemma2002 - [ a r:Fact; r:gives {(2000 2) math:difference 1998}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1998 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1998 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1000}] + [ a r:Fact; r:gives {(1000 2000) math:sum 3000}] + skolem:lemma2999 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. -skolem:lemma1001 a r:Extraction; +skolem:lemma1001 a r:Inference; r:gives { - @forAll var:x_0, var:x_1, var:x_2. { - 1000 log:repeat var:x_0. - (var:x_0 2000) math:sum var:x_1. - var:x_1 :kaprekar (0 var:x_2). - } => { - var:x_1 :recursionCount var:x_2. - }. + 3001 :recursionCount 3 . }; - r:because [ a r:Parsing; r:source ]. + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1001}] + [ a r:Fact; r:gives {(1001 2000) math:sum 3001}] + skolem:lemma3000 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1001]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3001]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1002 a r:Inference; r:gives { - 2001 :kaprekar (0 3). + 3002 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2001 math:notEqualTo 0}] - skolem:lemma2004 - [ a r:Fact; r:gives {((2 0 0 1) "=<") list:sort (0 0 1 2)}] - [ a r:Fact; r:gives {((2 0 0 1) ">=") list:sort (2 1 0 0)}] - skolem:lemma2005 - skolem:lemma2006 - [ a r:Fact; r:gives {(2100 12) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1002}] + [ a r:Fact; r:gives {(1002 2000) math:sum 3002}] + skolem:lemma3001 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2001]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2100]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1002]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3002]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1003 a r:Inference; r:gives { - 2002 :kaprekar (0 6). + 3003 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2002 math:notEqualTo 0}] - skolem:lemma2007 - [ a r:Fact; r:gives {((2 0 0 2) "=<") list:sort (0 0 2 2)}] - [ a r:Fact; r:gives {((2 0 0 2) ">=") list:sort (2 2 0 0)}] - skolem:lemma2008 - skolem:lemma2009 - [ a r:Fact; r:gives {(2200 22) math:difference 2178}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2178 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2178 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1003}] + [ a r:Fact; r:gives {(1003 2000) math:sum 3003}] + skolem:lemma3002 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2002]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2178]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1003]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3003]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1004 a r:Inference; r:gives { - 2003 :kaprekar (0 5). + 3004 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2003 math:notEqualTo 0}] - skolem:lemma2010 - [ a r:Fact; r:gives {((2 0 0 3) "=<") list:sort (0 0 2 3)}] - [ a r:Fact; r:gives {((2 0 0 3) ">=") list:sort (3 2 0 0)}] - skolem:lemma2011 - skolem:lemma2012 - [ a r:Fact; r:gives {(3200 23) math:difference 3177}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3177 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 3177 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1004}] + [ a r:Fact; r:gives {(1004 2000) math:sum 3004}] + skolem:lemma3003 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2003]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1004]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3004]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1005 a r:Inference; r:gives { - 2004 :kaprekar (0 2). + 3005 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2004 math:notEqualTo 0}] - skolem:lemma2013 - [ a r:Fact; r:gives {((2 0 0 4) "=<") list:sort (0 0 2 4)}] - [ a r:Fact; r:gives {((2 0 0 4) ">=") list:sort (4 2 0 0)}] - skolem:lemma2014 - skolem:lemma2015 - [ a r:Fact; r:gives {(4200 24) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1005}] + [ a r:Fact; r:gives {(1005 2000) math:sum 3005}] + skolem:lemma3004 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2004]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1005]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3005]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1006 a r:Inference; r:gives { - 2005 :kaprekar (0 7). + 3006 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2005 math:notEqualTo 0}] - skolem:lemma2016 - [ a r:Fact; r:gives {((2 0 0 5) "=<") list:sort (0 0 2 5)}] - [ a r:Fact; r:gives {((2 0 0 5) ">=") list:sort (5 2 0 0)}] - skolem:lemma2017 - skolem:lemma2018 - [ a r:Fact; r:gives {(5200 25) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1006}] + [ a r:Fact; r:gives {(1006 2000) math:sum 3006}] + skolem:lemma3005 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2005]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1006]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3006]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1007 a r:Inference; r:gives { - 2006 :kaprekar (0 1). + 3007 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2006 math:notEqualTo 0}] - skolem:lemma2019 - [ a r:Fact; r:gives {((2 0 0 6) "=<") list:sort (0 0 2 6)}] - [ a r:Fact; r:gives {((2 0 0 6) ">=") list:sort (6 2 0 0)}] - skolem:lemma2020 - skolem:lemma2021 - [ a r:Fact; r:gives {(6200 26) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1007}] + [ a r:Fact; r:gives {(1007 2000) math:sum 3007}] + skolem:lemma3006 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2006]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1007]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3007]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1008 a r:Inference; r:gives { - 2007 :kaprekar (0 5). + 3008 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2007 math:notEqualTo 0}] - skolem:lemma2022 - [ a r:Fact; r:gives {((2 0 0 7) "=<") list:sort (0 0 2 7)}] - [ a r:Fact; r:gives {((2 0 0 7) ">=") list:sort (7 2 0 0)}] - skolem:lemma2023 - skolem:lemma2024 - [ a r:Fact; r:gives {(7200 27) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1008}] + [ a r:Fact; r:gives {(1008 2000) math:sum 3008}] + skolem:lemma3007 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2007]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1008]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3008]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1009 a r:Inference; r:gives { - 2008 :kaprekar (0 6). + 3009 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2008 math:notEqualTo 0}] - skolem:lemma2025 - [ a r:Fact; r:gives {((2 0 0 8) "=<") list:sort (0 0 2 8)}] - [ a r:Fact; r:gives {((2 0 0 8) ">=") list:sort (8 2 0 0)}] - skolem:lemma2026 - skolem:lemma2027 - [ a r:Fact; r:gives {(8200 28) math:difference 8172}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8172 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 8172 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1009}] + [ a r:Fact; r:gives {(1009 2000) math:sum 3009}] + skolem:lemma3008 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2008]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1009]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3009]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1010 a r:Inference; r:gives { - 2009 :kaprekar (0 3). + 3010 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2009 math:notEqualTo 0}] - skolem:lemma2028 - [ a r:Fact; r:gives {((2 0 0 9) "=<") list:sort (0 0 2 9)}] - [ a r:Fact; r:gives {((2 0 0 9) ">=") list:sort (9 2 0 0)}] - skolem:lemma2029 - skolem:lemma2030 - [ a r:Fact; r:gives {(9200 29) math:difference 9171}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9171 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 9171 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1010}] + [ a r:Fact; r:gives {(1010 2000) math:sum 3010}] + skolem:lemma3009 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2009]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1010]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3010]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1011 a r:Inference; r:gives { - 2010 :kaprekar (0 3). + 3011 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2010 math:notEqualTo 0}] - skolem:lemma2031 - [ a r:Fact; r:gives {((2 0 1 0) "=<") list:sort (0 0 1 2)}] - [ a r:Fact; r:gives {((2 0 1 0) ">=") list:sort (2 1 0 0)}] - skolem:lemma2005 - skolem:lemma2006 - [ a r:Fact; r:gives {(2100 12) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1011}] + [ a r:Fact; r:gives {(1011 2000) math:sum 3011}] + skolem:lemma3010 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2010]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2100]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1011]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3011]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1012 a r:Inference; r:gives { - 2011 :kaprekar (0 4). + 3012 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2011 math:notEqualTo 0}] - skolem:lemma2032 - [ a r:Fact; r:gives {((2 0 1 1) "=<") list:sort (0 1 1 2)}] - [ a r:Fact; r:gives {((2 0 1 1) ">=") list:sort (2 1 1 0)}] - skolem:lemma2033 - skolem:lemma2034 - [ a r:Fact; r:gives {(2110 112) math:difference 1998}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1998 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1998 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1012}] + [ a r:Fact; r:gives {(1012 2000) math:sum 3012}] + skolem:lemma3011 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2011]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 112]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2110]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1012]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3012]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1013 a r:Inference; r:gives { - 2012 :kaprekar (0 3). + 3013 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2012 math:notEqualTo 0}] - skolem:lemma2035 - [ a r:Fact; r:gives {((2 0 1 2) "=<") list:sort (0 1 2 2)}] - [ a r:Fact; r:gives {((2 0 1 2) ">=") list:sort (2 2 1 0)}] - skolem:lemma2036 - skolem:lemma2037 - [ a r:Fact; r:gives {(2210 122) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1013}] + [ a r:Fact; r:gives {(1013 2000) math:sum 3013}] + skolem:lemma3012 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2012]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 122]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1013]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3013]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1014 a r:Inference; r:gives { - 2013 :kaprekar (0 3). + 3014 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2013 math:notEqualTo 0}] - skolem:lemma2038 - [ a r:Fact; r:gives {((2 0 1 3) "=<") list:sort (0 1 2 3)}] - [ a r:Fact; r:gives {((2 0 1 3) ">=") list:sort (3 2 1 0)}] - skolem:lemma2039 - skolem:lemma2040 - [ a r:Fact; r:gives {(3210 123) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1014}] + [ a r:Fact; r:gives {(1014 2000) math:sum 3014}] + skolem:lemma3013 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2013]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 123]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1014]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3014]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1015 a r:Inference; r:gives { - 2014 :kaprekar (0 7). + 3015 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2014 math:notEqualTo 0}] - skolem:lemma2041 - [ a r:Fact; r:gives {((2 0 1 4) "=<") list:sort (0 1 2 4)}] - [ a r:Fact; r:gives {((2 0 1 4) ">=") list:sort (4 2 1 0)}] - skolem:lemma2042 - skolem:lemma2043 - [ a r:Fact; r:gives {(4210 124) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1015}] + [ a r:Fact; r:gives {(1015 2000) math:sum 3015}] + skolem:lemma3014 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2014]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 124]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1015]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3015]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1016 a r:Inference; r:gives { - 2015 :kaprekar (0 7). + 3016 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2015 math:notEqualTo 0}] - skolem:lemma2044 - [ a r:Fact; r:gives {((2 0 1 5) "=<") list:sort (0 1 2 5)}] - [ a r:Fact; r:gives {((2 0 1 5) ">=") list:sort (5 2 1 0)}] - skolem:lemma2045 - skolem:lemma2046 - [ a r:Fact; r:gives {(5210 125) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1016}] + [ a r:Fact; r:gives {(1016 2000) math:sum 3016}] + skolem:lemma3015 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2015]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 125]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1016]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3016]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1017 a r:Inference; r:gives { - 2016 :kaprekar (0 7). + 3017 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2016 math:notEqualTo 0}] - skolem:lemma2047 - [ a r:Fact; r:gives {((2 0 1 6) "=<") list:sort (0 1 2 6)}] - [ a r:Fact; r:gives {((2 0 1 6) ">=") list:sort (6 2 1 0)}] - skolem:lemma2048 - skolem:lemma2049 - [ a r:Fact; r:gives {(6210 126) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1017}] + [ a r:Fact; r:gives {(1017 2000) math:sum 3017}] + skolem:lemma3016 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2016]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 126]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1017]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3017]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1018 a r:Inference; r:gives { - 2017 :kaprekar (0 3). + 3018 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2017 math:notEqualTo 0}] - skolem:lemma2050 - [ a r:Fact; r:gives {((2 0 1 7) "=<") list:sort (0 1 2 7)}] - [ a r:Fact; r:gives {((2 0 1 7) ">=") list:sort (7 2 1 0)}] - skolem:lemma2051 - skolem:lemma2052 - [ a r:Fact; r:gives {(7210 127) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1018}] + [ a r:Fact; r:gives {(1018 2000) math:sum 3018}] + skolem:lemma3017 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2017]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 127]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1018]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3018]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1019 a r:Inference; r:gives { - 2018 :kaprekar (0 3). + 3019 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2018 math:notEqualTo 0}] - skolem:lemma2053 - [ a r:Fact; r:gives {((2 0 1 8) "=<") list:sort (0 1 2 8)}] - [ a r:Fact; r:gives {((2 0 1 8) ">=") list:sort (8 2 1 0)}] - skolem:lemma2054 - skolem:lemma2055 - [ a r:Fact; r:gives {(8210 128) math:difference 8082}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8082 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 8082 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1019}] + [ a r:Fact; r:gives {(1019 2000) math:sum 3019}] + skolem:lemma3018 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2018]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 128]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1019]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3019]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1020 a r:Inference; r:gives { - 2019 :kaprekar (0 4). + 3020 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2019 math:notEqualTo 0}] - skolem:lemma2056 - [ a r:Fact; r:gives {((2 0 1 9) "=<") list:sort (0 1 2 9)}] - [ a r:Fact; r:gives {((2 0 1 9) ">=") list:sort (9 2 1 0)}] - skolem:lemma2057 - skolem:lemma2058 - [ a r:Fact; r:gives {(9210 129) math:difference 9081}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9081 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 9081 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1020}] + [ a r:Fact; r:gives {(1020 2000) math:sum 3020}] + skolem:lemma3019 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2019]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 129]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1020]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3020]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1021 a r:Inference; r:gives { - 2020 :kaprekar (0 6). + 3021 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2020 math:notEqualTo 0}] - skolem:lemma2059 - [ a r:Fact; r:gives {((2 0 2 0) "=<") list:sort (0 0 2 2)}] - [ a r:Fact; r:gives {((2 0 2 0) ">=") list:sort (2 2 0 0)}] - skolem:lemma2008 - skolem:lemma2009 - [ a r:Fact; r:gives {(2200 22) math:difference 2178}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2178 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2178 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1021}] + [ a r:Fact; r:gives {(1021 2000) math:sum 3021}] + skolem:lemma3020 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2020]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2178]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1021]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3021]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1022 a r:Inference; r:gives { - 2021 :kaprekar (0 3). + 3022 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2021 math:notEqualTo 0}] - skolem:lemma2060 - [ a r:Fact; r:gives {((2 0 2 1) "=<") list:sort (0 1 2 2)}] - [ a r:Fact; r:gives {((2 0 2 1) ">=") list:sort (2 2 1 0)}] - skolem:lemma2036 - skolem:lemma2037 - [ a r:Fact; r:gives {(2210 122) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1022}] + [ a r:Fact; r:gives {(1022 2000) math:sum 3022}] + skolem:lemma3021 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2021]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 122]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1022]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3022]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1023 a r:Inference; r:gives { - 2022 :kaprekar (0 4). + 3023 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2022 math:notEqualTo 0}] - skolem:lemma2061 - [ a r:Fact; r:gives {((2 0 2 2) "=<") list:sort (0 2 2 2)}] - [ a r:Fact; r:gives {((2 0 2 2) ">=") list:sort (2 2 2 0)}] - skolem:lemma2062 - skolem:lemma2063 - [ a r:Fact; r:gives {(2220 222) math:difference 1998}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1998 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1998 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1023}] + [ a r:Fact; r:gives {(1023 2000) math:sum 3023}] + skolem:lemma3022 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2022]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1023]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3023]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1024 a r:Inference; r:gives { - 2023 :kaprekar (0 6). + 3024 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2023 math:notEqualTo 0}] - skolem:lemma2064 - [ a r:Fact; r:gives {((2 0 2 3) "=<") list:sort (0 2 2 3)}] - [ a r:Fact; r:gives {((2 0 2 3) ">=") list:sort (3 2 2 0)}] - skolem:lemma2065 - skolem:lemma2066 - [ a r:Fact; r:gives {(3220 223) math:difference 2997}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2997 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2997 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1024}] + [ a r:Fact; r:gives {(1024 2000) math:sum 3024}] + skolem:lemma3023 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2023]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 223]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1024]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3024]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1025 a r:Inference; r:gives { - 2024 :kaprekar (0 4). + 3025 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2024 math:notEqualTo 0}] - skolem:lemma2067 - [ a r:Fact; r:gives {((2 0 2 4) "=<") list:sort (0 2 2 4)}] - [ a r:Fact; r:gives {((2 0 2 4) ">=") list:sort (4 2 2 0)}] - skolem:lemma2068 - skolem:lemma2069 - [ a r:Fact; r:gives {(4220 224) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1025}] + [ a r:Fact; r:gives {(1025 2000) math:sum 3025}] + skolem:lemma3024 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2024]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 224]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1025]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3025]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1026 a r:Inference; r:gives { - 2025 :kaprekar (0 6). + 3026 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2025 math:notEqualTo 0}] - skolem:lemma2070 - [ a r:Fact; r:gives {((2 0 2 5) "=<") list:sort (0 2 2 5)}] - [ a r:Fact; r:gives {((2 0 2 5) ">=") list:sort (5 2 2 0)}] - skolem:lemma2071 - skolem:lemma2072 - [ a r:Fact; r:gives {(5220 225) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1026}] + [ a r:Fact; r:gives {(1026 2000) math:sum 3026}] + skolem:lemma3025 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2025]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 225]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1026]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3026]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1027 a r:Inference; r:gives { - 2026 :kaprekar (0 6). + 3027 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2026 math:notEqualTo 0}] - skolem:lemma2073 - [ a r:Fact; r:gives {((2 0 2 6) "=<") list:sort (0 2 2 6)}] - [ a r:Fact; r:gives {((2 0 2 6) ">=") list:sort (6 2 2 0)}] - skolem:lemma2074 - skolem:lemma2075 - [ a r:Fact; r:gives {(6220 226) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1027}] + [ a r:Fact; r:gives {(1027 2000) math:sum 3027}] + skolem:lemma3026 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2026]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 226]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1027]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3027]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1028 a r:Inference; r:gives { - 2027 :kaprekar (0 4). + 3028 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2027 math:notEqualTo 0}] - skolem:lemma2076 - [ a r:Fact; r:gives {((2 0 2 7) "=<") list:sort (0 2 2 7)}] - [ a r:Fact; r:gives {((2 0 2 7) ">=") list:sort (7 2 2 0)}] - skolem:lemma2077 - skolem:lemma2078 - [ a r:Fact; r:gives {(7220 227) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1028}] + [ a r:Fact; r:gives {(1028 2000) math:sum 3028}] + skolem:lemma3027 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2027]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 227]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1028]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3028]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1029 a r:Inference; r:gives { - 2028 :kaprekar (0 6). + 3029 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2028 math:notEqualTo 0}] - skolem:lemma2079 - [ a r:Fact; r:gives {((2 0 2 8) "=<") list:sort (0 2 2 8)}] - [ a r:Fact; r:gives {((2 0 2 8) ">=") list:sort (8 2 2 0)}] - skolem:lemma2080 - skolem:lemma2081 - [ a r:Fact; r:gives {(8220 228) math:difference 7992}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7992 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7992 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1029}] + [ a r:Fact; r:gives {(1029 2000) math:sum 3029}] + skolem:lemma3028 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2028]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 228]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1029]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3029]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1030 a r:Inference; r:gives { - 2029 :kaprekar (0 4). + 3030 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2029 math:notEqualTo 0}] - skolem:lemma2082 - [ a r:Fact; r:gives {((2 0 2 9) "=<") list:sort (0 2 2 9)}] - [ a r:Fact; r:gives {((2 0 2 9) ">=") list:sort (9 2 2 0)}] - skolem:lemma2083 - skolem:lemma2084 - [ a r:Fact; r:gives {(9220 229) math:difference 8991}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8991 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 8991 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1030}] + [ a r:Fact; r:gives {(1030 2000) math:sum 3030}] + skolem:lemma3029 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2029]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 229]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8991]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1030]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3030]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1031 a r:Inference; r:gives { - 2030 :kaprekar (0 5). + 3031 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2030 math:notEqualTo 0}] - skolem:lemma2085 - [ a r:Fact; r:gives {((2 0 3 0) "=<") list:sort (0 0 2 3)}] - [ a r:Fact; r:gives {((2 0 3 0) ">=") list:sort (3 2 0 0)}] - skolem:lemma2011 - skolem:lemma2012 - [ a r:Fact; r:gives {(3200 23) math:difference 3177}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3177 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 3177 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1031}] + [ a r:Fact; r:gives {(1031 2000) math:sum 3031}] + skolem:lemma3030 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2030]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1031]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3031]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1032 a r:Inference; r:gives { - 2031 :kaprekar (0 3). + 3032 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2031 math:notEqualTo 0}] - skolem:lemma2086 - [ a r:Fact; r:gives {((2 0 3 1) "=<") list:sort (0 1 2 3)}] - [ a r:Fact; r:gives {((2 0 3 1) ">=") list:sort (3 2 1 0)}] - skolem:lemma2039 - skolem:lemma2040 - [ a r:Fact; r:gives {(3210 123) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1032}] + [ a r:Fact; r:gives {(1032 2000) math:sum 3032}] + skolem:lemma3031 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2031]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 123]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1032]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3032]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1033 a r:Inference; r:gives { - 2032 :kaprekar (0 6). + 3033 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2032 math:notEqualTo 0}] - skolem:lemma2087 - [ a r:Fact; r:gives {((2 0 3 2) "=<") list:sort (0 2 2 3)}] - [ a r:Fact; r:gives {((2 0 3 2) ">=") list:sort (3 2 2 0)}] - skolem:lemma2065 - skolem:lemma2066 - [ a r:Fact; r:gives {(3220 223) math:difference 2997}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2997 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2997 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1033}] + [ a r:Fact; r:gives {(1033 2000) math:sum 3033}] + skolem:lemma3032 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2032]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 223]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1033]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3033]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1034 a r:Inference; r:gives { - 2033 :kaprekar (0 3). + 3034 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2033 math:notEqualTo 0}] - skolem:lemma2088 - [ a r:Fact; r:gives {((2 0 3 3) "=<") list:sort (0 2 3 3)}] - [ a r:Fact; r:gives {((2 0 3 3) ">=") list:sort (3 3 2 0)}] - skolem:lemma2089 - skolem:lemma2090 - [ a r:Fact; r:gives {(3320 233) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1034}] + [ a r:Fact; r:gives {(1034 2000) math:sum 3034}] + skolem:lemma3033 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2033]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 233]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1034]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3034]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1035 a r:Inference; r:gives { - 2034 :kaprekar (0 7). + 3035 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2034 math:notEqualTo 0}] - skolem:lemma2091 - [ a r:Fact; r:gives {((2 0 3 4) "=<") list:sort (0 2 3 4)}] - [ a r:Fact; r:gives {((2 0 3 4) ">=") list:sort (4 3 2 0)}] - skolem:lemma2092 - skolem:lemma2093 - [ a r:Fact; r:gives {(4320 234) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1035}] + [ a r:Fact; r:gives {(1035 2000) math:sum 3035}] + skolem:lemma3034 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2034]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 234]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1035]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3035]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1036 a r:Inference; r:gives { - 2035 :kaprekar (0 7). + 3036 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2035 math:notEqualTo 0}] - skolem:lemma2094 - [ a r:Fact; r:gives {((2 0 3 5) "=<") list:sort (0 2 3 5)}] - [ a r:Fact; r:gives {((2 0 3 5) ">=") list:sort (5 3 2 0)}] - skolem:lemma2095 - skolem:lemma2096 - [ a r:Fact; r:gives {(5320 235) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1036}] + [ a r:Fact; r:gives {(1036 2000) math:sum 3036}] + skolem:lemma3035 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2035]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 235]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1036]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3036]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1037 a r:Inference; r:gives { - 2036 :kaprekar (0 7). + 3037 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2036 math:notEqualTo 0}] - skolem:lemma2097 - [ a r:Fact; r:gives {((2 0 3 6) "=<") list:sort (0 2 3 6)}] - [ a r:Fact; r:gives {((2 0 3 6) ">=") list:sort (6 3 2 0)}] - skolem:lemma2098 - skolem:lemma2099 - [ a r:Fact; r:gives {(6320 236) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1037}] + [ a r:Fact; r:gives {(1037 2000) math:sum 3037}] + skolem:lemma3036 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2036]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 236]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1037]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3037]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1038 a r:Inference; r:gives { - 2037 :kaprekar (0 3). + 3038 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2037 math:notEqualTo 0}] - skolem:lemma2100 - [ a r:Fact; r:gives {((2 0 3 7) "=<") list:sort (0 2 3 7)}] - [ a r:Fact; r:gives {((2 0 3 7) ">=") list:sort (7 3 2 0)}] - skolem:lemma2101 - skolem:lemma2102 - [ a r:Fact; r:gives {(7320 237) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1038}] + [ a r:Fact; r:gives {(1038 2000) math:sum 3038}] + skolem:lemma3037 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2037]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 237]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1038]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3038]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1039 a r:Inference; r:gives { - 2038 :kaprekar (0 3). + 3039 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2038 math:notEqualTo 0}] - skolem:lemma2103 - [ a r:Fact; r:gives {((2 0 3 8) "=<") list:sort (0 2 3 8)}] - [ a r:Fact; r:gives {((2 0 3 8) ">=") list:sort (8 3 2 0)}] - skolem:lemma2104 - skolem:lemma2105 - [ a r:Fact; r:gives {(8320 238) math:difference 8082}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8082 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 8082 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1039}] + [ a r:Fact; r:gives {(1039 2000) math:sum 3039}] + skolem:lemma3038 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2038]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 238]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1039]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3039]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1040 a r:Inference; r:gives { - 2039 :kaprekar (0 4). + 3040 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2039 math:notEqualTo 0}] - skolem:lemma2106 - [ a r:Fact; r:gives {((2 0 3 9) "=<") list:sort (0 2 3 9)}] - [ a r:Fact; r:gives {((2 0 3 9) ">=") list:sort (9 3 2 0)}] - skolem:lemma2107 - skolem:lemma2108 - [ a r:Fact; r:gives {(9320 239) math:difference 9081}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9081 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 9081 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1040}] + [ a r:Fact; r:gives {(1040 2000) math:sum 3040}] + skolem:lemma3039 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2039]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 239]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1040]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3040]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1041 a r:Inference; r:gives { - 2040 :kaprekar (0 2). + 3041 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2040 math:notEqualTo 0}] - skolem:lemma2109 - [ a r:Fact; r:gives {((2 0 4 0) "=<") list:sort (0 0 2 4)}] - [ a r:Fact; r:gives {((2 0 4 0) ">=") list:sort (4 2 0 0)}] - skolem:lemma2014 - skolem:lemma2015 - [ a r:Fact; r:gives {(4200 24) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1041}] + [ a r:Fact; r:gives {(1041 2000) math:sum 3041}] + skolem:lemma3040 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2040]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1041]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3041]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1042 a r:Inference; r:gives { - 2041 :kaprekar (0 7). + 3042 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2041 math:notEqualTo 0}] - skolem:lemma2110 - [ a r:Fact; r:gives {((2 0 4 1) "=<") list:sort (0 1 2 4)}] - [ a r:Fact; r:gives {((2 0 4 1) ">=") list:sort (4 2 1 0)}] - skolem:lemma2042 - skolem:lemma2043 - [ a r:Fact; r:gives {(4210 124) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1042}] + [ a r:Fact; r:gives {(1042 2000) math:sum 3042}] + skolem:lemma3041 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2041]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 124]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1042]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3042]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1043 a r:Inference; r:gives { - 2042 :kaprekar (0 4). + 3043 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2042 math:notEqualTo 0}] - skolem:lemma2111 - [ a r:Fact; r:gives {((2 0 4 2) "=<") list:sort (0 2 2 4)}] - [ a r:Fact; r:gives {((2 0 4 2) ">=") list:sort (4 2 2 0)}] - skolem:lemma2068 - skolem:lemma2069 - [ a r:Fact; r:gives {(4220 224) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1043}] + [ a r:Fact; r:gives {(1043 2000) math:sum 3043}] + skolem:lemma3042 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2042]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 224]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1043]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3043]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1044 a r:Inference; r:gives { - 2043 :kaprekar (0 7). + 3044 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2043 math:notEqualTo 0}] - skolem:lemma2112 - [ a r:Fact; r:gives {((2 0 4 3) "=<") list:sort (0 2 3 4)}] - [ a r:Fact; r:gives {((2 0 4 3) ">=") list:sort (4 3 2 0)}] - skolem:lemma2092 - skolem:lemma2093 - [ a r:Fact; r:gives {(4320 234) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1044}] + [ a r:Fact; r:gives {(1044 2000) math:sum 3044}] + skolem:lemma3043 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2043]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 234]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1044]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3044]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1045 a r:Inference; r:gives { - 2044 :kaprekar (0 2). + 3045 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2044 math:notEqualTo 0}] - skolem:lemma2113 - [ a r:Fact; r:gives {((2 0 4 4) "=<") list:sort (0 2 4 4)}] - [ a r:Fact; r:gives {((2 0 4 4) ">=") list:sort (4 4 2 0)}] - skolem:lemma2114 - skolem:lemma2115 - [ a r:Fact; r:gives {(4420 244) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1045}] + [ a r:Fact; r:gives {(1045 2000) math:sum 3045}] + skolem:lemma3044 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2044]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 244]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1045]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3045]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1046 a r:Inference; r:gives { - 2045 :kaprekar (0 7). + 3046 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2045 math:notEqualTo 0}] - skolem:lemma2116 - [ a r:Fact; r:gives {((2 0 4 5) "=<") list:sort (0 2 4 5)}] - [ a r:Fact; r:gives {((2 0 4 5) ">=") list:sort (5 4 2 0)}] - skolem:lemma2117 - skolem:lemma2118 - [ a r:Fact; r:gives {(5420 245) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1046}] + [ a r:Fact; r:gives {(1046 2000) math:sum 3046}] + skolem:lemma3045 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2045]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 245]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1046]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3046]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1047 a r:Inference; r:gives { - 2046 :kaprekar (0 1). + 3047 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2046 math:notEqualTo 0}] - skolem:lemma2119 - [ a r:Fact; r:gives {((2 0 4 6) "=<") list:sort (0 2 4 6)}] - [ a r:Fact; r:gives {((2 0 4 6) ">=") list:sort (6 4 2 0)}] - skolem:lemma2120 - skolem:lemma2121 - [ a r:Fact; r:gives {(6420 246) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1047}] + [ a r:Fact; r:gives {(1047 2000) math:sum 3047}] + skolem:lemma3046 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2046]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 246]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1047]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3047]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1048 a r:Inference; r:gives { - 2047 :kaprekar (0 5). + 3048 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2047 math:notEqualTo 0}] - skolem:lemma2122 - [ a r:Fact; r:gives {((2 0 4 7) "=<") list:sort (0 2 4 7)}] - [ a r:Fact; r:gives {((2 0 4 7) ">=") list:sort (7 4 2 0)}] - skolem:lemma2123 - skolem:lemma2124 - [ a r:Fact; r:gives {(7420 247) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1048}] + [ a r:Fact; r:gives {(1048 2000) math:sum 3048}] + skolem:lemma3047 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2047]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 247]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1048]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3048]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1049 a r:Inference; r:gives { - 2048 :kaprekar (0 6). + 3049 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2048 math:notEqualTo 0}] - skolem:lemma2125 - [ a r:Fact; r:gives {((2 0 4 8) "=<") list:sort (0 2 4 8)}] - [ a r:Fact; r:gives {((2 0 4 8) ">=") list:sort (8 4 2 0)}] - skolem:lemma2126 - skolem:lemma2127 - [ a r:Fact; r:gives {(8420 248) math:difference 8172}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8172 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 8172 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1049}] + [ a r:Fact; r:gives {(1049 2000) math:sum 3049}] + skolem:lemma3048 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2048]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 248]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1049]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3049]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1050 a r:Inference; r:gives { - 2049 :kaprekar (0 3). + 3050 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2049 math:notEqualTo 0}] - skolem:lemma2128 - [ a r:Fact; r:gives {((2 0 4 9) "=<") list:sort (0 2 4 9)}] - [ a r:Fact; r:gives {((2 0 4 9) ">=") list:sort (9 4 2 0)}] - skolem:lemma2129 - skolem:lemma2130 - [ a r:Fact; r:gives {(9420 249) math:difference 9171}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9171 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 9171 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1050}] + [ a r:Fact; r:gives {(1050 2000) math:sum 3050}] + skolem:lemma3049 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2049]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 249]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1050]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3050]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1051 a r:Inference; r:gives { - 2050 :kaprekar (0 7). + 3051 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2050 math:notEqualTo 0}] - skolem:lemma2131 - [ a r:Fact; r:gives {((2 0 5 0) "=<") list:sort (0 0 2 5)}] - [ a r:Fact; r:gives {((2 0 5 0) ">=") list:sort (5 2 0 0)}] - skolem:lemma2017 - skolem:lemma2018 - [ a r:Fact; r:gives {(5200 25) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1051}] + [ a r:Fact; r:gives {(1051 2000) math:sum 3051}] + skolem:lemma3050 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2050]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1051]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3051]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1052 a r:Inference; r:gives { - 2051 :kaprekar (0 7). + 3052 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2051 math:notEqualTo 0}] - skolem:lemma2132 - [ a r:Fact; r:gives {((2 0 5 1) "=<") list:sort (0 1 2 5)}] - [ a r:Fact; r:gives {((2 0 5 1) ">=") list:sort (5 2 1 0)}] - skolem:lemma2045 - skolem:lemma2046 - [ a r:Fact; r:gives {(5210 125) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1052}] + [ a r:Fact; r:gives {(1052 2000) math:sum 3052}] + skolem:lemma3051 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2051]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 125]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1052]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3052]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1053 a r:Inference; r:gives { - 2052 :kaprekar (0 6). + 3053 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2052 math:notEqualTo 0}] - skolem:lemma2133 - [ a r:Fact; r:gives {((2 0 5 2) "=<") list:sort (0 2 2 5)}] - [ a r:Fact; r:gives {((2 0 5 2) ">=") list:sort (5 2 2 0)}] - skolem:lemma2071 - skolem:lemma2072 - [ a r:Fact; r:gives {(5220 225) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1053}] + [ a r:Fact; r:gives {(1053 2000) math:sum 3053}] + skolem:lemma3052 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2052]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 225]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1053]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3053]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1054 a r:Inference; r:gives { - 2053 :kaprekar (0 7). + 3054 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2053 math:notEqualTo 0}] - skolem:lemma2134 - [ a r:Fact; r:gives {((2 0 5 3) "=<") list:sort (0 2 3 5)}] - [ a r:Fact; r:gives {((2 0 5 3) ">=") list:sort (5 3 2 0)}] - skolem:lemma2095 - skolem:lemma2096 - [ a r:Fact; r:gives {(5320 235) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1054}] + [ a r:Fact; r:gives {(1054 2000) math:sum 3054}] + skolem:lemma3053 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2053]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 235]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1054]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3054]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1055 a r:Inference; r:gives { - 2054 :kaprekar (0 7). + 3055 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2054 math:notEqualTo 0}] - skolem:lemma2135 - [ a r:Fact; r:gives {((2 0 5 4) "=<") list:sort (0 2 4 5)}] - [ a r:Fact; r:gives {((2 0 5 4) ">=") list:sort (5 4 2 0)}] - skolem:lemma2117 - skolem:lemma2118 - [ a r:Fact; r:gives {(5420 245) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1055}] + [ a r:Fact; r:gives {(1055 2000) math:sum 3055}] + skolem:lemma3054 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2054]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 245]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1055]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3055]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1056 a r:Inference; r:gives { - 2055 :kaprekar (0 5). + 3056 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2055 math:notEqualTo 0}] - skolem:lemma2136 - [ a r:Fact; r:gives {((2 0 5 5) "=<") list:sort (0 2 5 5)}] - [ a r:Fact; r:gives {((2 0 5 5) ">=") list:sort (5 5 2 0)}] - skolem:lemma2137 - skolem:lemma2138 - [ a r:Fact; r:gives {(5520 255) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1056}] + [ a r:Fact; r:gives {(1056 2000) math:sum 3056}] + skolem:lemma3055 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2055]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 255]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1056]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3056]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1057 a r:Inference; r:gives { - 2056 :kaprekar (0 3). + 3057 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2056 math:notEqualTo 0}] - skolem:lemma2139 - [ a r:Fact; r:gives {((2 0 5 6) "=<") list:sort (0 2 5 6)}] - [ a r:Fact; r:gives {((2 0 5 6) ">=") list:sort (6 5 2 0)}] - skolem:lemma2140 - skolem:lemma2141 - [ a r:Fact; r:gives {(6520 256) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1057}] + [ a r:Fact; r:gives {(1057 2000) math:sum 3057}] + skolem:lemma3056 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2056]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 256]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1057]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3057]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1058 a r:Inference; r:gives { - 2057 :kaprekar (0 6). + 3058 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2057 math:notEqualTo 0}] - skolem:lemma2142 - [ a r:Fact; r:gives {((2 0 5 7) "=<") list:sort (0 2 5 7)}] - [ a r:Fact; r:gives {((2 0 5 7) ">=") list:sort (7 5 2 0)}] - skolem:lemma2143 - skolem:lemma2144 - [ a r:Fact; r:gives {(7520 257) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1058}] + [ a r:Fact; r:gives {(1058 2000) math:sum 3058}] + skolem:lemma3057 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2057]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 257]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1058]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3058]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1059 a r:Inference; r:gives { - 2058 :kaprekar (0 5). + 3059 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2058 math:notEqualTo 0}] - skolem:lemma2145 - [ a r:Fact; r:gives {((2 0 5 8) "=<") list:sort (0 2 5 8)}] - [ a r:Fact; r:gives {((2 0 5 8) ">=") list:sort (8 5 2 0)}] - skolem:lemma2146 - skolem:lemma2147 - [ a r:Fact; r:gives {(8520 258) math:difference 8262}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8262 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 8262 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1059}] + [ a r:Fact; r:gives {(1059 2000) math:sum 3059}] + skolem:lemma3058 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2058]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 258]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1059]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3059]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1060 a r:Inference; r:gives { - 2059 :kaprekar (0 3). + 3060 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2059 math:notEqualTo 0}] - skolem:lemma2148 - [ a r:Fact; r:gives {((2 0 5 9) "=<") list:sort (0 2 5 9)}] - [ a r:Fact; r:gives {((2 0 5 9) ">=") list:sort (9 5 2 0)}] - skolem:lemma2149 - skolem:lemma2150 - [ a r:Fact; r:gives {(9520 259) math:difference 9261}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9261 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 9261 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1060}] + [ a r:Fact; r:gives {(1060 2000) math:sum 3060}] + skolem:lemma3059 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2059]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 259]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9261]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1060]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3060]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1061 a r:Inference; r:gives { - 2060 :kaprekar (0 1). + 3061 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2060 math:notEqualTo 0}] - skolem:lemma2151 - [ a r:Fact; r:gives {((2 0 6 0) "=<") list:sort (0 0 2 6)}] - [ a r:Fact; r:gives {((2 0 6 0) ">=") list:sort (6 2 0 0)}] - skolem:lemma2020 - skolem:lemma2021 - [ a r:Fact; r:gives {(6200 26) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1061}] + [ a r:Fact; r:gives {(1061 2000) math:sum 3061}] + skolem:lemma3060 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2060]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1061]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3061]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1062 a r:Inference; r:gives { - 2061 :kaprekar (0 7). + 3062 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2061 math:notEqualTo 0}] - skolem:lemma2152 - [ a r:Fact; r:gives {((2 0 6 1) "=<") list:sort (0 1 2 6)}] - [ a r:Fact; r:gives {((2 0 6 1) ">=") list:sort (6 2 1 0)}] - skolem:lemma2048 - skolem:lemma2049 - [ a r:Fact; r:gives {(6210 126) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1062}] + [ a r:Fact; r:gives {(1062 2000) math:sum 3062}] + skolem:lemma3061 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2061]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 126]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1062]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3062]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1063 a r:Inference; r:gives { - 2062 :kaprekar (0 6). + 3063 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2062 math:notEqualTo 0}] - skolem:lemma2153 - [ a r:Fact; r:gives {((2 0 6 2) "=<") list:sort (0 2 2 6)}] - [ a r:Fact; r:gives {((2 0 6 2) ">=") list:sort (6 2 2 0)}] - skolem:lemma2074 - skolem:lemma2075 - [ a r:Fact; r:gives {(6220 226) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1063}] + [ a r:Fact; r:gives {(1063 2000) math:sum 3063}] + skolem:lemma3062 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2062]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 226]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1063]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3063]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1064 a r:Inference; r:gives { - 2063 :kaprekar (0 7). + 3064 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2063 math:notEqualTo 0}] - skolem:lemma2154 - [ a r:Fact; r:gives {((2 0 6 3) "=<") list:sort (0 2 3 6)}] - [ a r:Fact; r:gives {((2 0 6 3) ">=") list:sort (6 3 2 0)}] - skolem:lemma2098 - skolem:lemma2099 - [ a r:Fact; r:gives {(6320 236) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1064}] + [ a r:Fact; r:gives {(1064 2000) math:sum 3064}] + skolem:lemma3063 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2063]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 236]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1064]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3064]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1065 a r:Inference; r:gives { - 2064 :kaprekar (0 1). + 3065 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2064 math:notEqualTo 0}] - skolem:lemma2155 - [ a r:Fact; r:gives {((2 0 6 4) "=<") list:sort (0 2 4 6)}] - [ a r:Fact; r:gives {((2 0 6 4) ">=") list:sort (6 4 2 0)}] - skolem:lemma2120 - skolem:lemma2121 - [ a r:Fact; r:gives {(6420 246) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1065}] + [ a r:Fact; r:gives {(1065 2000) math:sum 3065}] + skolem:lemma3064 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2064]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 246]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1065]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3065]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1066 a r:Inference; r:gives { - 2065 :kaprekar (0 3). + 3066 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2065 math:notEqualTo 0}] - skolem:lemma2156 - [ a r:Fact; r:gives {((2 0 6 5) "=<") list:sort (0 2 5 6)}] - [ a r:Fact; r:gives {((2 0 6 5) ">=") list:sort (6 5 2 0)}] - skolem:lemma2140 - skolem:lemma2141 - [ a r:Fact; r:gives {(6520 256) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1066}] + [ a r:Fact; r:gives {(1066 2000) math:sum 3066}] + skolem:lemma3065 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2065]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 256]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1066]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3066]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1067 a r:Inference; r:gives { - 2066 :kaprekar (0 4). + 3067 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2066 math:notEqualTo 0}] - skolem:lemma2157 - [ a r:Fact; r:gives {((2 0 6 6) "=<") list:sort (0 2 6 6)}] - [ a r:Fact; r:gives {((2 0 6 6) ">=") list:sort (6 6 2 0)}] - skolem:lemma2158 - skolem:lemma2159 - [ a r:Fact; r:gives {(6620 266) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1067}] + [ a r:Fact; r:gives {(1067 2000) math:sum 3067}] + skolem:lemma3066 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2066]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6620]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1067]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3067]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1068 a r:Inference; r:gives { - 2067 :kaprekar (0 3). + 3068 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2067 math:notEqualTo 0}] - skolem:lemma2160 - [ a r:Fact; r:gives {((2 0 6 7) "=<") list:sort (0 2 6 7)}] - [ a r:Fact; r:gives {((2 0 6 7) ">=") list:sort (7 6 2 0)}] - skolem:lemma2161 - skolem:lemma2162 - [ a r:Fact; r:gives {(7620 267) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1068}] + [ a r:Fact; r:gives {(1068 2000) math:sum 3068}] + skolem:lemma3067 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2067]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7620]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1068]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3068]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1069 a r:Inference; r:gives { - 2068 :kaprekar (0 2). + 3069 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2068 math:notEqualTo 0}] - skolem:lemma2163 - [ a r:Fact; r:gives {((2 0 6 8) "=<") list:sort (0 2 6 8)}] - [ a r:Fact; r:gives {((2 0 6 8) ">=") list:sort (8 6 2 0)}] - skolem:lemma2164 - skolem:lemma2165 - [ a r:Fact; r:gives {(8620 268) math:difference 8352}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8352 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 8352 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1069}] + [ a r:Fact; r:gives {(1069 2000) math:sum 3069}] + skolem:lemma3068 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2068]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 268]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8620]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1069]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3069]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1070 a r:Inference; r:gives { - 2069 :kaprekar (0 7). + 3070 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2069 math:notEqualTo 0}] - skolem:lemma2166 - [ a r:Fact; r:gives {((2 0 6 9) "=<") list:sort (0 2 6 9)}] - [ a r:Fact; r:gives {((2 0 6 9) ">=") list:sort (9 6 2 0)}] - skolem:lemma2167 - skolem:lemma2168 - [ a r:Fact; r:gives {(9620 269) math:difference 9351}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9351 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 9351 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1070}] + [ a r:Fact; r:gives {(1070 2000) math:sum 3070}] + skolem:lemma3069 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2069]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 269]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9620]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9351]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1070]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3070]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1071 a r:Inference; r:gives { - 2070 :kaprekar (0 5). + 3071 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2070 math:notEqualTo 0}] - skolem:lemma2169 - [ a r:Fact; r:gives {((2 0 7 0) "=<") list:sort (0 0 2 7)}] - [ a r:Fact; r:gives {((2 0 7 0) ">=") list:sort (7 2 0 0)}] - skolem:lemma2023 - skolem:lemma2024 - [ a r:Fact; r:gives {(7200 27) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1071}] + [ a r:Fact; r:gives {(1071 2000) math:sum 3071}] + skolem:lemma3070 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2070]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1071]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3071]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1072 a r:Inference; r:gives { - 2071 :kaprekar (0 3). + 3072 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2071 math:notEqualTo 0}] - skolem:lemma2170 - [ a r:Fact; r:gives {((2 0 7 1) "=<") list:sort (0 1 2 7)}] - [ a r:Fact; r:gives {((2 0 7 1) ">=") list:sort (7 2 1 0)}] - skolem:lemma2051 - skolem:lemma2052 - [ a r:Fact; r:gives {(7210 127) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1072}] + [ a r:Fact; r:gives {(1072 2000) math:sum 3072}] + skolem:lemma3071 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2071]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 127]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1072]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3072]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1073 a r:Inference; r:gives { - 2072 :kaprekar (0 4). + 3073 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2072 math:notEqualTo 0}] - skolem:lemma2171 - [ a r:Fact; r:gives {((2 0 7 2) "=<") list:sort (0 2 2 7)}] - [ a r:Fact; r:gives {((2 0 7 2) ">=") list:sort (7 2 2 0)}] - skolem:lemma2077 - skolem:lemma2078 - [ a r:Fact; r:gives {(7220 227) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1073}] + [ a r:Fact; r:gives {(1073 2000) math:sum 3073}] + skolem:lemma3072 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2072]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 227]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1073]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3073]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1074 a r:Inference; r:gives { - 2073 :kaprekar (0 3). + 3074 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2073 math:notEqualTo 0}] - skolem:lemma2172 - [ a r:Fact; r:gives {((2 0 7 3) "=<") list:sort (0 2 3 7)}] - [ a r:Fact; r:gives {((2 0 7 3) ">=") list:sort (7 3 2 0)}] - skolem:lemma2101 - skolem:lemma2102 - [ a r:Fact; r:gives {(7320 237) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1074}] + [ a r:Fact; r:gives {(1074 2000) math:sum 3074}] + skolem:lemma3073 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2073]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 237]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1074]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3074]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1075 a r:Inference; r:gives { - 2074 :kaprekar (0 5). + 3075 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2074 math:notEqualTo 0}] - skolem:lemma2173 - [ a r:Fact; r:gives {((2 0 7 4) "=<") list:sort (0 2 4 7)}] - [ a r:Fact; r:gives {((2 0 7 4) ">=") list:sort (7 4 2 0)}] - skolem:lemma2123 - skolem:lemma2124 - [ a r:Fact; r:gives {(7420 247) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1075}] + [ a r:Fact; r:gives {(1075 2000) math:sum 3075}] + skolem:lemma3074 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2074]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 247]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1075]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3075]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1076 a r:Inference; r:gives { - 2075 :kaprekar (0 6). + 3076 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2075 math:notEqualTo 0}] - skolem:lemma2174 - [ a r:Fact; r:gives {((2 0 7 5) "=<") list:sort (0 2 5 7)}] - [ a r:Fact; r:gives {((2 0 7 5) ">=") list:sort (7 5 2 0)}] - skolem:lemma2143 - skolem:lemma2144 - [ a r:Fact; r:gives {(7520 257) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1076}] + [ a r:Fact; r:gives {(1076 2000) math:sum 3076}] + skolem:lemma3075 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2075]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 257]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1076]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3076]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1077 a r:Inference; r:gives { - 2076 :kaprekar (0 3). + 3077 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2076 math:notEqualTo 0}] - skolem:lemma2175 - [ a r:Fact; r:gives {((2 0 7 6) "=<") list:sort (0 2 6 7)}] - [ a r:Fact; r:gives {((2 0 7 6) ">=") list:sort (7 6 2 0)}] - skolem:lemma2161 - skolem:lemma2162 - [ a r:Fact; r:gives {(7620 267) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1077}] + [ a r:Fact; r:gives {(1077 2000) math:sum 3077}] + skolem:lemma3076 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2076]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7620]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1077]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3077]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1078 a r:Inference; r:gives { - 2077 :kaprekar (0 5). + 3078 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2077 math:notEqualTo 0}] - skolem:lemma2176 - [ a r:Fact; r:gives {((2 0 7 7) "=<") list:sort (0 2 7 7)}] - [ a r:Fact; r:gives {((2 0 7 7) ">=") list:sort (7 7 2 0)}] - skolem:lemma2177 - skolem:lemma2178 - [ a r:Fact; r:gives {(7720 277) math:difference 7443}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7443 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1078}] + [ a r:Fact; r:gives {(1078 2000) math:sum 3078}] + skolem:lemma3077 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2077]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 277]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7720]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1078]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3078]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1079 a r:Inference; r:gives { - 2078 :kaprekar (0 7). + 3079 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2078 math:notEqualTo 0}] - skolem:lemma2179 - [ a r:Fact; r:gives {((2 0 7 8) "=<") list:sort (0 2 7 8)}] - [ a r:Fact; r:gives {((2 0 7 8) ">=") list:sort (8 7 2 0)}] - skolem:lemma2180 - skolem:lemma2181 - [ a r:Fact; r:gives {(8720 278) math:difference 8442}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8442 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 8442 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1079}] + [ a r:Fact; r:gives {(1079 2000) math:sum 3079}] + skolem:lemma3078 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2078]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 278]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8720]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1079]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3079]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1080 a r:Inference; r:gives { - 2079 :kaprekar (0 7). + 3080 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2079 math:notEqualTo 0}] - skolem:lemma2182 - [ a r:Fact; r:gives {((2 0 7 9) "=<") list:sort (0 2 7 9)}] - [ a r:Fact; r:gives {((2 0 7 9) ">=") list:sort (9 7 2 0)}] - skolem:lemma2183 - skolem:lemma2184 - [ a r:Fact; r:gives {(9720 279) math:difference 9441}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9441 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 9441 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1080}] + [ a r:Fact; r:gives {(1080 2000) math:sum 3080}] + skolem:lemma3079 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2079]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 279]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9720]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9441]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1080]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3080]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1081 a r:Inference; r:gives { - 2080 :kaprekar (0 6). + 3081 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2080 math:notEqualTo 0}] - skolem:lemma2185 - [ a r:Fact; r:gives {((2 0 8 0) "=<") list:sort (0 0 2 8)}] - [ a r:Fact; r:gives {((2 0 8 0) ">=") list:sort (8 2 0 0)}] - skolem:lemma2026 - skolem:lemma2027 - [ a r:Fact; r:gives {(8200 28) math:difference 8172}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8172 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 8172 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1081}] + [ a r:Fact; r:gives {(1081 2000) math:sum 3081}] + skolem:lemma3080 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2080]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1082 a r:Inference; r:gives { - 2081 :kaprekar (0 3). + 3082 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2081 math:notEqualTo 0}] - skolem:lemma2186 - [ a r:Fact; r:gives {((2 0 8 1) "=<") list:sort (0 1 2 8)}] - [ a r:Fact; r:gives {((2 0 8 1) ">=") list:sort (8 2 1 0)}] - skolem:lemma2054 - skolem:lemma2055 - [ a r:Fact; r:gives {(8210 128) math:difference 8082}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8082 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 8082 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1082}] + [ a r:Fact; r:gives {(1082 2000) math:sum 3082}] + skolem:lemma3081 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 128]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1083 a r:Inference; r:gives { - 2082 :kaprekar (0 6). + 3083 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2082 math:notEqualTo 0}] - skolem:lemma2187 - [ a r:Fact; r:gives {((2 0 8 2) "=<") list:sort (0 2 2 8)}] - [ a r:Fact; r:gives {((2 0 8 2) ">=") list:sort (8 2 2 0)}] - skolem:lemma2080 - skolem:lemma2081 - [ a r:Fact; r:gives {(8220 228) math:difference 7992}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7992 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7992 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1083}] + [ a r:Fact; r:gives {(1083 2000) math:sum 3083}] + skolem:lemma3082 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 228]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1084 a r:Inference; r:gives { - 2083 :kaprekar (0 3). + 3084 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2083 math:notEqualTo 0}] - skolem:lemma2188 - [ a r:Fact; r:gives {((2 0 8 3) "=<") list:sort (0 2 3 8)}] - [ a r:Fact; r:gives {((2 0 8 3) ">=") list:sort (8 3 2 0)}] - skolem:lemma2104 - skolem:lemma2105 - [ a r:Fact; r:gives {(8320 238) math:difference 8082}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8082 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 8082 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1084}] + [ a r:Fact; r:gives {(1084 2000) math:sum 3084}] + skolem:lemma3083 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 238]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1085 a r:Inference; r:gives { - 2084 :kaprekar (0 6). + 3085 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2084 math:notEqualTo 0}] - skolem:lemma2189 - [ a r:Fact; r:gives {((2 0 8 4) "=<") list:sort (0 2 4 8)}] - [ a r:Fact; r:gives {((2 0 8 4) ">=") list:sort (8 4 2 0)}] - skolem:lemma2126 - skolem:lemma2127 - [ a r:Fact; r:gives {(8420 248) math:difference 8172}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8172 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 8172 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1085}] + [ a r:Fact; r:gives {(1085 2000) math:sum 3085}] + skolem:lemma3084 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 248]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1086 a r:Inference; r:gives { - 2085 :kaprekar (0 5). + 3086 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2085 math:notEqualTo 0}] - skolem:lemma2190 - [ a r:Fact; r:gives {((2 0 8 5) "=<") list:sort (0 2 5 8)}] - [ a r:Fact; r:gives {((2 0 8 5) ">=") list:sort (8 5 2 0)}] - skolem:lemma2146 - skolem:lemma2147 - [ a r:Fact; r:gives {(8520 258) math:difference 8262}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8262 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 8262 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1086}] + [ a r:Fact; r:gives {(1086 2000) math:sum 3086}] + skolem:lemma3085 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 258]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1087 a r:Inference; r:gives { - 2086 :kaprekar (0 2). + 3087 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2086 math:notEqualTo 0}] - skolem:lemma2191 - [ a r:Fact; r:gives {((2 0 8 6) "=<") list:sort (0 2 6 8)}] - [ a r:Fact; r:gives {((2 0 8 6) ">=") list:sort (8 6 2 0)}] - skolem:lemma2164 - skolem:lemma2165 - [ a r:Fact; r:gives {(8620 268) math:difference 8352}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8352 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 8352 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1087}] + [ a r:Fact; r:gives {(1087 2000) math:sum 3087}] + skolem:lemma3086 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 268]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8620]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1088 a r:Inference; r:gives { - 2087 :kaprekar (0 7). + 3088 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2087 math:notEqualTo 0}] - skolem:lemma2192 - [ a r:Fact; r:gives {((2 0 8 7) "=<") list:sort (0 2 7 8)}] - [ a r:Fact; r:gives {((2 0 8 7) ">=") list:sort (8 7 2 0)}] - skolem:lemma2180 - skolem:lemma2181 - [ a r:Fact; r:gives {(8720 278) math:difference 8442}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8442 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 8442 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1088}] + [ a r:Fact; r:gives {(1088 2000) math:sum 3088}] + skolem:lemma3087 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 278]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8720]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1089 a r:Inference; r:gives { - 2088 :kaprekar (0 2). + 3089 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2088 math:notEqualTo 0}] - skolem:lemma2193 - [ a r:Fact; r:gives {((2 0 8 8) "=<") list:sort (0 2 8 8)}] - [ a r:Fact; r:gives {((2 0 8 8) ">=") list:sort (8 8 2 0)}] - skolem:lemma2194 - skolem:lemma2195 - [ a r:Fact; r:gives {(8820 288) math:difference 8532}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8532 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 8532 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1089}] + [ a r:Fact; r:gives {(1089 2000) math:sum 3089}] + skolem:lemma3088 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 288]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8820]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1089]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3089]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1090 a r:Inference; r:gives { - 2089 :kaprekar (0 7). + 3090 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2089 math:notEqualTo 0}] - skolem:lemma2196 - [ a r:Fact; r:gives {((2 0 8 9) "=<") list:sort (0 2 8 9)}] - [ a r:Fact; r:gives {((2 0 8 9) ">=") list:sort (9 8 2 0)}] - skolem:lemma2197 - skolem:lemma2198 - [ a r:Fact; r:gives {(9820 289) math:difference 9531}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9531 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 9531 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1090}] + [ a r:Fact; r:gives {(1090 2000) math:sum 3090}] + skolem:lemma3089 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2089]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 289]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9820]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9531]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1090]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3090]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1091 a r:Inference; r:gives { - 2090 :kaprekar (0 3). + 3091 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2090 math:notEqualTo 0}] - skolem:lemma2199 - [ a r:Fact; r:gives {((2 0 9 0) "=<") list:sort (0 0 2 9)}] - [ a r:Fact; r:gives {((2 0 9 0) ">=") list:sort (9 2 0 0)}] - skolem:lemma2029 - skolem:lemma2030 - [ a r:Fact; r:gives {(9200 29) math:difference 9171}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9171 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 9171 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1091}] + [ a r:Fact; r:gives {(1091 2000) math:sum 3091}] + skolem:lemma3090 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2090]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1091]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3091]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1092 a r:Inference; r:gives { - 2091 :kaprekar (0 4). + 3092 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2091 math:notEqualTo 0}] - skolem:lemma2200 - [ a r:Fact; r:gives {((2 0 9 1) "=<") list:sort (0 1 2 9)}] - [ a r:Fact; r:gives {((2 0 9 1) ">=") list:sort (9 2 1 0)}] - skolem:lemma2057 - skolem:lemma2058 - [ a r:Fact; r:gives {(9210 129) math:difference 9081}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9081 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 9081 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1092}] + [ a r:Fact; r:gives {(1092 2000) math:sum 3092}] + skolem:lemma3091 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2091]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 129]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1092]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3092]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1093 a r:Inference; r:gives { - 2092 :kaprekar (0 4). + 3093 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2092 math:notEqualTo 0}] - skolem:lemma2201 - [ a r:Fact; r:gives {((2 0 9 2) "=<") list:sort (0 2 2 9)}] - [ a r:Fact; r:gives {((2 0 9 2) ">=") list:sort (9 2 2 0)}] - skolem:lemma2083 - skolem:lemma2084 - [ a r:Fact; r:gives {(9220 229) math:difference 8991}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8991 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 8991 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1093}] + [ a r:Fact; r:gives {(1093 2000) math:sum 3093}] + skolem:lemma3092 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2092]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 229]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8991]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1093]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3093]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1094 a r:Inference; r:gives { - 2093 :kaprekar (0 4). + 3094 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2093 math:notEqualTo 0}] - skolem:lemma2202 - [ a r:Fact; r:gives {((2 0 9 3) "=<") list:sort (0 2 3 9)}] - [ a r:Fact; r:gives {((2 0 9 3) ">=") list:sort (9 3 2 0)}] - skolem:lemma2107 - skolem:lemma2108 - [ a r:Fact; r:gives {(9320 239) math:difference 9081}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9081 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 9081 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1094}] + [ a r:Fact; r:gives {(1094 2000) math:sum 3094}] + skolem:lemma3093 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2093]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 239]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1094]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3094]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1095 a r:Inference; r:gives { - 2094 :kaprekar (0 3). + 3095 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2094 math:notEqualTo 0}] - skolem:lemma2203 - [ a r:Fact; r:gives {((2 0 9 4) "=<") list:sort (0 2 4 9)}] - [ a r:Fact; r:gives {((2 0 9 4) ">=") list:sort (9 4 2 0)}] - skolem:lemma2129 - skolem:lemma2130 - [ a r:Fact; r:gives {(9420 249) math:difference 9171}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9171 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 9171 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1095}] + [ a r:Fact; r:gives {(1095 2000) math:sum 3095}] + skolem:lemma3094 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2094]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 249]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1095]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3095]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1096 a r:Inference; r:gives { - 2095 :kaprekar (0 3). + 3096 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2095 math:notEqualTo 0}] - skolem:lemma2204 - [ a r:Fact; r:gives {((2 0 9 5) "=<") list:sort (0 2 5 9)}] - [ a r:Fact; r:gives {((2 0 9 5) ">=") list:sort (9 5 2 0)}] - skolem:lemma2149 - skolem:lemma2150 - [ a r:Fact; r:gives {(9520 259) math:difference 9261}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9261 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 9261 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1096}] + [ a r:Fact; r:gives {(1096 2000) math:sum 3096}] + skolem:lemma3095 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2095]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 259]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9261]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1096]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3096]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1097 a r:Inference; r:gives { - 2096 :kaprekar (0 7). + 3097 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2096 math:notEqualTo 0}] - skolem:lemma2205 - [ a r:Fact; r:gives {((2 0 9 6) "=<") list:sort (0 2 6 9)}] - [ a r:Fact; r:gives {((2 0 9 6) ">=") list:sort (9 6 2 0)}] - skolem:lemma2167 - skolem:lemma2168 - [ a r:Fact; r:gives {(9620 269) math:difference 9351}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9351 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 9351 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1097}] + [ a r:Fact; r:gives {(1097 2000) math:sum 3097}] + skolem:lemma3096 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2096]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 269]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9620]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9351]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1097]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3097]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1098 a r:Inference; r:gives { - 2097 :kaprekar (0 7). + 3098 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2097 math:notEqualTo 0}] - skolem:lemma2206 - [ a r:Fact; r:gives {((2 0 9 7) "=<") list:sort (0 2 7 9)}] - [ a r:Fact; r:gives {((2 0 9 7) ">=") list:sort (9 7 2 0)}] - skolem:lemma2183 - skolem:lemma2184 - [ a r:Fact; r:gives {(9720 279) math:difference 9441}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9441 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 9441 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1098}] + [ a r:Fact; r:gives {(1098 2000) math:sum 3098}] + skolem:lemma3097 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2097]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 279]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9720]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9441]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1098]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3098]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1099 a r:Inference; r:gives { - 2098 :kaprekar (0 7). + 3099 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2098 math:notEqualTo 0}] - skolem:lemma2207 - [ a r:Fact; r:gives {((2 0 9 8) "=<") list:sort (0 2 8 9)}] - [ a r:Fact; r:gives {((2 0 9 8) ">=") list:sort (9 8 2 0)}] - skolem:lemma2197 - skolem:lemma2198 - [ a r:Fact; r:gives {(9820 289) math:difference 9531}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9531 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 9531 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1099}] + [ a r:Fact; r:gives {(1099 2000) math:sum 3099}] + skolem:lemma3098 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2098]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 289]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9820]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9531]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1099]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3099]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1100 a r:Inference; r:gives { - 2099 :kaprekar (0 3). + 3100 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2099 math:notEqualTo 0}] - skolem:lemma2208 - [ a r:Fact; r:gives {((2 0 9 9) "=<") list:sort (0 2 9 9)}] - [ a r:Fact; r:gives {((2 0 9 9) ">=") list:sort (9 9 2 0)}] - skolem:lemma2209 - skolem:lemma2210 - [ a r:Fact; r:gives {(9920 299) math:difference 9621}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9621 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 9621 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1100}] + [ a r:Fact; r:gives {(1100 2000) math:sum 3100}] + skolem:lemma3099 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2099]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 299]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9920]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1101 a r:Inference; r:gives { - 2100 :kaprekar (0 3). + 3101 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2100 math:notEqualTo 0}] - skolem:lemma2211 - [ a r:Fact; r:gives {((2 1 0 0) "=<") list:sort (0 0 1 2)}] - [ a r:Fact; r:gives {((2 1 0 0) ">=") list:sort (2 1 0 0)}] - skolem:lemma2005 - skolem:lemma2006 - [ a r:Fact; r:gives {(2100 12) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1101}] + [ a r:Fact; r:gives {(1101 2000) math:sum 3101}] + skolem:lemma3100 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2100]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2100]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1101]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3101]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1102 a r:Inference; r:gives { - 2101 :kaprekar (0 4). + 3102 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2101 math:notEqualTo 0}] - skolem:lemma2212 - [ a r:Fact; r:gives {((2 1 0 1) "=<") list:sort (0 1 1 2)}] - [ a r:Fact; r:gives {((2 1 0 1) ">=") list:sort (2 1 1 0)}] - skolem:lemma2033 - skolem:lemma2034 - [ a r:Fact; r:gives {(2110 112) math:difference 1998}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1998 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1998 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1102}] + [ a r:Fact; r:gives {(1102 2000) math:sum 3102}] + skolem:lemma3101 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2101]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 112]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2110]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1102]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3102]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1103 a r:Inference; r:gives { - 2102 :kaprekar (0 3). + 3103 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2102 math:notEqualTo 0}] - skolem:lemma2213 - [ a r:Fact; r:gives {((2 1 0 2) "=<") list:sort (0 1 2 2)}] - [ a r:Fact; r:gives {((2 1 0 2) ">=") list:sort (2 2 1 0)}] - skolem:lemma2036 - skolem:lemma2037 - [ a r:Fact; r:gives {(2210 122) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1103}] + [ a r:Fact; r:gives {(1103 2000) math:sum 3103}] + skolem:lemma3102 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2102]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 122]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1103]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3103]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1104 a r:Inference; r:gives { - 2103 :kaprekar (0 3). + 3104 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2103 math:notEqualTo 0}] - skolem:lemma2214 - [ a r:Fact; r:gives {((2 1 0 3) "=<") list:sort (0 1 2 3)}] - [ a r:Fact; r:gives {((2 1 0 3) ">=") list:sort (3 2 1 0)}] - skolem:lemma2039 - skolem:lemma2040 - [ a r:Fact; r:gives {(3210 123) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1104}] + [ a r:Fact; r:gives {(1104 2000) math:sum 3104}] + skolem:lemma3103 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2103]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 123]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1104]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3104]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1105 a r:Inference; r:gives { - 2104 :kaprekar (0 7). + 3105 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2104 math:notEqualTo 0}] - skolem:lemma2215 - [ a r:Fact; r:gives {((2 1 0 4) "=<") list:sort (0 1 2 4)}] - [ a r:Fact; r:gives {((2 1 0 4) ">=") list:sort (4 2 1 0)}] - skolem:lemma2042 - skolem:lemma2043 - [ a r:Fact; r:gives {(4210 124) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1105}] + [ a r:Fact; r:gives {(1105 2000) math:sum 3105}] + skolem:lemma3104 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2104]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 124]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1105]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3105]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1106 a r:Inference; r:gives { - 2105 :kaprekar (0 7). + 3106 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2105 math:notEqualTo 0}] - skolem:lemma2216 - [ a r:Fact; r:gives {((2 1 0 5) "=<") list:sort (0 1 2 5)}] - [ a r:Fact; r:gives {((2 1 0 5) ">=") list:sort (5 2 1 0)}] - skolem:lemma2045 - skolem:lemma2046 - [ a r:Fact; r:gives {(5210 125) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1106}] + [ a r:Fact; r:gives {(1106 2000) math:sum 3106}] + skolem:lemma3105 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2105]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 125]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1106]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3106]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1107 a r:Inference; r:gives { - 2106 :kaprekar (0 7). + 3107 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2106 math:notEqualTo 0}] - skolem:lemma2217 - [ a r:Fact; r:gives {((2 1 0 6) "=<") list:sort (0 1 2 6)}] - [ a r:Fact; r:gives {((2 1 0 6) ">=") list:sort (6 2 1 0)}] - skolem:lemma2048 - skolem:lemma2049 - [ a r:Fact; r:gives {(6210 126) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1107}] + [ a r:Fact; r:gives {(1107 2000) math:sum 3107}] + skolem:lemma3106 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2106]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 126]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1107]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3107]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1108 a r:Inference; r:gives { - 2107 :kaprekar (0 3). + 3108 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2107 math:notEqualTo 0}] - skolem:lemma2218 - [ a r:Fact; r:gives {((2 1 0 7) "=<") list:sort (0 1 2 7)}] - [ a r:Fact; r:gives {((2 1 0 7) ">=") list:sort (7 2 1 0)}] - skolem:lemma2051 - skolem:lemma2052 - [ a r:Fact; r:gives {(7210 127) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1108}] + [ a r:Fact; r:gives {(1108 2000) math:sum 3108}] + skolem:lemma3107 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2107]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 127]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1108]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3108]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1109 a r:Inference; r:gives { - 2108 :kaprekar (0 3). + 3109 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2108 math:notEqualTo 0}] - skolem:lemma2219 - [ a r:Fact; r:gives {((2 1 0 8) "=<") list:sort (0 1 2 8)}] - [ a r:Fact; r:gives {((2 1 0 8) ">=") list:sort (8 2 1 0)}] - skolem:lemma2054 - skolem:lemma2055 - [ a r:Fact; r:gives {(8210 128) math:difference 8082}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8082 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 8082 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1109}] + [ a r:Fact; r:gives {(1109 2000) math:sum 3109}] + skolem:lemma3108 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2108]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 128]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1109]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3109]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1110 a r:Inference; r:gives { - 2109 :kaprekar (0 4). + 3110 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2109 math:notEqualTo 0}] - skolem:lemma2220 - [ a r:Fact; r:gives {((2 1 0 9) "=<") list:sort (0 1 2 9)}] - [ a r:Fact; r:gives {((2 1 0 9) ">=") list:sort (9 2 1 0)}] - skolem:lemma2057 - skolem:lemma2058 - [ a r:Fact; r:gives {(9210 129) math:difference 9081}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9081 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 9081 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1110}] + [ a r:Fact; r:gives {(1110 2000) math:sum 3110}] + skolem:lemma3109 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2109]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 129]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1110]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3110]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1111 a r:Inference; r:gives { - 2110 :kaprekar (0 4). + 3111 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2110 math:notEqualTo 0}] - skolem:lemma2221 - [ a r:Fact; r:gives {((2 1 1 0) "=<") list:sort (0 1 1 2)}] - [ a r:Fact; r:gives {((2 1 1 0) ">=") list:sort (2 1 1 0)}] - skolem:lemma2033 - skolem:lemma2034 - [ a r:Fact; r:gives {(2110 112) math:difference 1998}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1998 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1998 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1111}] + [ a r:Fact; r:gives {(1111 2000) math:sum 3111}] + skolem:lemma3110 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2110]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 112]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2110]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1111]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3111]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1112 a r:Inference; r:gives { - 2111 :kaprekar (0 5). + 3112 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2111 math:notEqualTo 0}] - skolem:lemma2222 - [ a r:Fact; r:gives {((2 1 1 1) "=<") list:sort (1 1 1 2)}] - [ a r:Fact; r:gives {((2 1 1 1) ">=") list:sort (2 1 1 1)}] - skolem:lemma2223 - skolem:lemma2224 - [ a r:Fact; r:gives {(2111 1112) math:difference 999}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 999 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 999 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1112}] + [ a r:Fact; r:gives {(1112 2000) math:sum 3112}] + skolem:lemma3111 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2111]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1112]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2111]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1112]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3112]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1113 a r:Inference; r:gives { - 2112 :kaprekar (0 4). + 3113 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2112 math:notEqualTo 0}] - skolem:lemma2225 - [ a r:Fact; r:gives {((2 1 1 2) "=<") list:sort (1 1 2 2)}] - [ a r:Fact; r:gives {((2 1 1 2) ">=") list:sort (2 2 1 1)}] - skolem:lemma2226 - skolem:lemma2227 - [ a r:Fact; r:gives {(2211 1122) math:difference 1089}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1089 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1089 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1113}] + [ a r:Fact; r:gives {(1113 2000) math:sum 3113}] + skolem:lemma3112 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2112]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1122]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1089]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1113]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3113]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1114 a r:Inference; r:gives { - 2113 :kaprekar (0 3). + 3114 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2113 math:notEqualTo 0}] - skolem:lemma2228 - [ a r:Fact; r:gives {((2 1 1 3) "=<") list:sort (1 1 2 3)}] - [ a r:Fact; r:gives {((2 1 1 3) ">=") list:sort (3 2 1 1)}] - skolem:lemma2229 - skolem:lemma2230 - [ a r:Fact; r:gives {(3211 1123) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1114}] + [ a r:Fact; r:gives {(1114 2000) math:sum 3114}] + skolem:lemma3113 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2113]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1123]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1114]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3114]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1115 a r:Inference; r:gives { - 2114 :kaprekar (0 3). + 3115 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2114 math:notEqualTo 0}] - skolem:lemma2231 - [ a r:Fact; r:gives {((2 1 1 4) "=<") list:sort (1 1 2 4)}] - [ a r:Fact; r:gives {((2 1 1 4) ">=") list:sort (4 2 1 1)}] - skolem:lemma2232 - skolem:lemma2233 - [ a r:Fact; r:gives {(4211 1124) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1115}] + [ a r:Fact; r:gives {(1115 2000) math:sum 3115}] + skolem:lemma3114 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2114]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1124]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1115]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3115]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1116 a r:Inference; r:gives { - 2115 :kaprekar (0 7). + 3116 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2115 math:notEqualTo 0}] - skolem:lemma2234 - [ a r:Fact; r:gives {((2 1 1 5) "=<") list:sort (1 1 2 5)}] - [ a r:Fact; r:gives {((2 1 1 5) ">=") list:sort (5 2 1 1)}] - skolem:lemma2235 - skolem:lemma2236 - [ a r:Fact; r:gives {(5211 1125) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1116}] + [ a r:Fact; r:gives {(1116 2000) math:sum 3116}] + skolem:lemma3115 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2115]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1125]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1116]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3116]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1117 a r:Inference; r:gives { - 2116 :kaprekar (0 7). + 3117 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2116 math:notEqualTo 0}] - skolem:lemma2237 - [ a r:Fact; r:gives {((2 1 1 6) "=<") list:sort (1 1 2 6)}] - [ a r:Fact; r:gives {((2 1 1 6) ">=") list:sort (6 2 1 1)}] - skolem:lemma2238 - skolem:lemma2239 - [ a r:Fact; r:gives {(6211 1126) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1117}] + [ a r:Fact; r:gives {(1117 2000) math:sum 3117}] + skolem:lemma3116 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2116]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1126]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1117]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3117]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1118 a r:Inference; r:gives { - 2117 :kaprekar (0 7). + 3118 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2117 math:notEqualTo 0}] - skolem:lemma2240 - [ a r:Fact; r:gives {((2 1 1 7) "=<") list:sort (1 1 2 7)}] - [ a r:Fact; r:gives {((2 1 1 7) ">=") list:sort (7 2 1 1)}] - skolem:lemma2241 - skolem:lemma2242 - [ a r:Fact; r:gives {(7211 1127) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1118}] + [ a r:Fact; r:gives {(1118 2000) math:sum 3118}] + skolem:lemma3117 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2117]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1127]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1118]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3118]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1119 a r:Inference; r:gives { - 2118 :kaprekar (0 3). + 3119 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2118 math:notEqualTo 0}] - skolem:lemma2243 - [ a r:Fact; r:gives {((2 1 1 8) "=<") list:sort (1 1 2 8)}] - [ a r:Fact; r:gives {((2 1 1 8) ">=") list:sort (8 2 1 1)}] - skolem:lemma2244 - skolem:lemma2245 - [ a r:Fact; r:gives {(8211 1128) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1119}] + [ a r:Fact; r:gives {(1119 2000) math:sum 3119}] + skolem:lemma3118 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2118]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1128]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1119]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3119]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1120 a r:Inference; r:gives { - 2119 :kaprekar (0 3). + 3120 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2119 math:notEqualTo 0}] - skolem:lemma2246 - [ a r:Fact; r:gives {((2 1 1 9) "=<") list:sort (1 1 2 9)}] - [ a r:Fact; r:gives {((2 1 1 9) ">=") list:sort (9 2 1 1)}] - skolem:lemma2247 - skolem:lemma2248 - [ a r:Fact; r:gives {(9211 1129) math:difference 8082}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8082 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 8082 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1120}] + [ a r:Fact; r:gives {(1120 2000) math:sum 3120}] + skolem:lemma3119 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2119]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1129]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1120]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3120]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1121 a r:Inference; r:gives { - 2120 :kaprekar (0 3). + 3121 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2120 math:notEqualTo 0}] - skolem:lemma2249 - [ a r:Fact; r:gives {((2 1 2 0) "=<") list:sort (0 1 2 2)}] - [ a r:Fact; r:gives {((2 1 2 0) ">=") list:sort (2 2 1 0)}] - skolem:lemma2036 - skolem:lemma2037 - [ a r:Fact; r:gives {(2210 122) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1121}] + [ a r:Fact; r:gives {(1121 2000) math:sum 3121}] + skolem:lemma3120 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2120]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 122]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1121]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3121]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1122 a r:Inference; r:gives { - 2121 :kaprekar (0 4). + 3122 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2121 math:notEqualTo 0}] - skolem:lemma2250 - [ a r:Fact; r:gives {((2 1 2 1) "=<") list:sort (1 1 2 2)}] - [ a r:Fact; r:gives {((2 1 2 1) ">=") list:sort (2 2 1 1)}] - skolem:lemma2226 - skolem:lemma2227 - [ a r:Fact; r:gives {(2211 1122) math:difference 1089}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1089 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1089 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1122}] + [ a r:Fact; r:gives {(1122 2000) math:sum 3122}] + skolem:lemma3121 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2121]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1122]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1089]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1122]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3122]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1123 a r:Inference; r:gives { - 2122 :kaprekar (0 5). + 3123 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2122 math:notEqualTo 0}] - skolem:lemma2251 - [ a r:Fact; r:gives {((2 1 2 2) "=<") list:sort (1 2 2 2)}] - [ a r:Fact; r:gives {((2 1 2 2) ">=") list:sort (2 2 2 1)}] - skolem:lemma2252 - skolem:lemma2253 - [ a r:Fact; r:gives {(2221 1222) math:difference 999}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 999 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 999 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1123}] + [ a r:Fact; r:gives {(1123 2000) math:sum 3123}] + skolem:lemma3122 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2122]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1124 a r:Inference; r:gives { - 2123 :kaprekar (0 4). + 3124 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2123 math:notEqualTo 0}] - skolem:lemma2254 - [ a r:Fact; r:gives {((2 1 2 3) "=<") list:sort (1 2 2 3)}] - [ a r:Fact; r:gives {((2 1 2 3) ">=") list:sort (3 2 2 1)}] - skolem:lemma2255 - skolem:lemma2256 - [ a r:Fact; r:gives {(3221 1223) math:difference 1998}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1998 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1998 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1124}] + [ a r:Fact; r:gives {(1124 2000) math:sum 3124}] + skolem:lemma3123 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2123]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1223]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1125 a r:Inference; r:gives { - 2124 :kaprekar (0 6). + 3125 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2124 math:notEqualTo 0}] - skolem:lemma2257 - [ a r:Fact; r:gives {((2 1 2 4) "=<") list:sort (1 2 2 4)}] - [ a r:Fact; r:gives {((2 1 2 4) ">=") list:sort (4 2 2 1)}] - skolem:lemma2258 - skolem:lemma2259 - [ a r:Fact; r:gives {(4221 1224) math:difference 2997}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2997 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2997 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1125}] + [ a r:Fact; r:gives {(1125 2000) math:sum 3125}] + skolem:lemma3124 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2124]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1224]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1126 a r:Inference; r:gives { - 2125 :kaprekar (0 4). + 3126 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2125 math:notEqualTo 0}] - skolem:lemma2260 - [ a r:Fact; r:gives {((2 1 2 5) "=<") list:sort (1 2 2 5)}] - [ a r:Fact; r:gives {((2 1 2 5) ">=") list:sort (5 2 2 1)}] - skolem:lemma2261 - skolem:lemma2262 - [ a r:Fact; r:gives {(5221 1225) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1126}] + [ a r:Fact; r:gives {(1126 2000) math:sum 3126}] + skolem:lemma3125 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2125]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1225]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1127 a r:Inference; r:gives { - 2126 :kaprekar (0 6). + 3127 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2126 math:notEqualTo 0}] - skolem:lemma2263 - [ a r:Fact; r:gives {((2 1 2 6) "=<") list:sort (1 2 2 6)}] - [ a r:Fact; r:gives {((2 1 2 6) ">=") list:sort (6 2 2 1)}] - skolem:lemma2264 - skolem:lemma2265 - [ a r:Fact; r:gives {(6221 1226) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1127}] + [ a r:Fact; r:gives {(1127 2000) math:sum 3127}] + skolem:lemma3126 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2126]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1226]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1128 a r:Inference; r:gives { - 2127 :kaprekar (0 6). + 3128 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2127 math:notEqualTo 0}] - skolem:lemma2266 - [ a r:Fact; r:gives {((2 1 2 7) "=<") list:sort (1 2 2 7)}] - [ a r:Fact; r:gives {((2 1 2 7) ">=") list:sort (7 2 2 1)}] - skolem:lemma2267 - skolem:lemma2268 - [ a r:Fact; r:gives {(7221 1227) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1128}] + [ a r:Fact; r:gives {(1128 2000) math:sum 3128}] + skolem:lemma3127 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2127]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1227]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1129 a r:Inference; r:gives { - 2128 :kaprekar (0 4). + 3129 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2128 math:notEqualTo 0}] - skolem:lemma2269 - [ a r:Fact; r:gives {((2 1 2 8) "=<") list:sort (1 2 2 8)}] - [ a r:Fact; r:gives {((2 1 2 8) ">=") list:sort (8 2 2 1)}] - skolem:lemma2270 - skolem:lemma2271 - [ a r:Fact; r:gives {(8221 1228) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1129}] + [ a r:Fact; r:gives {(1129 2000) math:sum 3129}] + skolem:lemma3128 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2128]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1228]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1130 a r:Inference; r:gives { - 2129 :kaprekar (0 6). + 3130 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2129 math:notEqualTo 0}] - skolem:lemma2272 - [ a r:Fact; r:gives {((2 1 2 9) "=<") list:sort (1 2 2 9)}] - [ a r:Fact; r:gives {((2 1 2 9) ">=") list:sort (9 2 2 1)}] - skolem:lemma2273 - skolem:lemma2274 - [ a r:Fact; r:gives {(9221 1229) math:difference 7992}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7992 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7992 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1130}] + [ a r:Fact; r:gives {(1130 2000) math:sum 3130}] + skolem:lemma3129 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2129]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1229]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1130]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3130]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1131 a r:Inference; r:gives { - 2130 :kaprekar (0 3). + 3131 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2130 math:notEqualTo 0}] - skolem:lemma2275 - [ a r:Fact; r:gives {((2 1 3 0) "=<") list:sort (0 1 2 3)}] - [ a r:Fact; r:gives {((2 1 3 0) ">=") list:sort (3 2 1 0)}] - skolem:lemma2039 - skolem:lemma2040 - [ a r:Fact; r:gives {(3210 123) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1131}] + [ a r:Fact; r:gives {(1131 2000) math:sum 3131}] + skolem:lemma3130 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2130]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 123]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1131]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3131]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1132 a r:Inference; r:gives { - 2131 :kaprekar (0 3). + 3132 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2131 math:notEqualTo 0}] - skolem:lemma2276 - [ a r:Fact; r:gives {((2 1 3 1) "=<") list:sort (1 1 2 3)}] - [ a r:Fact; r:gives {((2 1 3 1) ">=") list:sort (3 2 1 1)}] - skolem:lemma2229 - skolem:lemma2230 - [ a r:Fact; r:gives {(3211 1123) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1132}] + [ a r:Fact; r:gives {(1132 2000) math:sum 3132}] + skolem:lemma3131 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2131]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1123]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1132]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3132]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1133 a r:Inference; r:gives { - 2132 :kaprekar (0 4). + 3133 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2132 math:notEqualTo 0}] - skolem:lemma2277 - [ a r:Fact; r:gives {((2 1 3 2) "=<") list:sort (1 2 2 3)}] - [ a r:Fact; r:gives {((2 1 3 2) ">=") list:sort (3 2 2 1)}] - skolem:lemma2255 - skolem:lemma2256 - [ a r:Fact; r:gives {(3221 1223) math:difference 1998}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1998 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1998 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1133}] + [ a r:Fact; r:gives {(1133 2000) math:sum 3133}] + skolem:lemma3132 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2132]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1223]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1133]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3133]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1134 a r:Inference; r:gives { - 2133 :kaprekar (0 3). + 3134 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2133 math:notEqualTo 0}] - skolem:lemma2278 - [ a r:Fact; r:gives {((2 1 3 3) "=<") list:sort (1 2 3 3)}] - [ a r:Fact; r:gives {((2 1 3 3) ">=") list:sort (3 3 2 1)}] - skolem:lemma2279 - skolem:lemma2280 - [ a r:Fact; r:gives {(3321 1233) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1134}] + [ a r:Fact; r:gives {(1134 2000) math:sum 3134}] + skolem:lemma3133 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2133]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1233]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1134]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3134]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1135 a r:Inference; r:gives { - 2134 :kaprekar (0 3). + 3135 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2134 math:notEqualTo 0}] - skolem:lemma2281 - [ a r:Fact; r:gives {((2 1 3 4) "=<") list:sort (1 2 3 4)}] - [ a r:Fact; r:gives {((2 1 3 4) ">=") list:sort (4 3 2 1)}] - skolem:lemma2282 - skolem:lemma2283 - [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1135}] + [ a r:Fact; r:gives {(1135 2000) math:sum 3135}] + skolem:lemma3134 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2134]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1234]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1135]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3135]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1136 a r:Inference; r:gives { - 2135 :kaprekar (0 7). + 3136 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2135 math:notEqualTo 0}] - skolem:lemma2284 - [ a r:Fact; r:gives {((2 1 3 5) "=<") list:sort (1 2 3 5)}] - [ a r:Fact; r:gives {((2 1 3 5) ">=") list:sort (5 3 2 1)}] - skolem:lemma2285 - skolem:lemma2286 - [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1136}] + [ a r:Fact; r:gives {(1136 2000) math:sum 3136}] + skolem:lemma3135 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2135]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1235]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1136]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3136]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1137 a r:Inference; r:gives { - 2136 :kaprekar (0 7). + 3137 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2136 math:notEqualTo 0}] - skolem:lemma2287 - [ a r:Fact; r:gives {((2 1 3 6) "=<") list:sort (1 2 3 6)}] - [ a r:Fact; r:gives {((2 1 3 6) ">=") list:sort (6 3 2 1)}] - skolem:lemma2288 - skolem:lemma2289 - [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1137}] + [ a r:Fact; r:gives {(1137 2000) math:sum 3137}] + skolem:lemma3136 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2136]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1236]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1137]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3137]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1138 a r:Inference; r:gives { - 2137 :kaprekar (0 7). + 3138 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2137 math:notEqualTo 0}] - skolem:lemma2290 - [ a r:Fact; r:gives {((2 1 3 7) "=<") list:sort (1 2 3 7)}] - [ a r:Fact; r:gives {((2 1 3 7) ">=") list:sort (7 3 2 1)}] - skolem:lemma2291 - skolem:lemma2292 - [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1138}] + [ a r:Fact; r:gives {(1138 2000) math:sum 3138}] + skolem:lemma3137 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2137]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1237]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1138]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3138]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1139 a r:Inference; r:gives { - 2138 :kaprekar (0 3). + 3139 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2138 math:notEqualTo 0}] - skolem:lemma2293 - [ a r:Fact; r:gives {((2 1 3 8) "=<") list:sort (1 2 3 8)}] - [ a r:Fact; r:gives {((2 1 3 8) ">=") list:sort (8 3 2 1)}] - skolem:lemma2294 - skolem:lemma2295 - [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1139}] + [ a r:Fact; r:gives {(1139 2000) math:sum 3139}] + skolem:lemma3138 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2138]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1238]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1139]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3139]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1140 a r:Inference; r:gives { - 2139 :kaprekar (0 3). + 3140 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2139 math:notEqualTo 0}] - skolem:lemma2296 - [ a r:Fact; r:gives {((2 1 3 9) "=<") list:sort (1 2 3 9)}] - [ a r:Fact; r:gives {((2 1 3 9) ">=") list:sort (9 3 2 1)}] - skolem:lemma2297 - skolem:lemma2298 - [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8082 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 8082 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1140}] + [ a r:Fact; r:gives {(1140 2000) math:sum 3140}] + skolem:lemma3139 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2139]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1239]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1140]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3140]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1141 a r:Inference; r:gives { - 2140 :kaprekar (0 7). + 3141 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2140 math:notEqualTo 0}] - skolem:lemma2299 - [ a r:Fact; r:gives {((2 1 4 0) "=<") list:sort (0 1 2 4)}] - [ a r:Fact; r:gives {((2 1 4 0) ">=") list:sort (4 2 1 0)}] - skolem:lemma2042 - skolem:lemma2043 - [ a r:Fact; r:gives {(4210 124) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1141}] + [ a r:Fact; r:gives {(1141 2000) math:sum 3141}] + skolem:lemma3140 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2140]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 124]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1141]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3141]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1142 a r:Inference; r:gives { - 2141 :kaprekar (0 3). + 3142 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2141 math:notEqualTo 0}] - skolem:lemma2300 - [ a r:Fact; r:gives {((2 1 4 1) "=<") list:sort (1 1 2 4)}] - [ a r:Fact; r:gives {((2 1 4 1) ">=") list:sort (4 2 1 1)}] - skolem:lemma2232 - skolem:lemma2233 - [ a r:Fact; r:gives {(4211 1124) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1142}] + [ a r:Fact; r:gives {(1142 2000) math:sum 3142}] + skolem:lemma3141 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2141]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1124]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1142]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3142]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1143 a r:Inference; r:gives { - 2142 :kaprekar (0 6). + 3143 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2142 math:notEqualTo 0}] - skolem:lemma2301 - [ a r:Fact; r:gives {((2 1 4 2) "=<") list:sort (1 2 2 4)}] - [ a r:Fact; r:gives {((2 1 4 2) ">=") list:sort (4 2 2 1)}] - skolem:lemma2258 - skolem:lemma2259 - [ a r:Fact; r:gives {(4221 1224) math:difference 2997}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2997 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2997 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1143}] + [ a r:Fact; r:gives {(1143 2000) math:sum 3143}] + skolem:lemma3142 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2142]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1224]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1143]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3143]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1144 a r:Inference; r:gives { - 2143 :kaprekar (0 3). + 3144 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2143 math:notEqualTo 0}] - skolem:lemma2302 - [ a r:Fact; r:gives {((2 1 4 3) "=<") list:sort (1 2 3 4)}] - [ a r:Fact; r:gives {((2 1 4 3) ">=") list:sort (4 3 2 1)}] - skolem:lemma2282 - skolem:lemma2283 - [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1144}] + [ a r:Fact; r:gives {(1144 2000) math:sum 3144}] + skolem:lemma3143 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2143]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1234]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1144]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3144]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1145 a r:Inference; r:gives { - 2144 :kaprekar (0 5). + 3145 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2144 math:notEqualTo 0}] - skolem:lemma2303 - [ a r:Fact; r:gives {((2 1 4 4) "=<") list:sort (1 2 4 4)}] - [ a r:Fact; r:gives {((2 1 4 4) ">=") list:sort (4 4 2 1)}] - skolem:lemma2304 - skolem:lemma2305 - [ a r:Fact; r:gives {(4421 1244) math:difference 3177}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3177 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 3177 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1145}] + [ a r:Fact; r:gives {(1145 2000) math:sum 3145}] + skolem:lemma3144 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2144]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1244]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1145]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3145]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1146 a r:Inference; r:gives { - 2145 :kaprekar (0 2). + 3146 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2145 math:notEqualTo 0}] - skolem:lemma2306 - [ a r:Fact; r:gives {((2 1 4 5) "=<") list:sort (1 2 4 5)}] - [ a r:Fact; r:gives {((2 1 4 5) ">=") list:sort (5 4 2 1)}] - skolem:lemma2307 - skolem:lemma2308 - [ a r:Fact; r:gives {(5421 1245) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1146}] + [ a r:Fact; r:gives {(1146 2000) math:sum 3146}] + skolem:lemma3145 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2145]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1245]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1146]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3146]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1147 a r:Inference; r:gives { - 2146 :kaprekar (0 7). + 3147 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2146 math:notEqualTo 0}] - skolem:lemma2309 - [ a r:Fact; r:gives {((2 1 4 6) "=<") list:sort (1 2 4 6)}] - [ a r:Fact; r:gives {((2 1 4 6) ">=") list:sort (6 4 2 1)}] - skolem:lemma2310 - skolem:lemma2311 - [ a r:Fact; r:gives {(6421 1246) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1147}] + [ a r:Fact; r:gives {(1147 2000) math:sum 3147}] + skolem:lemma3146 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2146]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1246]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1147]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3147]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1148 a r:Inference; r:gives { - 2147 :kaprekar (0 1). + 3148 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2147 math:notEqualTo 0}] - skolem:lemma2312 - [ a r:Fact; r:gives {((2 1 4 7) "=<") list:sort (1 2 4 7)}] - [ a r:Fact; r:gives {((2 1 4 7) ">=") list:sort (7 4 2 1)}] - skolem:lemma2313 - skolem:lemma2314 - [ a r:Fact; r:gives {(7421 1247) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1148}] + [ a r:Fact; r:gives {(1148 2000) math:sum 3148}] + skolem:lemma3147 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2147]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1247]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1148]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3148]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1149 a r:Inference; r:gives { - 2148 :kaprekar (0 5). + 3149 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2148 math:notEqualTo 0}] - skolem:lemma2315 - [ a r:Fact; r:gives {((2 1 4 8) "=<") list:sort (1 2 4 8)}] - [ a r:Fact; r:gives {((2 1 4 8) ">=") list:sort (8 4 2 1)}] - skolem:lemma2316 - skolem:lemma2317 - [ a r:Fact; r:gives {(8421 1248) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1149}] + [ a r:Fact; r:gives {(1149 2000) math:sum 3149}] + skolem:lemma3148 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2148]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1248]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1149]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3149]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1150 a r:Inference; r:gives { - 2149 :kaprekar (0 6). + 3150 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2149 math:notEqualTo 0}] - skolem:lemma2318 - [ a r:Fact; r:gives {((2 1 4 9) "=<") list:sort (1 2 4 9)}] - [ a r:Fact; r:gives {((2 1 4 9) ">=") list:sort (9 4 2 1)}] - skolem:lemma2319 - skolem:lemma2320 - [ a r:Fact; r:gives {(9421 1249) math:difference 8172}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8172 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 8172 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1150}] + [ a r:Fact; r:gives {(1150 2000) math:sum 3150}] + skolem:lemma3149 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2149]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1249]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1150]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3150]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1151 a r:Inference; r:gives { - 2150 :kaprekar (0 7). + 3151 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2150 math:notEqualTo 0}] - skolem:lemma2321 - [ a r:Fact; r:gives {((2 1 5 0) "=<") list:sort (0 1 2 5)}] - [ a r:Fact; r:gives {((2 1 5 0) ">=") list:sort (5 2 1 0)}] - skolem:lemma2045 - skolem:lemma2046 - [ a r:Fact; r:gives {(5210 125) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1151}] + [ a r:Fact; r:gives {(1151 2000) math:sum 3151}] + skolem:lemma3150 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2150]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 125]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1151]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3151]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1152 a r:Inference; r:gives { - 2151 :kaprekar (0 7). + 3152 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2151 math:notEqualTo 0}] - skolem:lemma2322 - [ a r:Fact; r:gives {((2 1 5 1) "=<") list:sort (1 1 2 5)}] - [ a r:Fact; r:gives {((2 1 5 1) ">=") list:sort (5 2 1 1)}] - skolem:lemma2235 - skolem:lemma2236 - [ a r:Fact; r:gives {(5211 1125) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1152}] + [ a r:Fact; r:gives {(1152 2000) math:sum 3152}] + skolem:lemma3151 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2151]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1125]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1152]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3152]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1153 a r:Inference; r:gives { - 2152 :kaprekar (0 4). + 3153 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2152 math:notEqualTo 0}] - skolem:lemma2323 - [ a r:Fact; r:gives {((2 1 5 2) "=<") list:sort (1 2 2 5)}] - [ a r:Fact; r:gives {((2 1 5 2) ">=") list:sort (5 2 2 1)}] - skolem:lemma2261 - skolem:lemma2262 - [ a r:Fact; r:gives {(5221 1225) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1153}] + [ a r:Fact; r:gives {(1153 2000) math:sum 3153}] + skolem:lemma3152 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2152]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1225]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1153]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3153]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1154 a r:Inference; r:gives { - 2153 :kaprekar (0 7). + 3154 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2153 math:notEqualTo 0}] - skolem:lemma2324 - [ a r:Fact; r:gives {((2 1 5 3) "=<") list:sort (1 2 3 5)}] - [ a r:Fact; r:gives {((2 1 5 3) ">=") list:sort (5 3 2 1)}] - skolem:lemma2285 - skolem:lemma2286 - [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1154}] + [ a r:Fact; r:gives {(1154 2000) math:sum 3154}] + skolem:lemma3153 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2153]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1235]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1154]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3154]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1155 a r:Inference; r:gives { - 2154 :kaprekar (0 2). + 3155 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2154 math:notEqualTo 0}] - skolem:lemma2325 - [ a r:Fact; r:gives {((2 1 5 4) "=<") list:sort (1 2 4 5)}] - [ a r:Fact; r:gives {((2 1 5 4) ">=") list:sort (5 4 2 1)}] - skolem:lemma2307 - skolem:lemma2308 - [ a r:Fact; r:gives {(5421 1245) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1155}] + [ a r:Fact; r:gives {(1155 2000) math:sum 3155}] + skolem:lemma3154 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2154]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1245]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1155]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3155]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1156 a r:Inference; r:gives { - 2155 :kaprekar (0 3). + 3156 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2155 math:notEqualTo 0}] - skolem:lemma2326 - [ a r:Fact; r:gives {((2 1 5 5) "=<") list:sort (1 2 5 5)}] - [ a r:Fact; r:gives {((2 1 5 5) ">=") list:sort (5 5 2 1)}] - skolem:lemma2327 - skolem:lemma2328 - [ a r:Fact; r:gives {(5521 1255) math:difference 4266}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4266 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 4266 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1156}] + [ a r:Fact; r:gives {(1156 2000) math:sum 3156}] + skolem:lemma3155 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2155]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1255]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1156]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3156]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1157 a r:Inference; r:gives { - 2156 :kaprekar (0 5). + 3157 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2156 math:notEqualTo 0}] - skolem:lemma2329 - [ a r:Fact; r:gives {((2 1 5 6) "=<") list:sort (1 2 5 6)}] - [ a r:Fact; r:gives {((2 1 5 6) ">=") list:sort (6 5 2 1)}] - skolem:lemma2330 - skolem:lemma2331 - [ a r:Fact; r:gives {(6521 1256) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1157}] + [ a r:Fact; r:gives {(1157 2000) math:sum 3157}] + skolem:lemma3156 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2156]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1256]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1157]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3157]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1158 a r:Inference; r:gives { - 2157 :kaprekar (0 3). + 3158 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2157 math:notEqualTo 0}] - skolem:lemma2332 - [ a r:Fact; r:gives {((2 1 5 7) "=<") list:sort (1 2 5 7)}] - [ a r:Fact; r:gives {((2 1 5 7) ">=") list:sort (7 5 2 1)}] - skolem:lemma2333 - skolem:lemma2334 - [ a r:Fact; r:gives {(7521 1257) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1158}] + [ a r:Fact; r:gives {(1158 2000) math:sum 3158}] + skolem:lemma3157 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2157]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1257]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1158]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3158]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1159 a r:Inference; r:gives { - 2158 :kaprekar (0 6). + 3159 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2158 math:notEqualTo 0}] - skolem:lemma2335 - [ a r:Fact; r:gives {((2 1 5 8) "=<") list:sort (1 2 5 8)}] - [ a r:Fact; r:gives {((2 1 5 8) ">=") list:sort (8 5 2 1)}] - skolem:lemma2336 - skolem:lemma2337 - [ a r:Fact; r:gives {(8521 1258) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1159}] + [ a r:Fact; r:gives {(1159 2000) math:sum 3159}] + skolem:lemma3158 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2158]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1258]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1159]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3159]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1160 a r:Inference; r:gives { - 2159 :kaprekar (0 5). + 3160 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2159 math:notEqualTo 0}] - skolem:lemma2338 - [ a r:Fact; r:gives {((2 1 5 9) "=<") list:sort (1 2 5 9)}] - [ a r:Fact; r:gives {((2 1 5 9) ">=") list:sort (9 5 2 1)}] - skolem:lemma2339 - skolem:lemma2340 - [ a r:Fact; r:gives {(9521 1259) math:difference 8262}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8262 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 8262 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1160}] + [ a r:Fact; r:gives {(1160 2000) math:sum 3160}] + skolem:lemma3159 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2159]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1259]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1160]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3160]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1161 a r:Inference; r:gives { - 2160 :kaprekar (0 7). + 3161 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2160 math:notEqualTo 0}] - skolem:lemma2341 - [ a r:Fact; r:gives {((2 1 6 0) "=<") list:sort (0 1 2 6)}] - [ a r:Fact; r:gives {((2 1 6 0) ">=") list:sort (6 2 1 0)}] - skolem:lemma2048 - skolem:lemma2049 - [ a r:Fact; r:gives {(6210 126) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1161}] + [ a r:Fact; r:gives {(1161 2000) math:sum 3161}] + skolem:lemma3160 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2160]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 126]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1161]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3161]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1162 a r:Inference; r:gives { - 2161 :kaprekar (0 7). + 3162 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2161 math:notEqualTo 0}] - skolem:lemma2342 - [ a r:Fact; r:gives {((2 1 6 1) "=<") list:sort (1 1 2 6)}] - [ a r:Fact; r:gives {((2 1 6 1) ">=") list:sort (6 2 1 1)}] - skolem:lemma2238 - skolem:lemma2239 - [ a r:Fact; r:gives {(6211 1126) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1162}] + [ a r:Fact; r:gives {(1162 2000) math:sum 3162}] + skolem:lemma3161 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2161]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1126]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1162]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3162]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1163 a r:Inference; r:gives { - 2162 :kaprekar (0 6). + 3163 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2162 math:notEqualTo 0}] - skolem:lemma2343 - [ a r:Fact; r:gives {((2 1 6 2) "=<") list:sort (1 2 2 6)}] - [ a r:Fact; r:gives {((2 1 6 2) ">=") list:sort (6 2 2 1)}] - skolem:lemma2264 - skolem:lemma2265 - [ a r:Fact; r:gives {(6221 1226) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1163}] + [ a r:Fact; r:gives {(1163 2000) math:sum 3163}] + skolem:lemma3162 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2162]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1226]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1163]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3163]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1164 a r:Inference; r:gives { - 2163 :kaprekar (0 7). + 3164 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2163 math:notEqualTo 0}] - skolem:lemma2344 - [ a r:Fact; r:gives {((2 1 6 3) "=<") list:sort (1 2 3 6)}] - [ a r:Fact; r:gives {((2 1 6 3) ">=") list:sort (6 3 2 1)}] - skolem:lemma2288 - skolem:lemma2289 - [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1164}] + [ a r:Fact; r:gives {(1164 2000) math:sum 3164}] + skolem:lemma3163 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2163]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1236]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1164]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3164]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1165 a r:Inference; r:gives { - 2164 :kaprekar (0 7). + 3165 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2164 math:notEqualTo 0}] - skolem:lemma2345 - [ a r:Fact; r:gives {((2 1 6 4) "=<") list:sort (1 2 4 6)}] - [ a r:Fact; r:gives {((2 1 6 4) ">=") list:sort (6 4 2 1)}] - skolem:lemma2310 - skolem:lemma2311 - [ a r:Fact; r:gives {(6421 1246) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1165}] + [ a r:Fact; r:gives {(1165 2000) math:sum 3165}] + skolem:lemma3164 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2164]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1246]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1165]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3165]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1166 a r:Inference; r:gives { - 2165 :kaprekar (0 5). + 3166 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2165 math:notEqualTo 0}] - skolem:lemma2346 - [ a r:Fact; r:gives {((2 1 6 5) "=<") list:sort (1 2 5 6)}] - [ a r:Fact; r:gives {((2 1 6 5) ">=") list:sort (6 5 2 1)}] - skolem:lemma2330 - skolem:lemma2331 - [ a r:Fact; r:gives {(6521 1256) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1166}] + [ a r:Fact; r:gives {(1166 2000) math:sum 3166}] + skolem:lemma3165 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2165]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1256]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1166]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3166]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1167 a r:Inference; r:gives { - 2166 :kaprekar (0 5). + 3167 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2166 math:notEqualTo 0}] - skolem:lemma2347 - [ a r:Fact; r:gives {((2 1 6 6) "=<") list:sort (1 2 6 6)}] - [ a r:Fact; r:gives {((2 1 6 6) ">=") list:sort (6 6 2 1)}] - skolem:lemma2348 - skolem:lemma2349 - [ a r:Fact; r:gives {(6621 1266) math:difference 5355}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5355 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5355 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1167}] + [ a r:Fact; r:gives {(1167 2000) math:sum 3167}] + skolem:lemma3166 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2166]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1167]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3167]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1168 a r:Inference; r:gives { - 2167 :kaprekar (0 4). + 3168 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2167 math:notEqualTo 0}] - skolem:lemma2350 - [ a r:Fact; r:gives {((2 1 6 7) "=<") list:sort (1 2 6 7)}] - [ a r:Fact; r:gives {((2 1 6 7) ">=") list:sort (7 6 2 1)}] - skolem:lemma2351 - skolem:lemma2352 - [ a r:Fact; r:gives {(7621 1267) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1168}] + [ a r:Fact; r:gives {(1168 2000) math:sum 3168}] + skolem:lemma3167 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2167]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1168]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3168]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1169 a r:Inference; r:gives { - 2168 :kaprekar (0 3). + 3169 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2168 math:notEqualTo 0}] - skolem:lemma2353 - [ a r:Fact; r:gives {((2 1 6 8) "=<") list:sort (1 2 6 8)}] - [ a r:Fact; r:gives {((2 1 6 8) ">=") list:sort (8 6 2 1)}] - skolem:lemma2354 - skolem:lemma2355 - [ a r:Fact; r:gives {(8621 1268) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1169}] + [ a r:Fact; r:gives {(1169 2000) math:sum 3169}] + skolem:lemma3168 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2168]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1268]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1169]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3169]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1170 a r:Inference; r:gives { - 2169 :kaprekar (0 2). + 3170 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2169 math:notEqualTo 0}] - skolem:lemma2356 - [ a r:Fact; r:gives {((2 1 6 9) "=<") list:sort (1 2 6 9)}] - [ a r:Fact; r:gives {((2 1 6 9) ">=") list:sort (9 6 2 1)}] - skolem:lemma2357 - skolem:lemma2358 - [ a r:Fact; r:gives {(9621 1269) math:difference 8352}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8352 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 8352 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1170}] + [ a r:Fact; r:gives {(1170 2000) math:sum 3170}] + skolem:lemma3169 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2169]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1269]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1170]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3170]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1171 a r:Inference; r:gives { - 2170 :kaprekar (0 3). + 3171 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2170 math:notEqualTo 0}] - skolem:lemma2359 - [ a r:Fact; r:gives {((2 1 7 0) "=<") list:sort (0 1 2 7)}] - [ a r:Fact; r:gives {((2 1 7 0) ">=") list:sort (7 2 1 0)}] - skolem:lemma2051 - skolem:lemma2052 - [ a r:Fact; r:gives {(7210 127) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1171}] + [ a r:Fact; r:gives {(1171 2000) math:sum 3171}] + skolem:lemma3170 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2170]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 127]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1172 a r:Inference; r:gives { - 2171 :kaprekar (0 7). + 3172 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2171 math:notEqualTo 0}] - skolem:lemma2360 - [ a r:Fact; r:gives {((2 1 7 1) "=<") list:sort (1 1 2 7)}] - [ a r:Fact; r:gives {((2 1 7 1) ">=") list:sort (7 2 1 1)}] - skolem:lemma2241 - skolem:lemma2242 - [ a r:Fact; r:gives {(7211 1127) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1172}] + [ a r:Fact; r:gives {(1172 2000) math:sum 3172}] + skolem:lemma3171 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2171]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1127]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1173 a r:Inference; r:gives { - 2172 :kaprekar (0 6). + 3173 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2172 math:notEqualTo 0}] - skolem:lemma2361 - [ a r:Fact; r:gives {((2 1 7 2) "=<") list:sort (1 2 2 7)}] - [ a r:Fact; r:gives {((2 1 7 2) ">=") list:sort (7 2 2 1)}] - skolem:lemma2267 - skolem:lemma2268 - [ a r:Fact; r:gives {(7221 1227) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1173}] + [ a r:Fact; r:gives {(1173 2000) math:sum 3173}] + skolem:lemma3172 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1227]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1174 a r:Inference; r:gives { - 2173 :kaprekar (0 7). + 3174 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2173 math:notEqualTo 0}] - skolem:lemma2362 - [ a r:Fact; r:gives {((2 1 7 3) "=<") list:sort (1 2 3 7)}] - [ a r:Fact; r:gives {((2 1 7 3) ">=") list:sort (7 3 2 1)}] - skolem:lemma2291 - skolem:lemma2292 - [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1174}] + [ a r:Fact; r:gives {(1174 2000) math:sum 3174}] + skolem:lemma3173 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1237]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1175 a r:Inference; r:gives { - 2174 :kaprekar (0 1). + 3175 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2174 math:notEqualTo 0}] - skolem:lemma2363 - [ a r:Fact; r:gives {((2 1 7 4) "=<") list:sort (1 2 4 7)}] - [ a r:Fact; r:gives {((2 1 7 4) ">=") list:sort (7 4 2 1)}] - skolem:lemma2313 - skolem:lemma2314 - [ a r:Fact; r:gives {(7421 1247) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1175}] + [ a r:Fact; r:gives {(1175 2000) math:sum 3175}] + skolem:lemma3174 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1247]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1176 a r:Inference; r:gives { - 2175 :kaprekar (0 3). + 3176 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2175 math:notEqualTo 0}] - skolem:lemma2364 - [ a r:Fact; r:gives {((2 1 7 5) "=<") list:sort (1 2 5 7)}] - [ a r:Fact; r:gives {((2 1 7 5) ">=") list:sort (7 5 2 1)}] - skolem:lemma2333 - skolem:lemma2334 - [ a r:Fact; r:gives {(7521 1257) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1176}] + [ a r:Fact; r:gives {(1176 2000) math:sum 3176}] + skolem:lemma3175 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1257]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1177 a r:Inference; r:gives { - 2176 :kaprekar (0 4). + 3177 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2176 math:notEqualTo 0}] - skolem:lemma2365 - [ a r:Fact; r:gives {((2 1 7 6) "=<") list:sort (1 2 6 7)}] - [ a r:Fact; r:gives {((2 1 7 6) ">=") list:sort (7 6 2 1)}] - skolem:lemma2351 - skolem:lemma2352 - [ a r:Fact; r:gives {(7621 1267) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1177}] + [ a r:Fact; r:gives {(1177 2000) math:sum 3177}] + skolem:lemma3176 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1178 a r:Inference; r:gives { - 2177 :kaprekar (0 5). + 3178 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2177 math:notEqualTo 0}] - skolem:lemma2366 - [ a r:Fact; r:gives {((2 1 7 7) "=<") list:sort (1 2 7 7)}] - [ a r:Fact; r:gives {((2 1 7 7) ">=") list:sort (7 7 2 1)}] - skolem:lemma2367 - skolem:lemma2368 - [ a r:Fact; r:gives {(7721 1277) math:difference 6444}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6444 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 6444 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1178}] + [ a r:Fact; r:gives {(1178 2000) math:sum 3178}] + skolem:lemma3177 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1277]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7721]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1178]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3178]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1179 a r:Inference; r:gives { - 2178 :kaprekar (0 5). + 3179 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2178 math:notEqualTo 0}] - skolem:lemma2369 - [ a r:Fact; r:gives {((2 1 7 8) "=<") list:sort (1 2 7 8)}] - [ a r:Fact; r:gives {((2 1 7 8) ">=") list:sort (8 7 2 1)}] - skolem:lemma2370 - skolem:lemma2371 - [ a r:Fact; r:gives {(8721 1278) math:difference 7443}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7443 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1179}] + [ a r:Fact; r:gives {(1179 2000) math:sum 3179}] + skolem:lemma3178 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2178]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1278]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8721]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1179]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3179]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1180 a r:Inference; r:gives { - 2179 :kaprekar (0 7). + 3180 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2179 math:notEqualTo 0}] - skolem:lemma2372 - [ a r:Fact; r:gives {((2 1 7 9) "=<") list:sort (1 2 7 9)}] - [ a r:Fact; r:gives {((2 1 7 9) ">=") list:sort (9 7 2 1)}] - skolem:lemma2373 - skolem:lemma2374 - [ a r:Fact; r:gives {(9721 1279) math:difference 8442}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8442 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 8442 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1180}] + [ a r:Fact; r:gives {(1180 2000) math:sum 3180}] + skolem:lemma3179 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2179]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1279]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9721]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1180]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3180]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1181 a r:Inference; r:gives { - 2180 :kaprekar (0 3). + 3181 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2180 math:notEqualTo 0}] - skolem:lemma2375 - [ a r:Fact; r:gives {((2 1 8 0) "=<") list:sort (0 1 2 8)}] - [ a r:Fact; r:gives {((2 1 8 0) ">=") list:sort (8 2 1 0)}] - skolem:lemma2054 - skolem:lemma2055 - [ a r:Fact; r:gives {(8210 128) math:difference 8082}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8082 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 8082 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1181}] + [ a r:Fact; r:gives {(1181 2000) math:sum 3181}] + skolem:lemma3180 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2180]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 128]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1181]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3181]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1182 a r:Inference; r:gives { - 2181 :kaprekar (0 3). + 3182 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2181 math:notEqualTo 0}] - skolem:lemma2376 - [ a r:Fact; r:gives {((2 1 8 1) "=<") list:sort (1 1 2 8)}] - [ a r:Fact; r:gives {((2 1 8 1) ">=") list:sort (8 2 1 1)}] - skolem:lemma2244 - skolem:lemma2245 - [ a r:Fact; r:gives {(8211 1128) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1182}] + [ a r:Fact; r:gives {(1182 2000) math:sum 3182}] + skolem:lemma3181 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2181]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1128]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1182]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3182]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1183 a r:Inference; r:gives { - 2182 :kaprekar (0 4). + 3183 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2182 math:notEqualTo 0}] - skolem:lemma2377 - [ a r:Fact; r:gives {((2 1 8 2) "=<") list:sort (1 2 2 8)}] - [ a r:Fact; r:gives {((2 1 8 2) ">=") list:sort (8 2 2 1)}] - skolem:lemma2270 - skolem:lemma2271 - [ a r:Fact; r:gives {(8221 1228) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1183}] + [ a r:Fact; r:gives {(1183 2000) math:sum 3183}] + skolem:lemma3182 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2182]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1228]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1183]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3183]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1184 a r:Inference; r:gives { - 2183 :kaprekar (0 3). + 3184 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2183 math:notEqualTo 0}] - skolem:lemma2378 - [ a r:Fact; r:gives {((2 1 8 3) "=<") list:sort (1 2 3 8)}] - [ a r:Fact; r:gives {((2 1 8 3) ">=") list:sort (8 3 2 1)}] - skolem:lemma2294 - skolem:lemma2295 - [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1184}] + [ a r:Fact; r:gives {(1184 2000) math:sum 3184}] + skolem:lemma3183 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2183]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1238]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1184]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3184]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1185 a r:Inference; r:gives { - 2184 :kaprekar (0 5). + 3185 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2184 math:notEqualTo 0}] - skolem:lemma2379 - [ a r:Fact; r:gives {((2 1 8 4) "=<") list:sort (1 2 4 8)}] - [ a r:Fact; r:gives {((2 1 8 4) ">=") list:sort (8 4 2 1)}] - skolem:lemma2316 - skolem:lemma2317 - [ a r:Fact; r:gives {(8421 1248) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1185}] + [ a r:Fact; r:gives {(1185 2000) math:sum 3185}] + skolem:lemma3184 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2184]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1248]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1185]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3185]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1186 a r:Inference; r:gives { - 2185 :kaprekar (0 6). + 3186 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2185 math:notEqualTo 0}] - skolem:lemma2380 - [ a r:Fact; r:gives {((2 1 8 5) "=<") list:sort (1 2 5 8)}] - [ a r:Fact; r:gives {((2 1 8 5) ">=") list:sort (8 5 2 1)}] - skolem:lemma2336 - skolem:lemma2337 - [ a r:Fact; r:gives {(8521 1258) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1186}] + [ a r:Fact; r:gives {(1186 2000) math:sum 3186}] + skolem:lemma3185 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2185]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1258]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1186]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3186]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1187 a r:Inference; r:gives { - 2186 :kaprekar (0 3). + 3187 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2186 math:notEqualTo 0}] - skolem:lemma2381 - [ a r:Fact; r:gives {((2 1 8 6) "=<") list:sort (1 2 6 8)}] - [ a r:Fact; r:gives {((2 1 8 6) ">=") list:sort (8 6 2 1)}] - skolem:lemma2354 - skolem:lemma2355 - [ a r:Fact; r:gives {(8621 1268) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1187}] + [ a r:Fact; r:gives {(1187 2000) math:sum 3187}] + skolem:lemma3186 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2186]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1268]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1187]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3187]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1188 a r:Inference; r:gives { - 2187 :kaprekar (0 5). + 3188 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2187 math:notEqualTo 0}] - skolem:lemma2382 - [ a r:Fact; r:gives {((2 1 8 7) "=<") list:sort (1 2 7 8)}] - [ a r:Fact; r:gives {((2 1 8 7) ">=") list:sort (8 7 2 1)}] - skolem:lemma2370 - skolem:lemma2371 - [ a r:Fact; r:gives {(8721 1278) math:difference 7443}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7443 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1188}] + [ a r:Fact; r:gives {(1188 2000) math:sum 3188}] + skolem:lemma3187 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2187]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1278]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8721]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1188]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3188]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1189 a r:Inference; r:gives { - 2188 :kaprekar (0 3). + 3189 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2188 math:notEqualTo 0}] - skolem:lemma2383 - [ a r:Fact; r:gives {((2 1 8 8) "=<") list:sort (1 2 8 8)}] - [ a r:Fact; r:gives {((2 1 8 8) ">=") list:sort (8 8 2 1)}] - skolem:lemma2384 - skolem:lemma2385 - [ a r:Fact; r:gives {(8821 1288) math:difference 7533}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7533 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7533 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1189}] + [ a r:Fact; r:gives {(1189 2000) math:sum 3189}] + skolem:lemma3188 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2188]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1288]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8821]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1189]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3189]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1190 a r:Inference; r:gives { - 2189 :kaprekar (0 2). + 3190 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2189 math:notEqualTo 0}] - skolem:lemma2386 - [ a r:Fact; r:gives {((2 1 8 9) "=<") list:sort (1 2 8 9)}] - [ a r:Fact; r:gives {((2 1 8 9) ">=") list:sort (9 8 2 1)}] - skolem:lemma2387 - skolem:lemma2388 - [ a r:Fact; r:gives {(9821 1289) math:difference 8532}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8532 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 8532 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1190}] + [ a r:Fact; r:gives {(1190 2000) math:sum 3190}] + skolem:lemma3189 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2189]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1289]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9821]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1190]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3190]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1191 a r:Inference; r:gives { - 2190 :kaprekar (0 4). + 3191 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2190 math:notEqualTo 0}] - skolem:lemma2389 - [ a r:Fact; r:gives {((2 1 9 0) "=<") list:sort (0 1 2 9)}] - [ a r:Fact; r:gives {((2 1 9 0) ">=") list:sort (9 2 1 0)}] - skolem:lemma2057 - skolem:lemma2058 - [ a r:Fact; r:gives {(9210 129) math:difference 9081}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9081 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 9081 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1191}] + [ a r:Fact; r:gives {(1191 2000) math:sum 3191}] + skolem:lemma3190 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2190]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 129]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1191]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3191]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1192 a r:Inference; r:gives { - 2191 :kaprekar (0 3). + 3192 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2191 math:notEqualTo 0}] - skolem:lemma2390 - [ a r:Fact; r:gives {((2 1 9 1) "=<") list:sort (1 1 2 9)}] - [ a r:Fact; r:gives {((2 1 9 1) ">=") list:sort (9 2 1 1)}] - skolem:lemma2247 - skolem:lemma2248 - [ a r:Fact; r:gives {(9211 1129) math:difference 8082}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8082 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 8082 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1192}] + [ a r:Fact; r:gives {(1192 2000) math:sum 3192}] + skolem:lemma3191 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2191]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1129]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1192]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3192]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1193 a r:Inference; r:gives { - 2192 :kaprekar (0 6). + 3193 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2192 math:notEqualTo 0}] - skolem:lemma2391 - [ a r:Fact; r:gives {((2 1 9 2) "=<") list:sort (1 2 2 9)}] - [ a r:Fact; r:gives {((2 1 9 2) ">=") list:sort (9 2 2 1)}] - skolem:lemma2273 - skolem:lemma2274 - [ a r:Fact; r:gives {(9221 1229) math:difference 7992}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7992 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7992 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1193}] + [ a r:Fact; r:gives {(1193 2000) math:sum 3193}] + skolem:lemma3192 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2192]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1229]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1193]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3193]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1194 a r:Inference; r:gives { - 2193 :kaprekar (0 3). + 3194 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2193 math:notEqualTo 0}] - skolem:lemma2392 - [ a r:Fact; r:gives {((2 1 9 3) "=<") list:sort (1 2 3 9)}] - [ a r:Fact; r:gives {((2 1 9 3) ">=") list:sort (9 3 2 1)}] - skolem:lemma2297 - skolem:lemma2298 - [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8082 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 8082 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1194}] + [ a r:Fact; r:gives {(1194 2000) math:sum 3194}] + skolem:lemma3193 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2193]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1239]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1194]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3194]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1195 a r:Inference; r:gives { - 2194 :kaprekar (0 6). + 3195 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2194 math:notEqualTo 0}] - skolem:lemma2393 - [ a r:Fact; r:gives {((2 1 9 4) "=<") list:sort (1 2 4 9)}] - [ a r:Fact; r:gives {((2 1 9 4) ">=") list:sort (9 4 2 1)}] - skolem:lemma2319 - skolem:lemma2320 - [ a r:Fact; r:gives {(9421 1249) math:difference 8172}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8172 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 8172 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1195}] + [ a r:Fact; r:gives {(1195 2000) math:sum 3195}] + skolem:lemma3194 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2194]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1249]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1195]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3195]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1196 a r:Inference; r:gives { - 2195 :kaprekar (0 5). + 3196 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2195 math:notEqualTo 0}] - skolem:lemma2394 - [ a r:Fact; r:gives {((2 1 9 5) "=<") list:sort (1 2 5 9)}] - [ a r:Fact; r:gives {((2 1 9 5) ">=") list:sort (9 5 2 1)}] - skolem:lemma2339 - skolem:lemma2340 - [ a r:Fact; r:gives {(9521 1259) math:difference 8262}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8262 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 8262 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1196}] + [ a r:Fact; r:gives {(1196 2000) math:sum 3196}] + skolem:lemma3195 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2195]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1259]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1196]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3196]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1197 a r:Inference; r:gives { - 2196 :kaprekar (0 2). + 3197 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2196 math:notEqualTo 0}] - skolem:lemma2395 - [ a r:Fact; r:gives {((2 1 9 6) "=<") list:sort (1 2 6 9)}] - [ a r:Fact; r:gives {((2 1 9 6) ">=") list:sort (9 6 2 1)}] - skolem:lemma2357 - skolem:lemma2358 - [ a r:Fact; r:gives {(9621 1269) math:difference 8352}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8352 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 8352 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1197}] + [ a r:Fact; r:gives {(1197 2000) math:sum 3197}] + skolem:lemma3196 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2196]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1269]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1197]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3197]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1198 a r:Inference; r:gives { - 2197 :kaprekar (0 7). + 3198 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2197 math:notEqualTo 0}] - skolem:lemma2396 - [ a r:Fact; r:gives {((2 1 9 7) "=<") list:sort (1 2 7 9)}] - [ a r:Fact; r:gives {((2 1 9 7) ">=") list:sort (9 7 2 1)}] - skolem:lemma2373 - skolem:lemma2374 - [ a r:Fact; r:gives {(9721 1279) math:difference 8442}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8442 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 8442 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1198}] + [ a r:Fact; r:gives {(1198 2000) math:sum 3198}] + skolem:lemma3197 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2197]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1279]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9721]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1198]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3198]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1199 a r:Inference; r:gives { - 2198 :kaprekar (0 2). + 3199 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2198 math:notEqualTo 0}] - skolem:lemma2397 - [ a r:Fact; r:gives {((2 1 9 8) "=<") list:sort (1 2 8 9)}] - [ a r:Fact; r:gives {((2 1 9 8) ">=") list:sort (9 8 2 1)}] - skolem:lemma2387 - skolem:lemma2388 - [ a r:Fact; r:gives {(9821 1289) math:difference 8532}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8532 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 8532 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1199}] + [ a r:Fact; r:gives {(1199 2000) math:sum 3199}] + skolem:lemma3198 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2198]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1289]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9821]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1199]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3199]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1200 a r:Inference; r:gives { - 2199 :kaprekar (0 5). + 3200 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2199 math:notEqualTo 0}] - skolem:lemma2398 - [ a r:Fact; r:gives {((2 1 9 9) "=<") list:sort (1 2 9 9)}] - [ a r:Fact; r:gives {((2 1 9 9) ">=") list:sort (9 9 2 1)}] - skolem:lemma2399 - skolem:lemma2400 - [ a r:Fact; r:gives {(9921 1299) math:difference 8622}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8622 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 8622 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1200}] + [ a r:Fact; r:gives {(1200 2000) math:sum 3200}] + skolem:lemma3199 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2199]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1299]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9921]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1201 a r:Inference; r:gives { - 2200 :kaprekar (0 6). + 3201 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2200 math:notEqualTo 0}] - skolem:lemma2401 - [ a r:Fact; r:gives {((2 2 0 0) "=<") list:sort (0 0 2 2)}] - [ a r:Fact; r:gives {((2 2 0 0) ">=") list:sort (2 2 0 0)}] - skolem:lemma2008 - skolem:lemma2009 - [ a r:Fact; r:gives {(2200 22) math:difference 2178}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2178 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2178 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1201}] + [ a r:Fact; r:gives {(1201 2000) math:sum 3201}] + skolem:lemma3200 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2178]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1201]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3201]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1202 a r:Inference; r:gives { - 2201 :kaprekar (0 3). + 3202 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2201 math:notEqualTo 0}] - skolem:lemma2402 - [ a r:Fact; r:gives {((2 2 0 1) "=<") list:sort (0 1 2 2)}] - [ a r:Fact; r:gives {((2 2 0 1) ">=") list:sort (2 2 1 0)}] - skolem:lemma2036 - skolem:lemma2037 - [ a r:Fact; r:gives {(2210 122) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1202}] + [ a r:Fact; r:gives {(1202 2000) math:sum 3202}] + skolem:lemma3201 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2201]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 122]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1202]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3202]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1203 a r:Inference; r:gives { - 2202 :kaprekar (0 4). + 3203 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2202 math:notEqualTo 0}] - skolem:lemma2403 - [ a r:Fact; r:gives {((2 2 0 2) "=<") list:sort (0 2 2 2)}] - [ a r:Fact; r:gives {((2 2 0 2) ">=") list:sort (2 2 2 0)}] - skolem:lemma2062 - skolem:lemma2063 - [ a r:Fact; r:gives {(2220 222) math:difference 1998}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1998 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1998 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1203}] + [ a r:Fact; r:gives {(1203 2000) math:sum 3203}] + skolem:lemma3202 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2202]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1203]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3203]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1204 a r:Inference; r:gives { - 2203 :kaprekar (0 6). + 3204 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2203 math:notEqualTo 0}] - skolem:lemma2404 - [ a r:Fact; r:gives {((2 2 0 3) "=<") list:sort (0 2 2 3)}] - [ a r:Fact; r:gives {((2 2 0 3) ">=") list:sort (3 2 2 0)}] - skolem:lemma2065 - skolem:lemma2066 - [ a r:Fact; r:gives {(3220 223) math:difference 2997}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2997 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2997 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1204}] + [ a r:Fact; r:gives {(1204 2000) math:sum 3204}] + skolem:lemma3203 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2203]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 223]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1204]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3204]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1205 a r:Inference; r:gives { - 2204 :kaprekar (0 4). + 3205 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2204 math:notEqualTo 0}] - skolem:lemma2405 - [ a r:Fact; r:gives {((2 2 0 4) "=<") list:sort (0 2 2 4)}] - [ a r:Fact; r:gives {((2 2 0 4) ">=") list:sort (4 2 2 0)}] - skolem:lemma2068 - skolem:lemma2069 - [ a r:Fact; r:gives {(4220 224) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1205}] + [ a r:Fact; r:gives {(1205 2000) math:sum 3205}] + skolem:lemma3204 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2204]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 224]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1205]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3205]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1206 a r:Inference; r:gives { - 2205 :kaprekar (0 6). + 3206 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2205 math:notEqualTo 0}] - skolem:lemma2406 - [ a r:Fact; r:gives {((2 2 0 5) "=<") list:sort (0 2 2 5)}] - [ a r:Fact; r:gives {((2 2 0 5) ">=") list:sort (5 2 2 0)}] - skolem:lemma2071 - skolem:lemma2072 - [ a r:Fact; r:gives {(5220 225) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1206}] + [ a r:Fact; r:gives {(1206 2000) math:sum 3206}] + skolem:lemma3205 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2205]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 225]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1206]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3206]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1207 a r:Inference; r:gives { - 2206 :kaprekar (0 6). + 3207 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2206 math:notEqualTo 0}] - skolem:lemma2407 - [ a r:Fact; r:gives {((2 2 0 6) "=<") list:sort (0 2 2 6)}] - [ a r:Fact; r:gives {((2 2 0 6) ">=") list:sort (6 2 2 0)}] - skolem:lemma2074 - skolem:lemma2075 - [ a r:Fact; r:gives {(6220 226) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1207}] + [ a r:Fact; r:gives {(1207 2000) math:sum 3207}] + skolem:lemma3206 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2206]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 226]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1207]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3207]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1208 a r:Inference; r:gives { - 2207 :kaprekar (0 4). + 3208 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2207 math:notEqualTo 0}] - skolem:lemma2408 - [ a r:Fact; r:gives {((2 2 0 7) "=<") list:sort (0 2 2 7)}] - [ a r:Fact; r:gives {((2 2 0 7) ">=") list:sort (7 2 2 0)}] - skolem:lemma2077 - skolem:lemma2078 - [ a r:Fact; r:gives {(7220 227) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1208}] + [ a r:Fact; r:gives {(1208 2000) math:sum 3208}] + skolem:lemma3207 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2207]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 227]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1208]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3208]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1209 a r:Inference; r:gives { - 2208 :kaprekar (0 6). + 3209 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2208 math:notEqualTo 0}] - skolem:lemma2409 - [ a r:Fact; r:gives {((2 2 0 8) "=<") list:sort (0 2 2 8)}] - [ a r:Fact; r:gives {((2 2 0 8) ">=") list:sort (8 2 2 0)}] - skolem:lemma2080 - skolem:lemma2081 - [ a r:Fact; r:gives {(8220 228) math:difference 7992}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7992 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7992 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1209}] + [ a r:Fact; r:gives {(1209 2000) math:sum 3209}] + skolem:lemma3208 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2208]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 228]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1209]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3209]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1210 a r:Inference; r:gives { - 2209 :kaprekar (0 4). + 3210 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2209 math:notEqualTo 0}] - skolem:lemma2410 - [ a r:Fact; r:gives {((2 2 0 9) "=<") list:sort (0 2 2 9)}] - [ a r:Fact; r:gives {((2 2 0 9) ">=") list:sort (9 2 2 0)}] - skolem:lemma2083 - skolem:lemma2084 - [ a r:Fact; r:gives {(9220 229) math:difference 8991}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8991 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 8991 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1210}] + [ a r:Fact; r:gives {(1210 2000) math:sum 3210}] + skolem:lemma3209 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2209]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 229]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8991]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1211 a r:Inference; r:gives { - 2210 :kaprekar (0 3). + 3211 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2210 math:notEqualTo 0}] - skolem:lemma2411 - [ a r:Fact; r:gives {((2 2 1 0) "=<") list:sort (0 1 2 2)}] - [ a r:Fact; r:gives {((2 2 1 0) ">=") list:sort (2 2 1 0)}] - skolem:lemma2036 - skolem:lemma2037 - [ a r:Fact; r:gives {(2210 122) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1211}] + [ a r:Fact; r:gives {(1211 2000) math:sum 3211}] + skolem:lemma3210 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 122]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1212 a r:Inference; r:gives { - 2211 :kaprekar (0 4). + 3212 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2211 math:notEqualTo 0}] - skolem:lemma2412 - [ a r:Fact; r:gives {((2 2 1 1) "=<") list:sort (1 1 2 2)}] - [ a r:Fact; r:gives {((2 2 1 1) ">=") list:sort (2 2 1 1)}] - skolem:lemma2226 - skolem:lemma2227 - [ a r:Fact; r:gives {(2211 1122) math:difference 1089}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1089 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1089 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1212}] + [ a r:Fact; r:gives {(1212 2000) math:sum 3212}] + skolem:lemma3211 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1122]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1089]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1212]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3212]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1213 a r:Inference; r:gives { - 2212 :kaprekar (0 5). + 3213 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2212 math:notEqualTo 0}] - skolem:lemma2413 - [ a r:Fact; r:gives {((2 2 1 2) "=<") list:sort (1 2 2 2)}] - [ a r:Fact; r:gives {((2 2 1 2) ">=") list:sort (2 2 2 1)}] - skolem:lemma2252 - skolem:lemma2253 - [ a r:Fact; r:gives {(2221 1222) math:difference 999}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 999 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 999 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1213}] + [ a r:Fact; r:gives {(1213 2000) math:sum 3213}] + skolem:lemma3212 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2212]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1213]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3213]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1214 a r:Inference; r:gives { - 2213 :kaprekar (0 4). + 3214 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2213 math:notEqualTo 0}] - skolem:lemma2414 - [ a r:Fact; r:gives {((2 2 1 3) "=<") list:sort (1 2 2 3)}] - [ a r:Fact; r:gives {((2 2 1 3) ">=") list:sort (3 2 2 1)}] - skolem:lemma2255 - skolem:lemma2256 - [ a r:Fact; r:gives {(3221 1223) math:difference 1998}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1998 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1998 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1214}] + [ a r:Fact; r:gives {(1214 2000) math:sum 3214}] + skolem:lemma3213 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2213]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1223]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1214]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3214]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1215 a r:Inference; r:gives { - 2214 :kaprekar (0 6). + 3215 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2214 math:notEqualTo 0}] - skolem:lemma2415 - [ a r:Fact; r:gives {((2 2 1 4) "=<") list:sort (1 2 2 4)}] - [ a r:Fact; r:gives {((2 2 1 4) ">=") list:sort (4 2 2 1)}] - skolem:lemma2258 - skolem:lemma2259 - [ a r:Fact; r:gives {(4221 1224) math:difference 2997}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2997 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2997 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1215}] + [ a r:Fact; r:gives {(1215 2000) math:sum 3215}] + skolem:lemma3214 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2214]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1224]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1215]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3215]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1216 a r:Inference; r:gives { - 2215 :kaprekar (0 4). + 3216 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2215 math:notEqualTo 0}] - skolem:lemma2416 - [ a r:Fact; r:gives {((2 2 1 5) "=<") list:sort (1 2 2 5)}] - [ a r:Fact; r:gives {((2 2 1 5) ">=") list:sort (5 2 2 1)}] - skolem:lemma2261 - skolem:lemma2262 - [ a r:Fact; r:gives {(5221 1225) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1216}] + [ a r:Fact; r:gives {(1216 2000) math:sum 3216}] + skolem:lemma3215 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2215]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1225]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1216]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3216]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1217 a r:Inference; r:gives { - 2216 :kaprekar (0 6). + 3217 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2216 math:notEqualTo 0}] - skolem:lemma2417 - [ a r:Fact; r:gives {((2 2 1 6) "=<") list:sort (1 2 2 6)}] - [ a r:Fact; r:gives {((2 2 1 6) ">=") list:sort (6 2 2 1)}] - skolem:lemma2264 - skolem:lemma2265 - [ a r:Fact; r:gives {(6221 1226) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1217}] + [ a r:Fact; r:gives {(1217 2000) math:sum 3217}] + skolem:lemma3216 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2216]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1226]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1217]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3217]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1218 a r:Inference; r:gives { - 2217 :kaprekar (0 6). + 3218 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2217 math:notEqualTo 0}] - skolem:lemma2418 - [ a r:Fact; r:gives {((2 2 1 7) "=<") list:sort (1 2 2 7)}] - [ a r:Fact; r:gives {((2 2 1 7) ">=") list:sort (7 2 2 1)}] - skolem:lemma2267 - skolem:lemma2268 - [ a r:Fact; r:gives {(7221 1227) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1218}] + [ a r:Fact; r:gives {(1218 2000) math:sum 3218}] + skolem:lemma3217 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2217]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1227]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1218]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3218]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1219 a r:Inference; r:gives { - 2218 :kaprekar (0 4). + 3219 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2218 math:notEqualTo 0}] - skolem:lemma2419 - [ a r:Fact; r:gives {((2 2 1 8) "=<") list:sort (1 2 2 8)}] - [ a r:Fact; r:gives {((2 2 1 8) ">=") list:sort (8 2 2 1)}] - skolem:lemma2270 - skolem:lemma2271 - [ a r:Fact; r:gives {(8221 1228) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1219}] + [ a r:Fact; r:gives {(1219 2000) math:sum 3219}] + skolem:lemma3218 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2218]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1228]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1219]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3219]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1220 a r:Inference; r:gives { - 2219 :kaprekar (0 6). + 3220 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2219 math:notEqualTo 0}] - skolem:lemma2420 - [ a r:Fact; r:gives {((2 2 1 9) "=<") list:sort (1 2 2 9)}] - [ a r:Fact; r:gives {((2 2 1 9) ">=") list:sort (9 2 2 1)}] - skolem:lemma2273 - skolem:lemma2274 - [ a r:Fact; r:gives {(9221 1229) math:difference 7992}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7992 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7992 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1220}] + [ a r:Fact; r:gives {(1220 2000) math:sum 3220}] + skolem:lemma3219 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2219]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1229]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1221 a r:Inference; r:gives { - 2220 :kaprekar (0 4). + 3221 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2220 math:notEqualTo 0}] - skolem:lemma2421 - [ a r:Fact; r:gives {((2 2 2 0) "=<") list:sort (0 2 2 2)}] - [ a r:Fact; r:gives {((2 2 2 0) ">=") list:sort (2 2 2 0)}] - skolem:lemma2062 - skolem:lemma2063 - [ a r:Fact; r:gives {(2220 222) math:difference 1998}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1998 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1998 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1221}] + [ a r:Fact; r:gives {(1221 2000) math:sum 3221}] + skolem:lemma3220 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1222 a r:Inference; r:gives { - 2221 :kaprekar (0 5). + 3222 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2221 math:notEqualTo 0}] - skolem:lemma2422 - [ a r:Fact; r:gives {((2 2 2 1) "=<") list:sort (1 2 2 2)}] - [ a r:Fact; r:gives {((2 2 2 1) ">=") list:sort (2 2 2 1)}] - skolem:lemma2252 - skolem:lemma2253 - [ a r:Fact; r:gives {(2221 1222) math:difference 999}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 999 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 999 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1222}] + [ a r:Fact; r:gives {(1222 2000) math:sum 3222}] + skolem:lemma3221 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1223 a r:Inference; r:gives { - 2223 :kaprekar (0 5). + 3223 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2223 math:notEqualTo 0}] - skolem:lemma2423 - [ a r:Fact; r:gives {((2 2 2 3) "=<") list:sort (2 2 2 3)}] - [ a r:Fact; r:gives {((2 2 2 3) ">=") list:sort (3 2 2 2)}] - skolem:lemma2424 - skolem:lemma2425 - [ a r:Fact; r:gives {(3222 2223) math:difference 999}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 999 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 999 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1223}] + [ a r:Fact; r:gives {(1223 2000) math:sum 3223}] + skolem:lemma3222 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2223]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2223]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1224 a r:Inference; r:gives { - 2224 :kaprekar (0 4). + 3224 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2224 math:notEqualTo 0}] - skolem:lemma2426 - [ a r:Fact; r:gives {((2 2 2 4) "=<") list:sort (2 2 2 4)}] - [ a r:Fact; r:gives {((2 2 2 4) ">=") list:sort (4 2 2 2)}] - skolem:lemma2427 - skolem:lemma2428 - [ a r:Fact; r:gives {(4222 2224) math:difference 1998}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1998 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1998 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1224}] + [ a r:Fact; r:gives {(1224 2000) math:sum 3224}] + skolem:lemma3223 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2224]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2224]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1225 a r:Inference; r:gives { - 2225 :kaprekar (0 6). + 3225 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2225 math:notEqualTo 0}] - skolem:lemma2429 - [ a r:Fact; r:gives {((2 2 2 5) "=<") list:sort (2 2 2 5)}] - [ a r:Fact; r:gives {((2 2 2 5) ">=") list:sort (5 2 2 2)}] - skolem:lemma2430 - skolem:lemma2431 - [ a r:Fact; r:gives {(5222 2225) math:difference 2997}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2997 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2997 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1225}] + [ a r:Fact; r:gives {(1225 2000) math:sum 3225}] + skolem:lemma3224 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2225]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2225]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1226 a r:Inference; r:gives { - 2226 :kaprekar (0 4). + 3226 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2226 math:notEqualTo 0}] - skolem:lemma2432 - [ a r:Fact; r:gives {((2 2 2 6) "=<") list:sort (2 2 2 6)}] - [ a r:Fact; r:gives {((2 2 2 6) ">=") list:sort (6 2 2 2)}] - skolem:lemma2433 - skolem:lemma2434 - [ a r:Fact; r:gives {(6222 2226) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1226}] + [ a r:Fact; r:gives {(1226 2000) math:sum 3226}] + skolem:lemma3225 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2226]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2226]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1227 a r:Inference; r:gives { - 2227 :kaprekar (0 6). + 3227 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2227 math:notEqualTo 0}] - skolem:lemma2435 - [ a r:Fact; r:gives {((2 2 2 7) "=<") list:sort (2 2 2 7)}] - [ a r:Fact; r:gives {((2 2 2 7) ">=") list:sort (7 2 2 2)}] - skolem:lemma2436 - skolem:lemma2437 - [ a r:Fact; r:gives {(7222 2227) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1227}] + [ a r:Fact; r:gives {(1227 2000) math:sum 3227}] + skolem:lemma3226 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2227]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2227]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1228 a r:Inference; r:gives { - 2228 :kaprekar (0 6). + 3228 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2228 math:notEqualTo 0}] - skolem:lemma2438 - [ a r:Fact; r:gives {((2 2 2 8) "=<") list:sort (2 2 2 8)}] - [ a r:Fact; r:gives {((2 2 2 8) ">=") list:sort (8 2 2 2)}] - skolem:lemma2439 - skolem:lemma2440 - [ a r:Fact; r:gives {(8222 2228) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1228}] + [ a r:Fact; r:gives {(1228 2000) math:sum 3228}] + skolem:lemma3227 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2228]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2228]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1229 a r:Inference; r:gives { - 2229 :kaprekar (0 4). + 3229 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2229 math:notEqualTo 0}] - skolem:lemma2441 - [ a r:Fact; r:gives {((2 2 2 9) "=<") list:sort (2 2 2 9)}] - [ a r:Fact; r:gives {((2 2 2 9) ">=") list:sort (9 2 2 2)}] - skolem:lemma2442 - skolem:lemma2443 - [ a r:Fact; r:gives {(9222 2229) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1229}] + [ a r:Fact; r:gives {(1229 2000) math:sum 3229}] + skolem:lemma3228 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2229]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2229]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1230 a r:Inference; r:gives { - 2230 :kaprekar (0 6). + 3230 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2230 math:notEqualTo 0}] - skolem:lemma2444 - [ a r:Fact; r:gives {((2 2 3 0) "=<") list:sort (0 2 2 3)}] - [ a r:Fact; r:gives {((2 2 3 0) ">=") list:sort (3 2 2 0)}] - skolem:lemma2065 - skolem:lemma2066 - [ a r:Fact; r:gives {(3220 223) math:difference 2997}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2997 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2997 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1230}] + [ a r:Fact; r:gives {(1230 2000) math:sum 3230}] + skolem:lemma3229 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2230]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 223]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1230]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3230]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1231 a r:Inference; r:gives { - 2231 :kaprekar (0 4). + 3231 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2231 math:notEqualTo 0}] - skolem:lemma2445 - [ a r:Fact; r:gives {((2 2 3 1) "=<") list:sort (1 2 2 3)}] - [ a r:Fact; r:gives {((2 2 3 1) ">=") list:sort (3 2 2 1)}] - skolem:lemma2255 - skolem:lemma2256 - [ a r:Fact; r:gives {(3221 1223) math:difference 1998}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1998 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1998 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1231}] + [ a r:Fact; r:gives {(1231 2000) math:sum 3231}] + skolem:lemma3230 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2231]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1223]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1231]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3231]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1232 a r:Inference; r:gives { - 2232 :kaprekar (0 5). + 3232 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2232 math:notEqualTo 0}] - skolem:lemma2446 - [ a r:Fact; r:gives {((2 2 3 2) "=<") list:sort (2 2 2 3)}] - [ a r:Fact; r:gives {((2 2 3 2) ">=") list:sort (3 2 2 2)}] - skolem:lemma2424 - skolem:lemma2425 - [ a r:Fact; r:gives {(3222 2223) math:difference 999}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 999 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 999 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1232}] + [ a r:Fact; r:gives {(1232 2000) math:sum 3232}] + skolem:lemma3231 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2232]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2223]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1232]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3232]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1233 a r:Inference; r:gives { - 2233 :kaprekar (0 4). + 3233 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2233 math:notEqualTo 0}] - skolem:lemma2447 - [ a r:Fact; r:gives {((2 2 3 3) "=<") list:sort (2 2 3 3)}] - [ a r:Fact; r:gives {((2 2 3 3) ">=") list:sort (3 3 2 2)}] - skolem:lemma2448 - skolem:lemma2449 - [ a r:Fact; r:gives {(3322 2233) math:difference 1089}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1089 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1089 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1233}] + [ a r:Fact; r:gives {(1233 2000) math:sum 3233}] + skolem:lemma3232 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2233]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2233]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1089]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1234 a r:Inference; r:gives { - 2234 :kaprekar (0 3). + 3234 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2234 math:notEqualTo 0}] - skolem:lemma2450 - [ a r:Fact; r:gives {((2 2 3 4) "=<") list:sort (2 2 3 4)}] - [ a r:Fact; r:gives {((2 2 3 4) ">=") list:sort (4 3 2 2)}] - skolem:lemma2451 - skolem:lemma2452 - [ a r:Fact; r:gives {(4322 2234) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1234}] + [ a r:Fact; r:gives {(1234 2000) math:sum 3234}] + skolem:lemma3233 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2234]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2234]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1235 a r:Inference; r:gives { - 2235 :kaprekar (0 3). + 3235 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2235 math:notEqualTo 0}] - skolem:lemma2453 - [ a r:Fact; r:gives {((2 2 3 5) "=<") list:sort (2 2 3 5)}] - [ a r:Fact; r:gives {((2 2 3 5) ">=") list:sort (5 3 2 2)}] - skolem:lemma2454 - skolem:lemma2455 - [ a r:Fact; r:gives {(5322 2235) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1235}] + [ a r:Fact; r:gives {(1235 2000) math:sum 3235}] + skolem:lemma3234 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2235]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2235]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1236 a r:Inference; r:gives { - 2236 :kaprekar (0 7). + 3236 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2236 math:notEqualTo 0}] - skolem:lemma2456 - [ a r:Fact; r:gives {((2 2 3 6) "=<") list:sort (2 2 3 6)}] - [ a r:Fact; r:gives {((2 2 3 6) ">=") list:sort (6 3 2 2)}] - skolem:lemma2457 - skolem:lemma2458 - [ a r:Fact; r:gives {(6322 2236) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1236}] + [ a r:Fact; r:gives {(1236 2000) math:sum 3236}] + skolem:lemma3235 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2236]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2236]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1237 a r:Inference; r:gives { - 2237 :kaprekar (0 7). + 3237 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2237 math:notEqualTo 0}] - skolem:lemma2459 - [ a r:Fact; r:gives {((2 2 3 7) "=<") list:sort (2 2 3 7)}] - [ a r:Fact; r:gives {((2 2 3 7) ">=") list:sort (7 3 2 2)}] - skolem:lemma2460 - skolem:lemma2461 - [ a r:Fact; r:gives {(7322 2237) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1237}] + [ a r:Fact; r:gives {(1237 2000) math:sum 3237}] + skolem:lemma3236 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2237]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2237]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1238 a r:Inference; r:gives { - 2238 :kaprekar (0 7). + 3238 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2238 math:notEqualTo 0}] - skolem:lemma2462 - [ a r:Fact; r:gives {((2 2 3 8) "=<") list:sort (2 2 3 8)}] - [ a r:Fact; r:gives {((2 2 3 8) ">=") list:sort (8 3 2 2)}] - skolem:lemma2463 - skolem:lemma2464 - [ a r:Fact; r:gives {(8322 2238) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1238}] + [ a r:Fact; r:gives {(1238 2000) math:sum 3238}] + skolem:lemma3237 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2238]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2238]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1239 a r:Inference; r:gives { - 2239 :kaprekar (0 3). + 3239 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2239 math:notEqualTo 0}] - skolem:lemma2465 - [ a r:Fact; r:gives {((2 2 3 9) "=<") list:sort (2 2 3 9)}] - [ a r:Fact; r:gives {((2 2 3 9) ">=") list:sort (9 3 2 2)}] - skolem:lemma2466 - skolem:lemma2467 - [ a r:Fact; r:gives {(9322 2239) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1239}] + [ a r:Fact; r:gives {(1239 2000) math:sum 3239}] + skolem:lemma3238 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2239]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2239]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1240 a r:Inference; r:gives { - 2240 :kaprekar (0 4). + 3240 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2240 math:notEqualTo 0}] - skolem:lemma2468 - [ a r:Fact; r:gives {((2 2 4 0) "=<") list:sort (0 2 2 4)}] - [ a r:Fact; r:gives {((2 2 4 0) ">=") list:sort (4 2 2 0)}] - skolem:lemma2068 - skolem:lemma2069 - [ a r:Fact; r:gives {(4220 224) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1240}] + [ a r:Fact; r:gives {(1240 2000) math:sum 3240}] + skolem:lemma3239 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2240]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 224]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1240]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3240]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1241 a r:Inference; r:gives { - 2241 :kaprekar (0 6). + 3241 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2241 math:notEqualTo 0}] - skolem:lemma2469 - [ a r:Fact; r:gives {((2 2 4 1) "=<") list:sort (1 2 2 4)}] - [ a r:Fact; r:gives {((2 2 4 1) ">=") list:sort (4 2 2 1)}] - skolem:lemma2258 - skolem:lemma2259 - [ a r:Fact; r:gives {(4221 1224) math:difference 2997}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2997 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2997 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1241}] + [ a r:Fact; r:gives {(1241 2000) math:sum 3241}] + skolem:lemma3240 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2241]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1224]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1241]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3241]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1242 a r:Inference; r:gives { - 2242 :kaprekar (0 4). + 3242 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2242 math:notEqualTo 0}] - skolem:lemma2470 - [ a r:Fact; r:gives {((2 2 4 2) "=<") list:sort (2 2 2 4)}] - [ a r:Fact; r:gives {((2 2 4 2) ">=") list:sort (4 2 2 2)}] - skolem:lemma2427 - skolem:lemma2428 - [ a r:Fact; r:gives {(4222 2224) math:difference 1998}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1998 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1998 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1242}] + [ a r:Fact; r:gives {(1242 2000) math:sum 3242}] + skolem:lemma3241 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2242]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2224]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1242]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3242]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1243 a r:Inference; r:gives { - 2243 :kaprekar (0 3). + 3243 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2243 math:notEqualTo 0}] - skolem:lemma2471 - [ a r:Fact; r:gives {((2 2 4 3) "=<") list:sort (2 2 3 4)}] - [ a r:Fact; r:gives {((2 2 4 3) ">=") list:sort (4 3 2 2)}] - skolem:lemma2451 - skolem:lemma2452 - [ a r:Fact; r:gives {(4322 2234) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1243}] + [ a r:Fact; r:gives {(1243 2000) math:sum 3243}] + skolem:lemma3242 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2243]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2234]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1243]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3243]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1244 a r:Inference; r:gives { - 2244 :kaprekar (0 6). + 3244 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2244 math:notEqualTo 0}] - skolem:lemma2472 - [ a r:Fact; r:gives {((2 2 4 4) "=<") list:sort (2 2 4 4)}] - [ a r:Fact; r:gives {((2 2 4 4) ">=") list:sort (4 4 2 2)}] - skolem:lemma2473 - skolem:lemma2474 - [ a r:Fact; r:gives {(4422 2244) math:difference 2178}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2178 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2178 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1244}] + [ a r:Fact; r:gives {(1244 2000) math:sum 3244}] + skolem:lemma3243 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2244]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2244]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2178]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1245 a r:Inference; r:gives { - 2245 :kaprekar (0 5). + 3245 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2245 math:notEqualTo 0}] - skolem:lemma2475 - [ a r:Fact; r:gives {((2 2 4 5) "=<") list:sort (2 2 4 5)}] - [ a r:Fact; r:gives {((2 2 4 5) ">=") list:sort (5 4 2 2)}] - skolem:lemma2476 - skolem:lemma2477 - [ a r:Fact; r:gives {(5422 2245) math:difference 3177}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3177 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 3177 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1245}] + [ a r:Fact; r:gives {(1245 2000) math:sum 3245}] + skolem:lemma3244 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2245]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2245]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1246 a r:Inference; r:gives { - 2246 :kaprekar (0 2). + 3246 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2246 math:notEqualTo 0}] - skolem:lemma2478 - [ a r:Fact; r:gives {((2 2 4 6) "=<") list:sort (2 2 4 6)}] - [ a r:Fact; r:gives {((2 2 4 6) ">=") list:sort (6 4 2 2)}] - skolem:lemma2479 - skolem:lemma2480 - [ a r:Fact; r:gives {(6422 2246) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1246}] + [ a r:Fact; r:gives {(1246 2000) math:sum 3246}] + skolem:lemma3245 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2246]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2246]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1247 a r:Inference; r:gives { - 2247 :kaprekar (0 7). + 3247 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2247 math:notEqualTo 0}] - skolem:lemma2481 - [ a r:Fact; r:gives {((2 2 4 7) "=<") list:sort (2 2 4 7)}] - [ a r:Fact; r:gives {((2 2 4 7) ">=") list:sort (7 4 2 2)}] - skolem:lemma2482 - skolem:lemma2483 - [ a r:Fact; r:gives {(7422 2247) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1247}] + [ a r:Fact; r:gives {(1247 2000) math:sum 3247}] + skolem:lemma3246 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2247]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2247]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1248 a r:Inference; r:gives { - 2248 :kaprekar (0 1). + 3248 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2248 math:notEqualTo 0}] - skolem:lemma2484 - [ a r:Fact; r:gives {((2 2 4 8) "=<") list:sort (2 2 4 8)}] - [ a r:Fact; r:gives {((2 2 4 8) ">=") list:sort (8 4 2 2)}] - skolem:lemma2485 - skolem:lemma2486 - [ a r:Fact; r:gives {(8422 2248) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1248}] + [ a r:Fact; r:gives {(1248 2000) math:sum 3248}] + skolem:lemma3247 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2248]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2248]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1249 a r:Inference; r:gives { - 2249 :kaprekar (0 5). + 3249 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2249 math:notEqualTo 0}] - skolem:lemma2487 - [ a r:Fact; r:gives {((2 2 4 9) "=<") list:sort (2 2 4 9)}] - [ a r:Fact; r:gives {((2 2 4 9) ">=") list:sort (9 4 2 2)}] - skolem:lemma2488 - skolem:lemma2489 - [ a r:Fact; r:gives {(9422 2249) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1249}] + [ a r:Fact; r:gives {(1249 2000) math:sum 3249}] + skolem:lemma3248 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2249]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2249]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1250 a r:Inference; r:gives { - 2250 :kaprekar (0 6). + 3250 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2250 math:notEqualTo 0}] - skolem:lemma2490 - [ a r:Fact; r:gives {((2 2 5 0) "=<") list:sort (0 2 2 5)}] - [ a r:Fact; r:gives {((2 2 5 0) ">=") list:sort (5 2 2 0)}] - skolem:lemma2071 - skolem:lemma2072 - [ a r:Fact; r:gives {(5220 225) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1250}] + [ a r:Fact; r:gives {(1250 2000) math:sum 3250}] + skolem:lemma3249 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2250]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 225]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1250]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3250]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1251 a r:Inference; r:gives { - 2251 :kaprekar (0 4). + 3251 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2251 math:notEqualTo 0}] - skolem:lemma2491 - [ a r:Fact; r:gives {((2 2 5 1) "=<") list:sort (1 2 2 5)}] - [ a r:Fact; r:gives {((2 2 5 1) ">=") list:sort (5 2 2 1)}] - skolem:lemma2261 - skolem:lemma2262 - [ a r:Fact; r:gives {(5221 1225) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1251}] + [ a r:Fact; r:gives {(1251 2000) math:sum 3251}] + skolem:lemma3250 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2251]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1225]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1251]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3251]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1252 a r:Inference; r:gives { - 2252 :kaprekar (0 6). + 3252 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2252 math:notEqualTo 0}] - skolem:lemma2492 - [ a r:Fact; r:gives {((2 2 5 2) "=<") list:sort (2 2 2 5)}] - [ a r:Fact; r:gives {((2 2 5 2) ">=") list:sort (5 2 2 2)}] - skolem:lemma2430 - skolem:lemma2431 - [ a r:Fact; r:gives {(5222 2225) math:difference 2997}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2997 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2997 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1252}] + [ a r:Fact; r:gives {(1252 2000) math:sum 3252}] + skolem:lemma3251 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2252]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2225]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1252]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3252]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1253 a r:Inference; r:gives { - 2253 :kaprekar (0 3). + 3253 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2253 math:notEqualTo 0}] - skolem:lemma2493 - [ a r:Fact; r:gives {((2 2 5 3) "=<") list:sort (2 2 3 5)}] - [ a r:Fact; r:gives {((2 2 5 3) ">=") list:sort (5 3 2 2)}] - skolem:lemma2454 - skolem:lemma2455 - [ a r:Fact; r:gives {(5322 2235) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1253}] + [ a r:Fact; r:gives {(1253 2000) math:sum 3253}] + skolem:lemma3252 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2253]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2235]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1253]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3253]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1254 a r:Inference; r:gives { - 2254 :kaprekar (0 5). + 3254 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2254 math:notEqualTo 0}] - skolem:lemma2494 - [ a r:Fact; r:gives {((2 2 5 4) "=<") list:sort (2 2 4 5)}] - [ a r:Fact; r:gives {((2 2 5 4) ">=") list:sort (5 4 2 2)}] - skolem:lemma2476 - skolem:lemma2477 - [ a r:Fact; r:gives {(5422 2245) math:difference 3177}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3177 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 3177 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1254}] + [ a r:Fact; r:gives {(1254 2000) math:sum 3254}] + skolem:lemma3253 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2254]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2245]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1254]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3254]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1255 a r:Inference; r:gives { - 2255 :kaprekar (0 6). + 3255 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2255 math:notEqualTo 0}] - skolem:lemma2495 - [ a r:Fact; r:gives {((2 2 5 5) "=<") list:sort (2 2 5 5)}] - [ a r:Fact; r:gives {((2 2 5 5) ">=") list:sort (5 5 2 2)}] - skolem:lemma2496 - skolem:lemma2497 - [ a r:Fact; r:gives {(5522 2255) math:difference 3267}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3267 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 3267 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1255}] + [ a r:Fact; r:gives {(1255 2000) math:sum 3255}] + skolem:lemma3254 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2255]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2255]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1256 a r:Inference; r:gives { - 2256 :kaprekar (0 3). + 3256 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2256 math:notEqualTo 0}] - skolem:lemma2498 - [ a r:Fact; r:gives {((2 2 5 6) "=<") list:sort (2 2 5 6)}] - [ a r:Fact; r:gives {((2 2 5 6) ">=") list:sort (6 5 2 2)}] - skolem:lemma2499 - skolem:lemma2500 - [ a r:Fact; r:gives {(6522 2256) math:difference 4266}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4266 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 4266 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1256}] + [ a r:Fact; r:gives {(1256 2000) math:sum 3256}] + skolem:lemma3255 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2256]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2256]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1257 a r:Inference; r:gives { - 2257 :kaprekar (0 5). + 3257 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2257 math:notEqualTo 0}] - skolem:lemma2501 - [ a r:Fact; r:gives {((2 2 5 7) "=<") list:sort (2 2 5 7)}] - [ a r:Fact; r:gives {((2 2 5 7) ">=") list:sort (7 5 2 2)}] - skolem:lemma2502 - skolem:lemma2503 - [ a r:Fact; r:gives {(7522 2257) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1257}] + [ a r:Fact; r:gives {(1257 2000) math:sum 3257}] + skolem:lemma3256 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2257]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2257]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1258 a r:Inference; r:gives { - 2258 :kaprekar (0 3). + 3258 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2258 math:notEqualTo 0}] - skolem:lemma2504 - [ a r:Fact; r:gives {((2 2 5 8) "=<") list:sort (2 2 5 8)}] - [ a r:Fact; r:gives {((2 2 5 8) ">=") list:sort (8 5 2 2)}] - skolem:lemma2505 - skolem:lemma2506 - [ a r:Fact; r:gives {(8522 2258) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1258}] + [ a r:Fact; r:gives {(1258 2000) math:sum 3258}] + skolem:lemma3257 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2258]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2258]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1259 a r:Inference; r:gives { - 2259 :kaprekar (0 6). + 3259 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2259 math:notEqualTo 0}] - skolem:lemma2507 - [ a r:Fact; r:gives {((2 2 5 9) "=<") list:sort (2 2 5 9)}] - [ a r:Fact; r:gives {((2 2 5 9) ">=") list:sort (9 5 2 2)}] - skolem:lemma2508 - skolem:lemma2509 - [ a r:Fact; r:gives {(9522 2259) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1259}] + [ a r:Fact; r:gives {(1259 2000) math:sum 3259}] + skolem:lemma3258 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2259]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2259]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1260 a r:Inference; r:gives { - 2260 :kaprekar (0 6). + 3260 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2260 math:notEqualTo 0}] - skolem:lemma2510 - [ a r:Fact; r:gives {((2 2 6 0) "=<") list:sort (0 2 2 6)}] - [ a r:Fact; r:gives {((2 2 6 0) ">=") list:sort (6 2 2 0)}] - skolem:lemma2074 - skolem:lemma2075 - [ a r:Fact; r:gives {(6220 226) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1260}] + [ a r:Fact; r:gives {(1260 2000) math:sum 3260}] + skolem:lemma3259 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2260]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 226]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1260]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3260]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1261 a r:Inference; r:gives { - 2261 :kaprekar (0 6). + 3261 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2261 math:notEqualTo 0}] - skolem:lemma2511 - [ a r:Fact; r:gives {((2 2 6 1) "=<") list:sort (1 2 2 6)}] - [ a r:Fact; r:gives {((2 2 6 1) ">=") list:sort (6 2 2 1)}] - skolem:lemma2264 - skolem:lemma2265 - [ a r:Fact; r:gives {(6221 1226) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1261}] + [ a r:Fact; r:gives {(1261 2000) math:sum 3261}] + skolem:lemma3260 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2261]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1226]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1261]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3261]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1262 a r:Inference; r:gives { - 2262 :kaprekar (0 4). + 3262 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2262 math:notEqualTo 0}] - skolem:lemma2512 - [ a r:Fact; r:gives {((2 2 6 2) "=<") list:sort (2 2 2 6)}] - [ a r:Fact; r:gives {((2 2 6 2) ">=") list:sort (6 2 2 2)}] - skolem:lemma2433 - skolem:lemma2434 - [ a r:Fact; r:gives {(6222 2226) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1262}] + [ a r:Fact; r:gives {(1262 2000) math:sum 3262}] + skolem:lemma3261 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2226]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1263 a r:Inference; r:gives { - 2263 :kaprekar (0 7). + 3263 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2263 math:notEqualTo 0}] - skolem:lemma2513 - [ a r:Fact; r:gives {((2 2 6 3) "=<") list:sort (2 2 3 6)}] - [ a r:Fact; r:gives {((2 2 6 3) ">=") list:sort (6 3 2 2)}] - skolem:lemma2457 - skolem:lemma2458 - [ a r:Fact; r:gives {(6322 2236) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1263}] + [ a r:Fact; r:gives {(1263 2000) math:sum 3263}] + skolem:lemma3262 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2236]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1264 a r:Inference; r:gives { - 2264 :kaprekar (0 2). + 3264 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2264 math:notEqualTo 0}] - skolem:lemma2514 - [ a r:Fact; r:gives {((2 2 6 4) "=<") list:sort (2 2 4 6)}] - [ a r:Fact; r:gives {((2 2 6 4) ">=") list:sort (6 4 2 2)}] - skolem:lemma2479 - skolem:lemma2480 - [ a r:Fact; r:gives {(6422 2246) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1264}] + [ a r:Fact; r:gives {(1264 2000) math:sum 3264}] + skolem:lemma3263 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2246]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1265 a r:Inference; r:gives { - 2265 :kaprekar (0 3). + 3265 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2265 math:notEqualTo 0}] - skolem:lemma2515 - [ a r:Fact; r:gives {((2 2 6 5) "=<") list:sort (2 2 5 6)}] - [ a r:Fact; r:gives {((2 2 6 5) ">=") list:sort (6 5 2 2)}] - skolem:lemma2499 - skolem:lemma2500 - [ a r:Fact; r:gives {(6522 2256) math:difference 4266}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4266 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 4266 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1265}] + [ a r:Fact; r:gives {(1265 2000) math:sum 3265}] + skolem:lemma3264 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2256]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1266 a r:Inference; r:gives { - 2266 :kaprekar (0 4). + 3266 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2266 math:notEqualTo 0}] - skolem:lemma2516 - [ a r:Fact; r:gives {((2 2 6 6) "=<") list:sort (2 2 6 6)}] - [ a r:Fact; r:gives {((2 2 6 6) ">=") list:sort (6 6 2 2)}] - skolem:lemma2517 - skolem:lemma2518 - [ a r:Fact; r:gives {(6622 2266) math:difference 4356}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4356 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 4356 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1266}] + [ a r:Fact; r:gives {(1266 2000) math:sum 3266}] + skolem:lemma3265 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4356]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1267 a r:Inference; r:gives { - 2267 :kaprekar (0 5). + 3267 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2267 math:notEqualTo 0}] - skolem:lemma2519 - [ a r:Fact; r:gives {((2 2 6 7) "=<") list:sort (2 2 6 7)}] - [ a r:Fact; r:gives {((2 2 6 7) ">=") list:sort (7 6 2 2)}] - skolem:lemma2520 - skolem:lemma2521 - [ a r:Fact; r:gives {(7622 2267) math:difference 5355}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5355 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5355 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1267}] + [ a r:Fact; r:gives {(1267 2000) math:sum 3267}] + skolem:lemma3266 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1268 a r:Inference; r:gives { - 2268 :kaprekar (0 4). + 3268 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2268 math:notEqualTo 0}] - skolem:lemma2522 - [ a r:Fact; r:gives {((2 2 6 8) "=<") list:sort (2 2 6 8)}] - [ a r:Fact; r:gives {((2 2 6 8) ">=") list:sort (8 6 2 2)}] - skolem:lemma2523 - skolem:lemma2524 - [ a r:Fact; r:gives {(8622 2268) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1268}] + [ a r:Fact; r:gives {(1268 2000) math:sum 3268}] + skolem:lemma3267 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2268]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2268]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1269 a r:Inference; r:gives { - 2269 :kaprekar (0 3). + 3269 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2269 math:notEqualTo 0}] - skolem:lemma2525 - [ a r:Fact; r:gives {((2 2 6 9) "=<") list:sort (2 2 6 9)}] - [ a r:Fact; r:gives {((2 2 6 9) ">=") list:sort (9 6 2 2)}] - skolem:lemma2526 - skolem:lemma2527 - [ a r:Fact; r:gives {(9622 2269) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1269}] + [ a r:Fact; r:gives {(1269 2000) math:sum 3269}] + skolem:lemma3268 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2269]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2269]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1270 a r:Inference; r:gives { - 2270 :kaprekar (0 4). + 3270 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2270 math:notEqualTo 0}] - skolem:lemma2528 - [ a r:Fact; r:gives {((2 2 7 0) "=<") list:sort (0 2 2 7)}] - [ a r:Fact; r:gives {((2 2 7 0) ">=") list:sort (7 2 2 0)}] - skolem:lemma2077 - skolem:lemma2078 - [ a r:Fact; r:gives {(7220 227) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1270}] + [ a r:Fact; r:gives {(1270 2000) math:sum 3270}] + skolem:lemma3269 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2270]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 227]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1270]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3270]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1271 a r:Inference; r:gives { - 2271 :kaprekar (0 6). + 3271 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2271 math:notEqualTo 0}] - skolem:lemma2529 - [ a r:Fact; r:gives {((2 2 7 1) "=<") list:sort (1 2 2 7)}] - [ a r:Fact; r:gives {((2 2 7 1) ">=") list:sort (7 2 2 1)}] - skolem:lemma2267 - skolem:lemma2268 - [ a r:Fact; r:gives {(7221 1227) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1271}] + [ a r:Fact; r:gives {(1271 2000) math:sum 3271}] + skolem:lemma3270 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2271]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1227]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1271]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3271]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1272 a r:Inference; r:gives { - 2272 :kaprekar (0 6). + 3272 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2272 math:notEqualTo 0}] - skolem:lemma2530 - [ a r:Fact; r:gives {((2 2 7 2) "=<") list:sort (2 2 2 7)}] - [ a r:Fact; r:gives {((2 2 7 2) ">=") list:sort (7 2 2 2)}] - skolem:lemma2436 - skolem:lemma2437 - [ a r:Fact; r:gives {(7222 2227) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1272}] + [ a r:Fact; r:gives {(1272 2000) math:sum 3272}] + skolem:lemma3271 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2272]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2227]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1272]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3272]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1273 a r:Inference; r:gives { - 2273 :kaprekar (0 7). + 3273 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2273 math:notEqualTo 0}] - skolem:lemma2531 - [ a r:Fact; r:gives {((2 2 7 3) "=<") list:sort (2 2 3 7)}] - [ a r:Fact; r:gives {((2 2 7 3) ">=") list:sort (7 3 2 2)}] - skolem:lemma2460 - skolem:lemma2461 - [ a r:Fact; r:gives {(7322 2237) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1273}] + [ a r:Fact; r:gives {(1273 2000) math:sum 3273}] + skolem:lemma3272 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2273]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2237]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1273]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3273]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1274 a r:Inference; r:gives { - 2274 :kaprekar (0 7). + 3274 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2274 math:notEqualTo 0}] - skolem:lemma2532 - [ a r:Fact; r:gives {((2 2 7 4) "=<") list:sort (2 2 4 7)}] - [ a r:Fact; r:gives {((2 2 7 4) ">=") list:sort (7 4 2 2)}] - skolem:lemma2482 - skolem:lemma2483 - [ a r:Fact; r:gives {(7422 2247) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1274}] + [ a r:Fact; r:gives {(1274 2000) math:sum 3274}] + skolem:lemma3273 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2274]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2247]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1274]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3274]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1275 a r:Inference; r:gives { - 2275 :kaprekar (0 5). + 3275 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2275 math:notEqualTo 0}] - skolem:lemma2533 - [ a r:Fact; r:gives {((2 2 7 5) "=<") list:sort (2 2 5 7)}] - [ a r:Fact; r:gives {((2 2 7 5) ">=") list:sort (7 5 2 2)}] - skolem:lemma2502 - skolem:lemma2503 - [ a r:Fact; r:gives {(7522 2257) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1275}] + [ a r:Fact; r:gives {(1275 2000) math:sum 3275}] + skolem:lemma3274 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2275]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2257]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1275]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3275]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1276 a r:Inference; r:gives { - 2276 :kaprekar (0 5). + 3276 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2276 math:notEqualTo 0}] - skolem:lemma2534 - [ a r:Fact; r:gives {((2 2 7 6) "=<") list:sort (2 2 6 7)}] - [ a r:Fact; r:gives {((2 2 7 6) ">=") list:sort (7 6 2 2)}] - skolem:lemma2520 - skolem:lemma2521 - [ a r:Fact; r:gives {(7622 2267) math:difference 5355}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5355 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5355 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1276}] + [ a r:Fact; r:gives {(1276 2000) math:sum 3276}] + skolem:lemma3275 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2276]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1276]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3276]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1277 a r:Inference; r:gives { - 2277 :kaprekar (0 5). + 3277 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2277 math:notEqualTo 0}] - skolem:lemma2535 - [ a r:Fact; r:gives {((2 2 7 7) "=<") list:sort (2 2 7 7)}] - [ a r:Fact; r:gives {((2 2 7 7) ">=") list:sort (7 7 2 2)}] - skolem:lemma2536 - skolem:lemma2537 - [ a r:Fact; r:gives {(7722 2277) math:difference 5445}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5445 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5445 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1277}] + [ a r:Fact; r:gives {(1277 2000) math:sum 3277}] + skolem:lemma3276 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2277]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2277]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7722]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5445]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1277]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3277]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1278 a r:Inference; r:gives { - 2278 :kaprekar (0 5). + 3278 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2278 math:notEqualTo 0}] - skolem:lemma2538 - [ a r:Fact; r:gives {((2 2 7 8) "=<") list:sort (2 2 7 8)}] - [ a r:Fact; r:gives {((2 2 7 8) ">=") list:sort (8 7 2 2)}] - skolem:lemma2539 - skolem:lemma2540 - [ a r:Fact; r:gives {(8722 2278) math:difference 6444}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6444 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 6444 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1278}] + [ a r:Fact; r:gives {(1278 2000) math:sum 3278}] + skolem:lemma3277 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2278]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2278]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8722]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1279 a r:Inference; r:gives { - 2279 :kaprekar (0 5). + 3279 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2279 math:notEqualTo 0}] - skolem:lemma2541 - [ a r:Fact; r:gives {((2 2 7 9) "=<") list:sort (2 2 7 9)}] - [ a r:Fact; r:gives {((2 2 7 9) ">=") list:sort (9 7 2 2)}] - skolem:lemma2542 - skolem:lemma2543 - [ a r:Fact; r:gives {(9722 2279) math:difference 7443}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7443 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1279}] + [ a r:Fact; r:gives {(1279 2000) math:sum 3279}] + skolem:lemma3278 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2279]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2279]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9722]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1280 a r:Inference; r:gives { - 2280 :kaprekar (0 6). + 3280 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2280 math:notEqualTo 0}] - skolem:lemma2544 - [ a r:Fact; r:gives {((2 2 8 0) "=<") list:sort (0 2 2 8)}] - [ a r:Fact; r:gives {((2 2 8 0) ">=") list:sort (8 2 2 0)}] - skolem:lemma2080 - skolem:lemma2081 - [ a r:Fact; r:gives {(8220 228) math:difference 7992}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7992 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7992 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1280}] + [ a r:Fact; r:gives {(1280 2000) math:sum 3280}] + skolem:lemma3279 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2280]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 228]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1280]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3280]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1281 a r:Inference; r:gives { - 2281 :kaprekar (0 4). + 3281 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2281 math:notEqualTo 0}] - skolem:lemma2545 - [ a r:Fact; r:gives {((2 2 8 1) "=<") list:sort (1 2 2 8)}] - [ a r:Fact; r:gives {((2 2 8 1) ">=") list:sort (8 2 2 1)}] - skolem:lemma2270 - skolem:lemma2271 - [ a r:Fact; r:gives {(8221 1228) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1281}] + [ a r:Fact; r:gives {(1281 2000) math:sum 3281}] + skolem:lemma3280 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2281]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1228]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1281]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3281]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1282 a r:Inference; r:gives { - 2282 :kaprekar (0 6). + 3282 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2282 math:notEqualTo 0}] - skolem:lemma2546 - [ a r:Fact; r:gives {((2 2 8 2) "=<") list:sort (2 2 2 8)}] - [ a r:Fact; r:gives {((2 2 8 2) ">=") list:sort (8 2 2 2)}] - skolem:lemma2439 - skolem:lemma2440 - [ a r:Fact; r:gives {(8222 2228) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1282}] + [ a r:Fact; r:gives {(1282 2000) math:sum 3282}] + skolem:lemma3281 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2282]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2228]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1282]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3282]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1283 a r:Inference; r:gives { - 2283 :kaprekar (0 7). + 3283 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2283 math:notEqualTo 0}] - skolem:lemma2547 - [ a r:Fact; r:gives {((2 2 8 3) "=<") list:sort (2 2 3 8)}] - [ a r:Fact; r:gives {((2 2 8 3) ">=") list:sort (8 3 2 2)}] - skolem:lemma2463 - skolem:lemma2464 - [ a r:Fact; r:gives {(8322 2238) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1283}] + [ a r:Fact; r:gives {(1283 2000) math:sum 3283}] + skolem:lemma3282 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2283]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2238]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1283]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3283]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1284 a r:Inference; r:gives { - 2284 :kaprekar (0 1). + 3284 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2284 math:notEqualTo 0}] - skolem:lemma2548 - [ a r:Fact; r:gives {((2 2 8 4) "=<") list:sort (2 2 4 8)}] - [ a r:Fact; r:gives {((2 2 8 4) ">=") list:sort (8 4 2 2)}] - skolem:lemma2485 - skolem:lemma2486 - [ a r:Fact; r:gives {(8422 2248) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1284}] + [ a r:Fact; r:gives {(1284 2000) math:sum 3284}] + skolem:lemma3283 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2284]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2248]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1284]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3284]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1285 a r:Inference; r:gives { - 2285 :kaprekar (0 3). + 3285 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2285 math:notEqualTo 0}] - skolem:lemma2549 - [ a r:Fact; r:gives {((2 2 8 5) "=<") list:sort (2 2 5 8)}] - [ a r:Fact; r:gives {((2 2 8 5) ">=") list:sort (8 5 2 2)}] - skolem:lemma2505 - skolem:lemma2506 - [ a r:Fact; r:gives {(8522 2258) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1285}] + [ a r:Fact; r:gives {(1285 2000) math:sum 3285}] + skolem:lemma3284 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2285]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2258]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1285]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3285]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1286 a r:Inference; r:gives { - 2286 :kaprekar (0 4). + 3286 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2286 math:notEqualTo 0}] - skolem:lemma2550 - [ a r:Fact; r:gives {((2 2 8 6) "=<") list:sort (2 2 6 8)}] - [ a r:Fact; r:gives {((2 2 8 6) ">=") list:sort (8 6 2 2)}] - skolem:lemma2523 - skolem:lemma2524 - [ a r:Fact; r:gives {(8622 2268) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1286}] + [ a r:Fact; r:gives {(1286 2000) math:sum 3286}] + skolem:lemma3285 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2286]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2268]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1286]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3286]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1287 a r:Inference; r:gives { - 2287 :kaprekar (0 5). + 3287 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2287 math:notEqualTo 0}] - skolem:lemma2551 - [ a r:Fact; r:gives {((2 2 8 7) "=<") list:sort (2 2 7 8)}] - [ a r:Fact; r:gives {((2 2 8 7) ">=") list:sort (8 7 2 2)}] - skolem:lemma2539 - skolem:lemma2540 - [ a r:Fact; r:gives {(8722 2278) math:difference 6444}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6444 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 6444 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1287}] + [ a r:Fact; r:gives {(1287 2000) math:sum 3287}] + skolem:lemma3286 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2287]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2278]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8722]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1287]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3287]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1288 a r:Inference; r:gives { - 2288 :kaprekar (0 4). + 3288 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2288 math:notEqualTo 0}] - skolem:lemma2552 - [ a r:Fact; r:gives {((2 2 8 8) "=<") list:sort (2 2 8 8)}] - [ a r:Fact; r:gives {((2 2 8 8) ">=") list:sort (8 8 2 2)}] - skolem:lemma2553 - skolem:lemma2554 - [ a r:Fact; r:gives {(8822 2288) math:difference 6534}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6534 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6534 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1288}] + [ a r:Fact; r:gives {(1288 2000) math:sum 3288}] + skolem:lemma3287 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2288]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2288]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8822]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6534]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1288]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3288]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1289 a r:Inference; r:gives { - 2289 :kaprekar (0 3). + 3289 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2289 math:notEqualTo 0}] - skolem:lemma2555 - [ a r:Fact; r:gives {((2 2 8 9) "=<") list:sort (2 2 8 9)}] - [ a r:Fact; r:gives {((2 2 8 9) ">=") list:sort (9 8 2 2)}] - skolem:lemma2556 - skolem:lemma2557 - [ a r:Fact; r:gives {(9822 2289) math:difference 7533}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7533 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7533 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1289}] + [ a r:Fact; r:gives {(1289 2000) math:sum 3289}] + skolem:lemma3288 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2289]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2289]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9822]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1290 a r:Inference; r:gives { - 2290 :kaprekar (0 4). + 3290 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2290 math:notEqualTo 0}] - skolem:lemma2558 - [ a r:Fact; r:gives {((2 2 9 0) "=<") list:sort (0 2 2 9)}] - [ a r:Fact; r:gives {((2 2 9 0) ">=") list:sort (9 2 2 0)}] - skolem:lemma2083 - skolem:lemma2084 - [ a r:Fact; r:gives {(9220 229) math:difference 8991}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8991 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 8991 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1290}] + [ a r:Fact; r:gives {(1290 2000) math:sum 3290}] + skolem:lemma3289 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2290]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 229]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8991]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1290]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3290]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1291 a r:Inference; r:gives { - 2291 :kaprekar (0 6). + 3291 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2291 math:notEqualTo 0}] - skolem:lemma2559 - [ a r:Fact; r:gives {((2 2 9 1) "=<") list:sort (1 2 2 9)}] - [ a r:Fact; r:gives {((2 2 9 1) ">=") list:sort (9 2 2 1)}] - skolem:lemma2273 - skolem:lemma2274 - [ a r:Fact; r:gives {(9221 1229) math:difference 7992}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7992 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7992 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1291}] + [ a r:Fact; r:gives {(1291 2000) math:sum 3291}] + skolem:lemma3290 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2291]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1229]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1291]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3291]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1292 a r:Inference; r:gives { - 2292 :kaprekar (0 4). + 3292 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2292 math:notEqualTo 0}] - skolem:lemma2560 - [ a r:Fact; r:gives {((2 2 9 2) "=<") list:sort (2 2 2 9)}] - [ a r:Fact; r:gives {((2 2 9 2) ">=") list:sort (9 2 2 2)}] - skolem:lemma2442 - skolem:lemma2443 - [ a r:Fact; r:gives {(9222 2229) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1292}] + [ a r:Fact; r:gives {(1292 2000) math:sum 3292}] + skolem:lemma3291 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2292]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2229]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1292]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3292]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1293 a r:Inference; r:gives { - 2293 :kaprekar (0 3). + 3293 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2293 math:notEqualTo 0}] - skolem:lemma2561 - [ a r:Fact; r:gives {((2 2 9 3) "=<") list:sort (2 2 3 9)}] - [ a r:Fact; r:gives {((2 2 9 3) ">=") list:sort (9 3 2 2)}] - skolem:lemma2466 - skolem:lemma2467 - [ a r:Fact; r:gives {(9322 2239) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1293}] + [ a r:Fact; r:gives {(1293 2000) math:sum 3293}] + skolem:lemma3292 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2293]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2239]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1293]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3293]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1294 a r:Inference; r:gives { - 2294 :kaprekar (0 5). + 3294 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2294 math:notEqualTo 0}] - skolem:lemma2562 - [ a r:Fact; r:gives {((2 2 9 4) "=<") list:sort (2 2 4 9)}] - [ a r:Fact; r:gives {((2 2 9 4) ">=") list:sort (9 4 2 2)}] - skolem:lemma2488 - skolem:lemma2489 - [ a r:Fact; r:gives {(9422 2249) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1294}] + [ a r:Fact; r:gives {(1294 2000) math:sum 3294}] + skolem:lemma3293 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2294]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2249]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1294]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3294]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1295 a r:Inference; r:gives { - 2295 :kaprekar (0 6). + 3295 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2295 math:notEqualTo 0}] - skolem:lemma2563 - [ a r:Fact; r:gives {((2 2 9 5) "=<") list:sort (2 2 5 9)}] - [ a r:Fact; r:gives {((2 2 9 5) ">=") list:sort (9 5 2 2)}] - skolem:lemma2508 - skolem:lemma2509 - [ a r:Fact; r:gives {(9522 2259) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1295}] + [ a r:Fact; r:gives {(1295 2000) math:sum 3295}] + skolem:lemma3294 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2295]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2259]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1295]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3295]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1296 a r:Inference; r:gives { - 2296 :kaprekar (0 3). + 3296 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2296 math:notEqualTo 0}] - skolem:lemma2564 - [ a r:Fact; r:gives {((2 2 9 6) "=<") list:sort (2 2 6 9)}] - [ a r:Fact; r:gives {((2 2 9 6) ">=") list:sort (9 6 2 2)}] - skolem:lemma2526 - skolem:lemma2527 - [ a r:Fact; r:gives {(9622 2269) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1296}] + [ a r:Fact; r:gives {(1296 2000) math:sum 3296}] + skolem:lemma3295 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2296]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2269]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1296]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3296]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1297 a r:Inference; r:gives { - 2297 :kaprekar (0 5). + 3297 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2297 math:notEqualTo 0}] - skolem:lemma2565 - [ a r:Fact; r:gives {((2 2 9 7) "=<") list:sort (2 2 7 9)}] - [ a r:Fact; r:gives {((2 2 9 7) ">=") list:sort (9 7 2 2)}] - skolem:lemma2542 - skolem:lemma2543 - [ a r:Fact; r:gives {(9722 2279) math:difference 7443}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7443 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1297}] + [ a r:Fact; r:gives {(1297 2000) math:sum 3297}] + skolem:lemma3296 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2297]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2279]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9722]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1297]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3297]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1298 a r:Inference; r:gives { - 2298 :kaprekar (0 3). + 3298 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2298 math:notEqualTo 0}] - skolem:lemma2566 - [ a r:Fact; r:gives {((2 2 9 8) "=<") list:sort (2 2 8 9)}] - [ a r:Fact; r:gives {((2 2 9 8) ">=") list:sort (9 8 2 2)}] - skolem:lemma2556 - skolem:lemma2557 - [ a r:Fact; r:gives {(9822 2289) math:difference 7533}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7533 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7533 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1298}] + [ a r:Fact; r:gives {(1298 2000) math:sum 3298}] + skolem:lemma3297 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2298]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2289]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9822]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1298]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3298]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1299 a r:Inference; r:gives { - 2299 :kaprekar (0 6). + 3299 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2299 math:notEqualTo 0}] - skolem:lemma2567 - [ a r:Fact; r:gives {((2 2 9 9) "=<") list:sort (2 2 9 9)}] - [ a r:Fact; r:gives {((2 2 9 9) ">=") list:sort (9 9 2 2)}] - skolem:lemma2568 - skolem:lemma2569 - [ a r:Fact; r:gives {(9922 2299) math:difference 7623}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7623 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7623 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1299}] + [ a r:Fact; r:gives {(1299 2000) math:sum 3299}] + skolem:lemma3298 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2299]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2299]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9922]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7623]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1300 a r:Inference; r:gives { - 2300 :kaprekar (0 5). + 3300 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2300 math:notEqualTo 0}] - skolem:lemma2570 - [ a r:Fact; r:gives {((2 3 0 0) "=<") list:sort (0 0 2 3)}] - [ a r:Fact; r:gives {((2 3 0 0) ">=") list:sort (3 2 0 0)}] - skolem:lemma2011 - skolem:lemma2012 - [ a r:Fact; r:gives {(3200 23) math:difference 3177}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3177 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 3177 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1300}] + [ a r:Fact; r:gives {(1300 2000) math:sum 3300}] + skolem:lemma3299 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2300]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1301 a r:Inference; r:gives { - 2301 :kaprekar (0 3). + 3301 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2301 math:notEqualTo 0}] - skolem:lemma2571 - [ a r:Fact; r:gives {((2 3 0 1) "=<") list:sort (0 1 2 3)}] - [ a r:Fact; r:gives {((2 3 0 1) ">=") list:sort (3 2 1 0)}] - skolem:lemma2039 - skolem:lemma2040 - [ a r:Fact; r:gives {(3210 123) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1301}] + [ a r:Fact; r:gives {(1301 2000) math:sum 3301}] + skolem:lemma3300 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2301]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 123]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1301]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3301]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1302 a r:Inference; r:gives { - 2302 :kaprekar (0 6). + 3302 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2302 math:notEqualTo 0}] - skolem:lemma2572 - [ a r:Fact; r:gives {((2 3 0 2) "=<") list:sort (0 2 2 3)}] - [ a r:Fact; r:gives {((2 3 0 2) ">=") list:sort (3 2 2 0)}] - skolem:lemma2065 - skolem:lemma2066 - [ a r:Fact; r:gives {(3220 223) math:difference 2997}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2997 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2997 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1302}] + [ a r:Fact; r:gives {(1302 2000) math:sum 3302}] + skolem:lemma3301 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2302]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 223]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1302]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3302]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1303 a r:Inference; r:gives { - 2303 :kaprekar (0 3). + 3303 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2303 math:notEqualTo 0}] - skolem:lemma2573 - [ a r:Fact; r:gives {((2 3 0 3) "=<") list:sort (0 2 3 3)}] - [ a r:Fact; r:gives {((2 3 0 3) ">=") list:sort (3 3 2 0)}] - skolem:lemma2089 - skolem:lemma2090 - [ a r:Fact; r:gives {(3320 233) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1303}] + [ a r:Fact; r:gives {(1303 2000) math:sum 3303}] + skolem:lemma3302 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2303]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 233]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1303]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3303]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1304 a r:Inference; r:gives { - 2304 :kaprekar (0 7). + 3304 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2304 math:notEqualTo 0}] - skolem:lemma2574 - [ a r:Fact; r:gives {((2 3 0 4) "=<") list:sort (0 2 3 4)}] - [ a r:Fact; r:gives {((2 3 0 4) ">=") list:sort (4 3 2 0)}] - skolem:lemma2092 - skolem:lemma2093 - [ a r:Fact; r:gives {(4320 234) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1304}] + [ a r:Fact; r:gives {(1304 2000) math:sum 3304}] + skolem:lemma3303 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2304]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 234]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1304]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3304]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1305 a r:Inference; r:gives { - 2305 :kaprekar (0 7). + 3305 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2305 math:notEqualTo 0}] - skolem:lemma2575 - [ a r:Fact; r:gives {((2 3 0 5) "=<") list:sort (0 2 3 5)}] - [ a r:Fact; r:gives {((2 3 0 5) ">=") list:sort (5 3 2 0)}] - skolem:lemma2095 - skolem:lemma2096 - [ a r:Fact; r:gives {(5320 235) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1305}] + [ a r:Fact; r:gives {(1305 2000) math:sum 3305}] + skolem:lemma3304 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2305]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 235]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1305]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3305]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1306 a r:Inference; r:gives { - 2306 :kaprekar (0 7). + 3306 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2306 math:notEqualTo 0}] - skolem:lemma2576 - [ a r:Fact; r:gives {((2 3 0 6) "=<") list:sort (0 2 3 6)}] - [ a r:Fact; r:gives {((2 3 0 6) ">=") list:sort (6 3 2 0)}] - skolem:lemma2098 - skolem:lemma2099 - [ a r:Fact; r:gives {(6320 236) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1306}] + [ a r:Fact; r:gives {(1306 2000) math:sum 3306}] + skolem:lemma3305 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2306]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 236]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1306]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3306]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1307 a r:Inference; r:gives { - 2307 :kaprekar (0 3). + 3307 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2307 math:notEqualTo 0}] - skolem:lemma2577 - [ a r:Fact; r:gives {((2 3 0 7) "=<") list:sort (0 2 3 7)}] - [ a r:Fact; r:gives {((2 3 0 7) ">=") list:sort (7 3 2 0)}] - skolem:lemma2101 - skolem:lemma2102 - [ a r:Fact; r:gives {(7320 237) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1307}] + [ a r:Fact; r:gives {(1307 2000) math:sum 3307}] + skolem:lemma3306 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2307]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 237]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1307]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3307]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1308 a r:Inference; r:gives { - 2308 :kaprekar (0 3). + 3308 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2308 math:notEqualTo 0}] - skolem:lemma2578 - [ a r:Fact; r:gives {((2 3 0 8) "=<") list:sort (0 2 3 8)}] - [ a r:Fact; r:gives {((2 3 0 8) ">=") list:sort (8 3 2 0)}] - skolem:lemma2104 - skolem:lemma2105 - [ a r:Fact; r:gives {(8320 238) math:difference 8082}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8082 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 8082 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1308}] + [ a r:Fact; r:gives {(1308 2000) math:sum 3308}] + skolem:lemma3307 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2308]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 238]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1308]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3308]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1309 a r:Inference; r:gives { - 2309 :kaprekar (0 4). + 3309 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2309 math:notEqualTo 0}] - skolem:lemma2579 - [ a r:Fact; r:gives {((2 3 0 9) "=<") list:sort (0 2 3 9)}] - [ a r:Fact; r:gives {((2 3 0 9) ">=") list:sort (9 3 2 0)}] - skolem:lemma2107 - skolem:lemma2108 - [ a r:Fact; r:gives {(9320 239) math:difference 9081}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9081 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 9081 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1309}] + [ a r:Fact; r:gives {(1309 2000) math:sum 3309}] + skolem:lemma3308 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2309]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 239]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1309]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3309]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1310 a r:Inference; r:gives { - 2310 :kaprekar (0 3). + 3310 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2310 math:notEqualTo 0}] - skolem:lemma2580 - [ a r:Fact; r:gives {((2 3 1 0) "=<") list:sort (0 1 2 3)}] - [ a r:Fact; r:gives {((2 3 1 0) ">=") list:sort (3 2 1 0)}] - skolem:lemma2039 - skolem:lemma2040 - [ a r:Fact; r:gives {(3210 123) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1310}] + [ a r:Fact; r:gives {(1310 2000) math:sum 3310}] + skolem:lemma3309 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2310]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 123]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1311 a r:Inference; r:gives { - 2311 :kaprekar (0 3). + 3311 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2311 math:notEqualTo 0}] - skolem:lemma2581 - [ a r:Fact; r:gives {((2 3 1 1) "=<") list:sort (1 1 2 3)}] - [ a r:Fact; r:gives {((2 3 1 1) ">=") list:sort (3 2 1 1)}] - skolem:lemma2229 - skolem:lemma2230 - [ a r:Fact; r:gives {(3211 1123) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1311}] + [ a r:Fact; r:gives {(1311 2000) math:sum 3311}] + skolem:lemma3310 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2311]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1123]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1312 a r:Inference; r:gives { - 2312 :kaprekar (0 4). + 3312 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2312 math:notEqualTo 0}] - skolem:lemma2582 - [ a r:Fact; r:gives {((2 3 1 2) "=<") list:sort (1 2 2 3)}] - [ a r:Fact; r:gives {((2 3 1 2) ">=") list:sort (3 2 2 1)}] - skolem:lemma2255 - skolem:lemma2256 - [ a r:Fact; r:gives {(3221 1223) math:difference 1998}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1998 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1998 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1312}] + [ a r:Fact; r:gives {(1312 2000) math:sum 3312}] + skolem:lemma3311 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2312]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1223]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1312]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3312]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1313 a r:Inference; r:gives { - 2313 :kaprekar (0 3). + 3313 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2313 math:notEqualTo 0}] - skolem:lemma2583 - [ a r:Fact; r:gives {((2 3 1 3) "=<") list:sort (1 2 3 3)}] - [ a r:Fact; r:gives {((2 3 1 3) ">=") list:sort (3 3 2 1)}] - skolem:lemma2279 - skolem:lemma2280 - [ a r:Fact; r:gives {(3321 1233) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1313}] + [ a r:Fact; r:gives {(1313 2000) math:sum 3313}] + skolem:lemma3312 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2313]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1233]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1313]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3313]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1314 a r:Inference; r:gives { - 2314 :kaprekar (0 3). + 3314 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2314 math:notEqualTo 0}] - skolem:lemma2584 - [ a r:Fact; r:gives {((2 3 1 4) "=<") list:sort (1 2 3 4)}] - [ a r:Fact; r:gives {((2 3 1 4) ">=") list:sort (4 3 2 1)}] - skolem:lemma2282 - skolem:lemma2283 - [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1314}] + [ a r:Fact; r:gives {(1314 2000) math:sum 3314}] + skolem:lemma3313 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2314]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1234]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1314]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3314]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1315 a r:Inference; r:gives { - 2315 :kaprekar (0 7). + 3315 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2315 math:notEqualTo 0}] - skolem:lemma2585 - [ a r:Fact; r:gives {((2 3 1 5) "=<") list:sort (1 2 3 5)}] - [ a r:Fact; r:gives {((2 3 1 5) ">=") list:sort (5 3 2 1)}] - skolem:lemma2285 - skolem:lemma2286 - [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1315}] + [ a r:Fact; r:gives {(1315 2000) math:sum 3315}] + skolem:lemma3314 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2315]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1235]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1315]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3315]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1316 a r:Inference; r:gives { - 2316 :kaprekar (0 7). + 3316 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2316 math:notEqualTo 0}] - skolem:lemma2586 - [ a r:Fact; r:gives {((2 3 1 6) "=<") list:sort (1 2 3 6)}] - [ a r:Fact; r:gives {((2 3 1 6) ">=") list:sort (6 3 2 1)}] - skolem:lemma2288 - skolem:lemma2289 - [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1316}] + [ a r:Fact; r:gives {(1316 2000) math:sum 3316}] + skolem:lemma3315 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2316]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1236]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1316]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3316]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1317 a r:Inference; r:gives { - 2317 :kaprekar (0 7). + 3317 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2317 math:notEqualTo 0}] - skolem:lemma2587 - [ a r:Fact; r:gives {((2 3 1 7) "=<") list:sort (1 2 3 7)}] - [ a r:Fact; r:gives {((2 3 1 7) ">=") list:sort (7 3 2 1)}] - skolem:lemma2291 - skolem:lemma2292 - [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1317}] + [ a r:Fact; r:gives {(1317 2000) math:sum 3317}] + skolem:lemma3316 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2317]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1237]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1317]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3317]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1318 a r:Inference; r:gives { - 2318 :kaprekar (0 3). + 3318 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2318 math:notEqualTo 0}] - skolem:lemma2588 - [ a r:Fact; r:gives {((2 3 1 8) "=<") list:sort (1 2 3 8)}] - [ a r:Fact; r:gives {((2 3 1 8) ">=") list:sort (8 3 2 1)}] - skolem:lemma2294 - skolem:lemma2295 - [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1318}] + [ a r:Fact; r:gives {(1318 2000) math:sum 3318}] + skolem:lemma3317 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2318]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1238]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1318]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3318]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1319 a r:Inference; r:gives { - 2319 :kaprekar (0 3). + 3319 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2319 math:notEqualTo 0}] - skolem:lemma2589 - [ a r:Fact; r:gives {((2 3 1 9) "=<") list:sort (1 2 3 9)}] - [ a r:Fact; r:gives {((2 3 1 9) ">=") list:sort (9 3 2 1)}] - skolem:lemma2297 - skolem:lemma2298 - [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8082 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 8082 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1319}] + [ a r:Fact; r:gives {(1319 2000) math:sum 3319}] + skolem:lemma3318 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2319]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1239]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1319]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3319]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1320 a r:Inference; r:gives { - 2320 :kaprekar (0 6). + 3320 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2320 math:notEqualTo 0}] - skolem:lemma2590 - [ a r:Fact; r:gives {((2 3 2 0) "=<") list:sort (0 2 2 3)}] - [ a r:Fact; r:gives {((2 3 2 0) ">=") list:sort (3 2 2 0)}] - skolem:lemma2065 - skolem:lemma2066 - [ a r:Fact; r:gives {(3220 223) math:difference 2997}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2997 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2997 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1320}] + [ a r:Fact; r:gives {(1320 2000) math:sum 3320}] + skolem:lemma3319 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 223]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1321 a r:Inference; r:gives { - 2321 :kaprekar (0 4). + 3321 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2321 math:notEqualTo 0}] - skolem:lemma2591 - [ a r:Fact; r:gives {((2 3 2 1) "=<") list:sort (1 2 2 3)}] - [ a r:Fact; r:gives {((2 3 2 1) ">=") list:sort (3 2 2 1)}] - skolem:lemma2255 - skolem:lemma2256 - [ a r:Fact; r:gives {(3221 1223) math:difference 1998}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1998 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1998 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1321}] + [ a r:Fact; r:gives {(1321 2000) math:sum 3321}] + skolem:lemma3320 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1223]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1322 a r:Inference; r:gives { - 2322 :kaprekar (0 5). + 3322 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2322 math:notEqualTo 0}] - skolem:lemma2592 - [ a r:Fact; r:gives {((2 3 2 2) "=<") list:sort (2 2 2 3)}] - [ a r:Fact; r:gives {((2 3 2 2) ">=") list:sort (3 2 2 2)}] - skolem:lemma2424 - skolem:lemma2425 - [ a r:Fact; r:gives {(3222 2223) math:difference 999}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 999 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 999 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1322}] + [ a r:Fact; r:gives {(1322 2000) math:sum 3322}] + skolem:lemma3321 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2223]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1323 a r:Inference; r:gives { - 2323 :kaprekar (0 4). + 3323 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2323 math:notEqualTo 0}] - skolem:lemma2593 - [ a r:Fact; r:gives {((2 3 2 3) "=<") list:sort (2 2 3 3)}] - [ a r:Fact; r:gives {((2 3 2 3) ">=") list:sort (3 3 2 2)}] - skolem:lemma2448 - skolem:lemma2449 - [ a r:Fact; r:gives {(3322 2233) math:difference 1089}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1089 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1089 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1323}] + [ a r:Fact; r:gives {(1323 2000) math:sum 3323}] + skolem:lemma3322 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2323]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2233]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1089]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1323]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3323]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1324 a r:Inference; r:gives { - 2324 :kaprekar (0 3). + 3324 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2324 math:notEqualTo 0}] - skolem:lemma2594 - [ a r:Fact; r:gives {((2 3 2 4) "=<") list:sort (2 2 3 4)}] - [ a r:Fact; r:gives {((2 3 2 4) ">=") list:sort (4 3 2 2)}] - skolem:lemma2451 - skolem:lemma2452 - [ a r:Fact; r:gives {(4322 2234) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1324}] + [ a r:Fact; r:gives {(1324 2000) math:sum 3324}] + skolem:lemma3323 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2324]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2234]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1324]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3324]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1325 a r:Inference; r:gives { - 2325 :kaprekar (0 3). + 3325 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2325 math:notEqualTo 0}] - skolem:lemma2595 - [ a r:Fact; r:gives {((2 3 2 5) "=<") list:sort (2 2 3 5)}] - [ a r:Fact; r:gives {((2 3 2 5) ">=") list:sort (5 3 2 2)}] - skolem:lemma2454 - skolem:lemma2455 - [ a r:Fact; r:gives {(5322 2235) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1325}] + [ a r:Fact; r:gives {(1325 2000) math:sum 3325}] + skolem:lemma3324 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2325]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2235]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1325]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3325]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1326 a r:Inference; r:gives { - 2326 :kaprekar (0 7). + 3326 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2326 math:notEqualTo 0}] - skolem:lemma2596 - [ a r:Fact; r:gives {((2 3 2 6) "=<") list:sort (2 2 3 6)}] - [ a r:Fact; r:gives {((2 3 2 6) ">=") list:sort (6 3 2 2)}] - skolem:lemma2457 - skolem:lemma2458 - [ a r:Fact; r:gives {(6322 2236) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1326}] + [ a r:Fact; r:gives {(1326 2000) math:sum 3326}] + skolem:lemma3325 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2326]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2236]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1326]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3326]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1327 a r:Inference; r:gives { - 2327 :kaprekar (0 7). + 3327 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2327 math:notEqualTo 0}] - skolem:lemma2597 - [ a r:Fact; r:gives {((2 3 2 7) "=<") list:sort (2 2 3 7)}] - [ a r:Fact; r:gives {((2 3 2 7) ">=") list:sort (7 3 2 2)}] - skolem:lemma2460 - skolem:lemma2461 - [ a r:Fact; r:gives {(7322 2237) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1327}] + [ a r:Fact; r:gives {(1327 2000) math:sum 3327}] + skolem:lemma3326 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2327]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2237]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1327]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3327]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1328 a r:Inference; r:gives { - 2328 :kaprekar (0 7). + 3328 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2328 math:notEqualTo 0}] - skolem:lemma2598 - [ a r:Fact; r:gives {((2 3 2 8) "=<") list:sort (2 2 3 8)}] - [ a r:Fact; r:gives {((2 3 2 8) ">=") list:sort (8 3 2 2)}] - skolem:lemma2463 - skolem:lemma2464 - [ a r:Fact; r:gives {(8322 2238) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1328}] + [ a r:Fact; r:gives {(1328 2000) math:sum 3328}] + skolem:lemma3327 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2328]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2238]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1328]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3328]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1329 a r:Inference; r:gives { - 2329 :kaprekar (0 3). + 3329 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2329 math:notEqualTo 0}] - skolem:lemma2599 - [ a r:Fact; r:gives {((2 3 2 9) "=<") list:sort (2 2 3 9)}] - [ a r:Fact; r:gives {((2 3 2 9) ">=") list:sort (9 3 2 2)}] - skolem:lemma2466 - skolem:lemma2467 - [ a r:Fact; r:gives {(9322 2239) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1329}] + [ a r:Fact; r:gives {(1329 2000) math:sum 3329}] + skolem:lemma3328 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2329]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2239]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1329]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3329]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1330 a r:Inference; r:gives { - 2330 :kaprekar (0 3). + 3330 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2330 math:notEqualTo 0}] - skolem:lemma2600 - [ a r:Fact; r:gives {((2 3 3 0) "=<") list:sort (0 2 3 3)}] - [ a r:Fact; r:gives {((2 3 3 0) ">=") list:sort (3 3 2 0)}] - skolem:lemma2089 - skolem:lemma2090 - [ a r:Fact; r:gives {(3320 233) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1330}] + [ a r:Fact; r:gives {(1330 2000) math:sum 3330}] + skolem:lemma3329 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2330]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 233]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1331 a r:Inference; r:gives { - 2331 :kaprekar (0 3). + 3331 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2331 math:notEqualTo 0}] - skolem:lemma2601 - [ a r:Fact; r:gives {((2 3 3 1) "=<") list:sort (1 2 3 3)}] - [ a r:Fact; r:gives {((2 3 3 1) ">=") list:sort (3 3 2 1)}] - skolem:lemma2279 - skolem:lemma2280 - [ a r:Fact; r:gives {(3321 1233) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1331}] + [ a r:Fact; r:gives {(1331 2000) math:sum 3331}] + skolem:lemma3330 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2331]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1233]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1332 a r:Inference; r:gives { - 2332 :kaprekar (0 4). + 3332 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2332 math:notEqualTo 0}] - skolem:lemma2602 - [ a r:Fact; r:gives {((2 3 3 2) "=<") list:sort (2 2 3 3)}] - [ a r:Fact; r:gives {((2 3 3 2) ">=") list:sort (3 3 2 2)}] - skolem:lemma2448 - skolem:lemma2449 - [ a r:Fact; r:gives {(3322 2233) math:difference 1089}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1089 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1089 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1332}] + [ a r:Fact; r:gives {(1332 2000) math:sum 3332}] + skolem:lemma3331 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2233]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1089]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1333 a r:Inference; r:gives { - 2333 :kaprekar (0 5). + 3334 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2333 math:notEqualTo 0}] - skolem:lemma2603 - [ a r:Fact; r:gives {((2 3 3 3) "=<") list:sort (2 3 3 3)}] - [ a r:Fact; r:gives {((2 3 3 3) ">=") list:sort (3 3 3 2)}] - skolem:lemma2604 - skolem:lemma2605 - [ a r:Fact; r:gives {(3332 2333) math:difference 999}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 999 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 999 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1334}] + [ a r:Fact; r:gives {(1334 2000) math:sum 3334}] + skolem:lemma3332 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2333]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2333]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1334 a r:Inference; r:gives { - 2334 :kaprekar (0 4). + 3335 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2334 math:notEqualTo 0}] - skolem:lemma2606 - [ a r:Fact; r:gives {((2 3 3 4) "=<") list:sort (2 3 3 4)}] - [ a r:Fact; r:gives {((2 3 3 4) ">=") list:sort (4 3 3 2)}] - skolem:lemma2607 - skolem:lemma2608 - [ a r:Fact; r:gives {(4332 2334) math:difference 1998}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1998 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1998 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1335}] + [ a r:Fact; r:gives {(1335 2000) math:sum 3335}] + skolem:lemma3333 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2334]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2334]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1335 a r:Inference; r:gives { - 2335 :kaprekar (0 6). + 3336 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2335 math:notEqualTo 0}] - skolem:lemma2609 - [ a r:Fact; r:gives {((2 3 3 5) "=<") list:sort (2 3 3 5)}] - [ a r:Fact; r:gives {((2 3 3 5) ">=") list:sort (5 3 3 2)}] - skolem:lemma2610 - skolem:lemma2611 - [ a r:Fact; r:gives {(5332 2335) math:difference 2997}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2997 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2997 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1336}] + [ a r:Fact; r:gives {(1336 2000) math:sum 3336}] + skolem:lemma3334 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2335]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2335]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1336 a r:Inference; r:gives { - 2336 :kaprekar (0 4). + 3337 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2336 math:notEqualTo 0}] - skolem:lemma2612 - [ a r:Fact; r:gives {((2 3 3 6) "=<") list:sort (2 3 3 6)}] - [ a r:Fact; r:gives {((2 3 3 6) ">=") list:sort (6 3 3 2)}] - skolem:lemma2613 - skolem:lemma2614 - [ a r:Fact; r:gives {(6332 2336) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1337}] + [ a r:Fact; r:gives {(1337 2000) math:sum 3337}] + skolem:lemma3335 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2336]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2336]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1337 a r:Inference; r:gives { - 2337 :kaprekar (0 6). + 3338 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2337 math:notEqualTo 0}] - skolem:lemma2615 - [ a r:Fact; r:gives {((2 3 3 7) "=<") list:sort (2 3 3 7)}] - [ a r:Fact; r:gives {((2 3 3 7) ">=") list:sort (7 3 3 2)}] - skolem:lemma2616 - skolem:lemma2617 - [ a r:Fact; r:gives {(7332 2337) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1338}] + [ a r:Fact; r:gives {(1338 2000) math:sum 3338}] + skolem:lemma3336 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2337]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2337]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1338 a r:Inference; r:gives { - 2338 :kaprekar (0 6). + 3339 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2338 math:notEqualTo 0}] - skolem:lemma2618 - [ a r:Fact; r:gives {((2 3 3 8) "=<") list:sort (2 3 3 8)}] - [ a r:Fact; r:gives {((2 3 3 8) ">=") list:sort (8 3 3 2)}] - skolem:lemma2619 - skolem:lemma2620 - [ a r:Fact; r:gives {(8332 2338) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1339}] + [ a r:Fact; r:gives {(1339 2000) math:sum 3339}] + skolem:lemma3337 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2338]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2338]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1339 a r:Inference; r:gives { - 2339 :kaprekar (0 4). + 3340 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2339 math:notEqualTo 0}] - skolem:lemma2621 - [ a r:Fact; r:gives {((2 3 3 9) "=<") list:sort (2 3 3 9)}] - [ a r:Fact; r:gives {((2 3 3 9) ">=") list:sort (9 3 3 2)}] - skolem:lemma2622 - skolem:lemma2623 - [ a r:Fact; r:gives {(9332 2339) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1340}] + [ a r:Fact; r:gives {(1340 2000) math:sum 3340}] + skolem:lemma3338 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2339]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2339]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1340]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3340]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1340 a r:Inference; r:gives { - 2340 :kaprekar (0 7). + 3341 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2340 math:notEqualTo 0}] - skolem:lemma2624 - [ a r:Fact; r:gives {((2 3 4 0) "=<") list:sort (0 2 3 4)}] - [ a r:Fact; r:gives {((2 3 4 0) ">=") list:sort (4 3 2 0)}] - skolem:lemma2092 - skolem:lemma2093 - [ a r:Fact; r:gives {(4320 234) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1341}] + [ a r:Fact; r:gives {(1341 2000) math:sum 3341}] + skolem:lemma3339 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2340]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 234]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1341]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3341]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1341 a r:Inference; r:gives { - 2341 :kaprekar (0 3). + 3342 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2341 math:notEqualTo 0}] - skolem:lemma2625 - [ a r:Fact; r:gives {((2 3 4 1) "=<") list:sort (1 2 3 4)}] - [ a r:Fact; r:gives {((2 3 4 1) ">=") list:sort (4 3 2 1)}] - skolem:lemma2282 - skolem:lemma2283 - [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1342}] + [ a r:Fact; r:gives {(1342 2000) math:sum 3342}] + skolem:lemma3340 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2341]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1234]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1342]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3342]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1342 a r:Inference; r:gives { - 2342 :kaprekar (0 3). + 3343 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2342 math:notEqualTo 0}] - skolem:lemma2626 - [ a r:Fact; r:gives {((2 3 4 2) "=<") list:sort (2 2 3 4)}] - [ a r:Fact; r:gives {((2 3 4 2) ">=") list:sort (4 3 2 2)}] - skolem:lemma2451 - skolem:lemma2452 - [ a r:Fact; r:gives {(4322 2234) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1343}] + [ a r:Fact; r:gives {(1343 2000) math:sum 3343}] + skolem:lemma3341 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2342]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2234]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1343]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3343]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1343 a r:Inference; r:gives { - 2343 :kaprekar (0 4). + 3344 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2343 math:notEqualTo 0}] - skolem:lemma2627 - [ a r:Fact; r:gives {((2 3 4 3) "=<") list:sort (2 3 3 4)}] - [ a r:Fact; r:gives {((2 3 4 3) ">=") list:sort (4 3 3 2)}] - skolem:lemma2607 - skolem:lemma2608 - [ a r:Fact; r:gives {(4332 2334) math:difference 1998}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1998 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1998 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1344}] + [ a r:Fact; r:gives {(1344 2000) math:sum 3344}] + skolem:lemma3342 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2343]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2334]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1344 a r:Inference; r:gives { - 2344 :kaprekar (0 3). + 3345 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2344 math:notEqualTo 0}] - skolem:lemma2628 - [ a r:Fact; r:gives {((2 3 4 4) "=<") list:sort (2 3 4 4)}] - [ a r:Fact; r:gives {((2 3 4 4) ">=") list:sort (4 4 3 2)}] - skolem:lemma2629 - skolem:lemma2630 - [ a r:Fact; r:gives {(4432 2344) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1345}] + [ a r:Fact; r:gives {(1345 2000) math:sum 3345}] + skolem:lemma3343 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2344]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2344]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1345 a r:Inference; r:gives { - 2345 :kaprekar (0 3). + 3346 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2345 math:notEqualTo 0}] - skolem:lemma2631 - [ a r:Fact; r:gives {((2 3 4 5) "=<") list:sort (2 3 4 5)}] - [ a r:Fact; r:gives {((2 3 4 5) ">=") list:sort (5 4 3 2)}] - skolem:lemma2632 - skolem:lemma2633 - [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1346}] + [ a r:Fact; r:gives {(1346 2000) math:sum 3346}] + skolem:lemma3344 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2345]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2345]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1346 a r:Inference; r:gives { - 2346 :kaprekar (0 7). + 3347 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2346 math:notEqualTo 0}] - skolem:lemma2634 - [ a r:Fact; r:gives {((2 3 4 6) "=<") list:sort (2 3 4 6)}] - [ a r:Fact; r:gives {((2 3 4 6) ">=") list:sort (6 4 3 2)}] - skolem:lemma2635 - skolem:lemma2636 - [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1347}] + [ a r:Fact; r:gives {(1347 2000) math:sum 3347}] + skolem:lemma3345 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2346]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2346]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1347 a r:Inference; r:gives { - 2347 :kaprekar (0 7). + 3348 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2347 math:notEqualTo 0}] - skolem:lemma2637 - [ a r:Fact; r:gives {((2 3 4 7) "=<") list:sort (2 3 4 7)}] - [ a r:Fact; r:gives {((2 3 4 7) ">=") list:sort (7 4 3 2)}] - skolem:lemma2638 - skolem:lemma2639 - [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1348}] + [ a r:Fact; r:gives {(1348 2000) math:sum 3348}] + skolem:lemma3346 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2347]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2347]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1348 a r:Inference; r:gives { - 2348 :kaprekar (0 7). + 3349 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2348 math:notEqualTo 0}] - skolem:lemma2640 - [ a r:Fact; r:gives {((2 3 4 8) "=<") list:sort (2 3 4 8)}] - [ a r:Fact; r:gives {((2 3 4 8) ">=") list:sort (8 4 3 2)}] - skolem:lemma2641 - skolem:lemma2642 - [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1349}] + [ a r:Fact; r:gives {(1349 2000) math:sum 3349}] + skolem:lemma3347 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2348]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2348]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1349 a r:Inference; r:gives { - 2349 :kaprekar (0 3). + 3350 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2349 math:notEqualTo 0}] - skolem:lemma2643 - [ a r:Fact; r:gives {((2 3 4 9) "=<") list:sort (2 3 4 9)}] - [ a r:Fact; r:gives {((2 3 4 9) ">=") list:sort (9 4 3 2)}] - skolem:lemma2644 - skolem:lemma2645 - [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1350}] + [ a r:Fact; r:gives {(1350 2000) math:sum 3350}] + skolem:lemma3348 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2349]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2349]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1350]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3350]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1350 a r:Inference; r:gives { - 2350 :kaprekar (0 7). + 3351 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2350 math:notEqualTo 0}] - skolem:lemma2646 - [ a r:Fact; r:gives {((2 3 5 0) "=<") list:sort (0 2 3 5)}] - [ a r:Fact; r:gives {((2 3 5 0) ">=") list:sort (5 3 2 0)}] - skolem:lemma2095 - skolem:lemma2096 - [ a r:Fact; r:gives {(5320 235) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1351}] + [ a r:Fact; r:gives {(1351 2000) math:sum 3351}] + skolem:lemma3349 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2350]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 235]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1351]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3351]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1351 a r:Inference; r:gives { - 2351 :kaprekar (0 7). + 3352 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2351 math:notEqualTo 0}] - skolem:lemma2647 - [ a r:Fact; r:gives {((2 3 5 1) "=<") list:sort (1 2 3 5)}] - [ a r:Fact; r:gives {((2 3 5 1) ">=") list:sort (5 3 2 1)}] - skolem:lemma2285 - skolem:lemma2286 - [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1352}] + [ a r:Fact; r:gives {(1352 2000) math:sum 3352}] + skolem:lemma3350 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2351]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1235]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1352 a r:Inference; r:gives { - 2352 :kaprekar (0 3). + 3353 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2352 math:notEqualTo 0}] - skolem:lemma2648 - [ a r:Fact; r:gives {((2 3 5 2) "=<") list:sort (2 2 3 5)}] - [ a r:Fact; r:gives {((2 3 5 2) ">=") list:sort (5 3 2 2)}] - skolem:lemma2454 - skolem:lemma2455 - [ a r:Fact; r:gives {(5322 2235) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1353}] + [ a r:Fact; r:gives {(1353 2000) math:sum 3353}] + skolem:lemma3351 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2235]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1353 a r:Inference; r:gives { - 2353 :kaprekar (0 6). + 3354 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2353 math:notEqualTo 0}] - skolem:lemma2649 - [ a r:Fact; r:gives {((2 3 5 3) "=<") list:sort (2 3 3 5)}] - [ a r:Fact; r:gives {((2 3 5 3) ">=") list:sort (5 3 3 2)}] - skolem:lemma2610 - skolem:lemma2611 - [ a r:Fact; r:gives {(5332 2335) math:difference 2997}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2997 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2997 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1354}] + [ a r:Fact; r:gives {(1354 2000) math:sum 3354}] + skolem:lemma3352 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2335]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1354 a r:Inference; r:gives { - 2354 :kaprekar (0 3). + 3355 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2354 math:notEqualTo 0}] - skolem:lemma2650 - [ a r:Fact; r:gives {((2 3 5 4) "=<") list:sort (2 3 4 5)}] - [ a r:Fact; r:gives {((2 3 5 4) ">=") list:sort (5 4 3 2)}] - skolem:lemma2632 - skolem:lemma2633 - [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1355}] + [ a r:Fact; r:gives {(1355 2000) math:sum 3355}] + skolem:lemma3353 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2345]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1355 a r:Inference; r:gives { - 2355 :kaprekar (0 5). + 3356 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2355 math:notEqualTo 0}] - skolem:lemma2651 - [ a r:Fact; r:gives {((2 3 5 5) "=<") list:sort (2 3 5 5)}] - [ a r:Fact; r:gives {((2 3 5 5) ">=") list:sort (5 5 3 2)}] - skolem:lemma2652 - skolem:lemma2653 - [ a r:Fact; r:gives {(5532 2355) math:difference 3177}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3177 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 3177 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1356}] + [ a r:Fact; r:gives {(1356 2000) math:sum 3356}] + skolem:lemma3354 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1356 a r:Inference; r:gives { - 2356 :kaprekar (0 2). + 3357 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2356 math:notEqualTo 0}] - skolem:lemma2654 - [ a r:Fact; r:gives {((2 3 5 6) "=<") list:sort (2 3 5 6)}] - [ a r:Fact; r:gives {((2 3 5 6) ">=") list:sort (6 5 3 2)}] - skolem:lemma2655 - skolem:lemma2656 - [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1357}] + [ a r:Fact; r:gives {(1357 2000) math:sum 3357}] + skolem:lemma3355 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2356]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2356]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1357 a r:Inference; r:gives { - 2357 :kaprekar (0 7). + 3358 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2357 math:notEqualTo 0}] - skolem:lemma2657 - [ a r:Fact; r:gives {((2 3 5 7) "=<") list:sort (2 3 5 7)}] - [ a r:Fact; r:gives {((2 3 5 7) ">=") list:sort (7 5 3 2)}] - skolem:lemma2658 - skolem:lemma2659 - [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1358}] + [ a r:Fact; r:gives {(1358 2000) math:sum 3358}] + skolem:lemma3356 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2357]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2357]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1358 a r:Inference; r:gives { - 2358 :kaprekar (0 1). + 3359 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2358 math:notEqualTo 0}] - skolem:lemma2660 - [ a r:Fact; r:gives {((2 3 5 8) "=<") list:sort (2 3 5 8)}] - [ a r:Fact; r:gives {((2 3 5 8) ">=") list:sort (8 5 3 2)}] - skolem:lemma2661 - skolem:lemma2662 - [ a r:Fact; r:gives {(8532 2358) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1359}] + [ a r:Fact; r:gives {(1359 2000) math:sum 3359}] + skolem:lemma3357 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2358]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2358]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1359 a r:Inference; r:gives { - 2359 :kaprekar (0 5). + 3360 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2359 math:notEqualTo 0}] - skolem:lemma2663 - [ a r:Fact; r:gives {((2 3 5 9) "=<") list:sort (2 3 5 9)}] - [ a r:Fact; r:gives {((2 3 5 9) ">=") list:sort (9 5 3 2)}] - skolem:lemma2664 - skolem:lemma2665 - [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1360}] + [ a r:Fact; r:gives {(1360 2000) math:sum 3360}] + skolem:lemma3358 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2359]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2359]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1360]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3360]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1360 a r:Inference; r:gives { - 2360 :kaprekar (0 7). + 3361 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2360 math:notEqualTo 0}] - skolem:lemma2666 - [ a r:Fact; r:gives {((2 3 6 0) "=<") list:sort (0 2 3 6)}] - [ a r:Fact; r:gives {((2 3 6 0) ">=") list:sort (6 3 2 0)}] - skolem:lemma2098 - skolem:lemma2099 - [ a r:Fact; r:gives {(6320 236) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1361}] + [ a r:Fact; r:gives {(1361 2000) math:sum 3361}] + skolem:lemma3359 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2360]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 236]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1361]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3361]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1361 a r:Inference; r:gives { - 2361 :kaprekar (0 7). + 3362 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2361 math:notEqualTo 0}] - skolem:lemma2667 - [ a r:Fact; r:gives {((2 3 6 1) "=<") list:sort (1 2 3 6)}] - [ a r:Fact; r:gives {((2 3 6 1) ">=") list:sort (6 3 2 1)}] - skolem:lemma2288 - skolem:lemma2289 - [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1362}] + [ a r:Fact; r:gives {(1362 2000) math:sum 3362}] + skolem:lemma3360 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2361]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1236]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1362]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3362]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1362 a r:Inference; r:gives { - 2362 :kaprekar (0 7). + 3363 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2362 math:notEqualTo 0}] - skolem:lemma2668 - [ a r:Fact; r:gives {((2 3 6 2) "=<") list:sort (2 2 3 6)}] - [ a r:Fact; r:gives {((2 3 6 2) ">=") list:sort (6 3 2 2)}] - skolem:lemma2457 - skolem:lemma2458 - [ a r:Fact; r:gives {(6322 2236) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1363}] + [ a r:Fact; r:gives {(1363 2000) math:sum 3363}] + skolem:lemma3361 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2362]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2236]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1363]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3363]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1363 a r:Inference; r:gives { - 2363 :kaprekar (0 4). + 3364 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2363 math:notEqualTo 0}] - skolem:lemma2669 - [ a r:Fact; r:gives {((2 3 6 3) "=<") list:sort (2 3 3 6)}] - [ a r:Fact; r:gives {((2 3 6 3) ">=") list:sort (6 3 3 2)}] - skolem:lemma2613 - skolem:lemma2614 - [ a r:Fact; r:gives {(6332 2336) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1364}] + [ a r:Fact; r:gives {(1364 2000) math:sum 3364}] + skolem:lemma3362 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2363]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2336]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1364]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3364]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1364 a r:Inference; r:gives { - 2364 :kaprekar (0 7). + 3365 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2364 math:notEqualTo 0}] - skolem:lemma2670 - [ a r:Fact; r:gives {((2 3 6 4) "=<") list:sort (2 3 4 6)}] - [ a r:Fact; r:gives {((2 3 6 4) ">=") list:sort (6 4 3 2)}] - skolem:lemma2635 - skolem:lemma2636 - [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1365}] + [ a r:Fact; r:gives {(1365 2000) math:sum 3365}] + skolem:lemma3363 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2364]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2346]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1365]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3365]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1365 a r:Inference; r:gives { - 2365 :kaprekar (0 2). + 3366 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2365 math:notEqualTo 0}] - skolem:lemma2671 - [ a r:Fact; r:gives {((2 3 6 5) "=<") list:sort (2 3 5 6)}] - [ a r:Fact; r:gives {((2 3 6 5) ">=") list:sort (6 5 3 2)}] - skolem:lemma2655 - skolem:lemma2656 - [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1366}] + [ a r:Fact; r:gives {(1366 2000) math:sum 3366}] + skolem:lemma3364 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2365]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2356]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1366 a r:Inference; r:gives { - 2366 :kaprekar (0 3). + 3367 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2366 math:notEqualTo 0}] - skolem:lemma2672 - [ a r:Fact; r:gives {((2 3 6 6) "=<") list:sort (2 3 6 6)}] - [ a r:Fact; r:gives {((2 3 6 6) ">=") list:sort (6 6 3 2)}] - skolem:lemma2673 - skolem:lemma2674 - [ a r:Fact; r:gives {(6632 2366) math:difference 4266}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4266 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 4266 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1367}] + [ a r:Fact; r:gives {(1367 2000) math:sum 3367}] + skolem:lemma3365 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2366]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2366]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1367 a r:Inference; r:gives { - 2367 :kaprekar (0 5). + 3368 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2367 math:notEqualTo 0}] - skolem:lemma2675 - [ a r:Fact; r:gives {((2 3 6 7) "=<") list:sort (2 3 6 7)}] - [ a r:Fact; r:gives {((2 3 6 7) ">=") list:sort (7 6 3 2)}] - skolem:lemma2676 - skolem:lemma2677 - [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1368}] + [ a r:Fact; r:gives {(1368 2000) math:sum 3368}] + skolem:lemma3366 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2367]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2367]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1368 a r:Inference; r:gives { - 2368 :kaprekar (0 3). + 3369 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2368 math:notEqualTo 0}] - skolem:lemma2678 - [ a r:Fact; r:gives {((2 3 6 8) "=<") list:sort (2 3 6 8)}] - [ a r:Fact; r:gives {((2 3 6 8) ">=") list:sort (8 6 3 2)}] - skolem:lemma2679 - skolem:lemma2680 - [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1369}] + [ a r:Fact; r:gives {(1369 2000) math:sum 3369}] + skolem:lemma3367 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2368]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2368]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1369 a r:Inference; r:gives { - 2369 :kaprekar (0 6). + 3370 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2369 math:notEqualTo 0}] - skolem:lemma2681 - [ a r:Fact; r:gives {((2 3 6 9) "=<") list:sort (2 3 6 9)}] - [ a r:Fact; r:gives {((2 3 6 9) ">=") list:sort (9 6 3 2)}] - skolem:lemma2682 - skolem:lemma2683 - [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1370}] + [ a r:Fact; r:gives {(1370 2000) math:sum 3370}] + skolem:lemma3368 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2369]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2369]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1370]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3370]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1370 a r:Inference; r:gives { - 2370 :kaprekar (0 3). + 3371 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2370 math:notEqualTo 0}] - skolem:lemma2684 - [ a r:Fact; r:gives {((2 3 7 0) "=<") list:sort (0 2 3 7)}] - [ a r:Fact; r:gives {((2 3 7 0) ">=") list:sort (7 3 2 0)}] - skolem:lemma2101 - skolem:lemma2102 - [ a r:Fact; r:gives {(7320 237) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1371}] + [ a r:Fact; r:gives {(1371 2000) math:sum 3371}] + skolem:lemma3369 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2370]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 237]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1371]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3371]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1371 a r:Inference; r:gives { - 2371 :kaprekar (0 7). + 3372 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2371 math:notEqualTo 0}] - skolem:lemma2685 - [ a r:Fact; r:gives {((2 3 7 1) "=<") list:sort (1 2 3 7)}] - [ a r:Fact; r:gives {((2 3 7 1) ">=") list:sort (7 3 2 1)}] - skolem:lemma2291 - skolem:lemma2292 - [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1372}] + [ a r:Fact; r:gives {(1372 2000) math:sum 3372}] + skolem:lemma3370 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2371]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1237]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1372]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3372]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1372 a r:Inference; r:gives { - 2372 :kaprekar (0 7). + 3373 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2372 math:notEqualTo 0}] - skolem:lemma2686 - [ a r:Fact; r:gives {((2 3 7 2) "=<") list:sort (2 2 3 7)}] - [ a r:Fact; r:gives {((2 3 7 2) ">=") list:sort (7 3 2 2)}] - skolem:lemma2460 - skolem:lemma2461 - [ a r:Fact; r:gives {(7322 2237) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1373}] + [ a r:Fact; r:gives {(1373 2000) math:sum 3373}] + skolem:lemma3371 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2372]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2237]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1373]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3373]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1373 a r:Inference; r:gives { - 2373 :kaprekar (0 6). + 3374 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2373 math:notEqualTo 0}] - skolem:lemma2687 - [ a r:Fact; r:gives {((2 3 7 3) "=<") list:sort (2 3 3 7)}] - [ a r:Fact; r:gives {((2 3 7 3) ">=") list:sort (7 3 3 2)}] - skolem:lemma2616 - skolem:lemma2617 - [ a r:Fact; r:gives {(7332 2337) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1374}] + [ a r:Fact; r:gives {(1374 2000) math:sum 3374}] + skolem:lemma3372 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2373]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2337]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1374]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3374]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1374 a r:Inference; r:gives { - 2374 :kaprekar (0 7). + 3375 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2374 math:notEqualTo 0}] - skolem:lemma2688 - [ a r:Fact; r:gives {((2 3 7 4) "=<") list:sort (2 3 4 7)}] - [ a r:Fact; r:gives {((2 3 7 4) ">=") list:sort (7 4 3 2)}] - skolem:lemma2638 - skolem:lemma2639 - [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1375}] + [ a r:Fact; r:gives {(1375 2000) math:sum 3375}] + skolem:lemma3373 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2374]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2347]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1375]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3375]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1375 a r:Inference; r:gives { - 2375 :kaprekar (0 7). + 3376 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2375 math:notEqualTo 0}] - skolem:lemma2689 - [ a r:Fact; r:gives {((2 3 7 5) "=<") list:sort (2 3 5 7)}] - [ a r:Fact; r:gives {((2 3 7 5) ">=") list:sort (7 5 3 2)}] - skolem:lemma2658 - skolem:lemma2659 - [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1376}] + [ a r:Fact; r:gives {(1376 2000) math:sum 3376}] + skolem:lemma3374 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2375]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2357]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1376]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3376]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1376 a r:Inference; r:gives { - 2376 :kaprekar (0 5). + 3377 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2376 math:notEqualTo 0}] - skolem:lemma2690 - [ a r:Fact; r:gives {((2 3 7 6) "=<") list:sort (2 3 6 7)}] - [ a r:Fact; r:gives {((2 3 7 6) ">=") list:sort (7 6 3 2)}] - skolem:lemma2676 - skolem:lemma2677 - [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1377}] + [ a r:Fact; r:gives {(1377 2000) math:sum 3377}] + skolem:lemma3375 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2376]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2367]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1377 a r:Inference; r:gives { - 2377 :kaprekar (0 5). + 3378 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2377 math:notEqualTo 0}] - skolem:lemma2691 - [ a r:Fact; r:gives {((2 3 7 7) "=<") list:sort (2 3 7 7)}] - [ a r:Fact; r:gives {((2 3 7 7) ">=") list:sort (7 7 3 2)}] - skolem:lemma2692 - skolem:lemma2693 - [ a r:Fact; r:gives {(7732 2377) math:difference 5355}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5355 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5355 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1378}] + [ a r:Fact; r:gives {(1378 2000) math:sum 3378}] + skolem:lemma3376 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2377]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2377]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7732]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1378 a r:Inference; r:gives { - 2378 :kaprekar (0 4). + 3379 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2378 math:notEqualTo 0}] - skolem:lemma2694 - [ a r:Fact; r:gives {((2 3 7 8) "=<") list:sort (2 3 7 8)}] - [ a r:Fact; r:gives {((2 3 7 8) ">=") list:sort (8 7 3 2)}] - skolem:lemma2695 - skolem:lemma2696 - [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1379}] + [ a r:Fact; r:gives {(1379 2000) math:sum 3379}] + skolem:lemma3377 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2378]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2378]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8732]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1379 a r:Inference; r:gives { - 2379 :kaprekar (0 3). + 3380 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2379 math:notEqualTo 0}] - skolem:lemma2697 - [ a r:Fact; r:gives {((2 3 7 9) "=<") list:sort (2 3 7 9)}] - [ a r:Fact; r:gives {((2 3 7 9) ">=") list:sort (9 7 3 2)}] - skolem:lemma2698 - skolem:lemma2699 - [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1380}] + [ a r:Fact; r:gives {(1380 2000) math:sum 3380}] + skolem:lemma3378 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2379]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2379]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9732]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1380]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3380]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1380 a r:Inference; r:gives { - 2380 :kaprekar (0 3). + 3381 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2380 math:notEqualTo 0}] - skolem:lemma2700 - [ a r:Fact; r:gives {((2 3 8 0) "=<") list:sort (0 2 3 8)}] - [ a r:Fact; r:gives {((2 3 8 0) ">=") list:sort (8 3 2 0)}] - skolem:lemma2104 - skolem:lemma2105 - [ a r:Fact; r:gives {(8320 238) math:difference 8082}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8082 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 8082 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1381}] + [ a r:Fact; r:gives {(1381 2000) math:sum 3381}] + skolem:lemma3379 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2380]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 238]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1381]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3381]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1381 a r:Inference; r:gives { - 2381 :kaprekar (0 3). + 3382 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2381 math:notEqualTo 0}] - skolem:lemma2701 - [ a r:Fact; r:gives {((2 3 8 1) "=<") list:sort (1 2 3 8)}] - [ a r:Fact; r:gives {((2 3 8 1) ">=") list:sort (8 3 2 1)}] - skolem:lemma2294 - skolem:lemma2295 - [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1382}] + [ a r:Fact; r:gives {(1382 2000) math:sum 3382}] + skolem:lemma3380 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2381]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1238]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1382]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3382]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1382 a r:Inference; r:gives { - 2382 :kaprekar (0 7). + 3383 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2382 math:notEqualTo 0}] - skolem:lemma2702 - [ a r:Fact; r:gives {((2 3 8 2) "=<") list:sort (2 2 3 8)}] - [ a r:Fact; r:gives {((2 3 8 2) ">=") list:sort (8 3 2 2)}] - skolem:lemma2463 - skolem:lemma2464 - [ a r:Fact; r:gives {(8322 2238) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1383}] + [ a r:Fact; r:gives {(1383 2000) math:sum 3383}] + skolem:lemma3381 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2382]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2238]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1383]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3383]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1383 a r:Inference; r:gives { - 2383 :kaprekar (0 6). + 3384 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2383 math:notEqualTo 0}] - skolem:lemma2703 - [ a r:Fact; r:gives {((2 3 8 3) "=<") list:sort (2 3 3 8)}] - [ a r:Fact; r:gives {((2 3 8 3) ">=") list:sort (8 3 3 2)}] - skolem:lemma2619 - skolem:lemma2620 - [ a r:Fact; r:gives {(8332 2338) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1384}] + [ a r:Fact; r:gives {(1384 2000) math:sum 3384}] + skolem:lemma3382 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2383]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2338]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1384]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3384]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1384 a r:Inference; r:gives { - 2384 :kaprekar (0 7). + 3385 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2384 math:notEqualTo 0}] - skolem:lemma2704 - [ a r:Fact; r:gives {((2 3 8 4) "=<") list:sort (2 3 4 8)}] - [ a r:Fact; r:gives {((2 3 8 4) ">=") list:sort (8 4 3 2)}] - skolem:lemma2641 - skolem:lemma2642 - [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1385}] + [ a r:Fact; r:gives {(1385 2000) math:sum 3385}] + skolem:lemma3383 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2384]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2348]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1385]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3385]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1385 a r:Inference; r:gives { - 2385 :kaprekar (0 1). + 3386 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2385 math:notEqualTo 0}] - skolem:lemma2705 - [ a r:Fact; r:gives {((2 3 8 5) "=<") list:sort (2 3 5 8)}] - [ a r:Fact; r:gives {((2 3 8 5) ">=") list:sort (8 5 3 2)}] - skolem:lemma2661 - skolem:lemma2662 - [ a r:Fact; r:gives {(8532 2358) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1386}] + [ a r:Fact; r:gives {(1386 2000) math:sum 3386}] + skolem:lemma3384 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2385]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2358]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1386]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3386]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1386 a r:Inference; r:gives { - 2386 :kaprekar (0 3). + 3387 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2386 math:notEqualTo 0}] - skolem:lemma2706 - [ a r:Fact; r:gives {((2 3 8 6) "=<") list:sort (2 3 6 8)}] - [ a r:Fact; r:gives {((2 3 8 6) ">=") list:sort (8 6 3 2)}] - skolem:lemma2679 - skolem:lemma2680 - [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1387}] + [ a r:Fact; r:gives {(1387 2000) math:sum 3387}] + skolem:lemma3385 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2386]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2368]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1387]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3387]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1387 a r:Inference; r:gives { - 2387 :kaprekar (0 4). + 3388 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2387 math:notEqualTo 0}] - skolem:lemma2707 - [ a r:Fact; r:gives {((2 3 8 7) "=<") list:sort (2 3 7 8)}] - [ a r:Fact; r:gives {((2 3 8 7) ">=") list:sort (8 7 3 2)}] - skolem:lemma2695 - skolem:lemma2696 - [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1388}] + [ a r:Fact; r:gives {(1388 2000) math:sum 3388}] + skolem:lemma3386 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2387]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2378]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8732]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1388 a r:Inference; r:gives { - 2388 :kaprekar (0 5). + 3389 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2388 math:notEqualTo 0}] - skolem:lemma2708 - [ a r:Fact; r:gives {((2 3 8 8) "=<") list:sort (2 3 8 8)}] - [ a r:Fact; r:gives {((2 3 8 8) ">=") list:sort (8 8 3 2)}] - skolem:lemma2709 - skolem:lemma2710 - [ a r:Fact; r:gives {(8832 2388) math:difference 6444}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6444 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 6444 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1389}] + [ a r:Fact; r:gives {(1389 2000) math:sum 3389}] + skolem:lemma3387 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2388]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2388]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8832]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1389 a r:Inference; r:gives { - 2389 :kaprekar (0 5). + 3390 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2389 math:notEqualTo 0}] - skolem:lemma2711 - [ a r:Fact; r:gives {((2 3 8 9) "=<") list:sort (2 3 8 9)}] - [ a r:Fact; r:gives {((2 3 8 9) ">=") list:sort (9 8 3 2)}] - skolem:lemma2712 - skolem:lemma2713 - [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7443 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1390}] + [ a r:Fact; r:gives {(1390 2000) math:sum 3390}] + skolem:lemma3388 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2389]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2389]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9832]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1390]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3390]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1390 a r:Inference; r:gives { - 2390 :kaprekar (0 4). + 3391 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2390 math:notEqualTo 0}] - skolem:lemma2714 - [ a r:Fact; r:gives {((2 3 9 0) "=<") list:sort (0 2 3 9)}] - [ a r:Fact; r:gives {((2 3 9 0) ">=") list:sort (9 3 2 0)}] - skolem:lemma2107 - skolem:lemma2108 - [ a r:Fact; r:gives {(9320 239) math:difference 9081}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9081 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 9081 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1391}] + [ a r:Fact; r:gives {(1391 2000) math:sum 3391}] + skolem:lemma3389 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2390]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 239]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1391]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3391]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1391 a r:Inference; r:gives { - 2391 :kaprekar (0 3). + 3392 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2391 math:notEqualTo 0}] - skolem:lemma2715 - [ a r:Fact; r:gives {((2 3 9 1) "=<") list:sort (1 2 3 9)}] - [ a r:Fact; r:gives {((2 3 9 1) ">=") list:sort (9 3 2 1)}] - skolem:lemma2297 - skolem:lemma2298 - [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8082 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 8082 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1392}] + [ a r:Fact; r:gives {(1392 2000) math:sum 3392}] + skolem:lemma3390 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2391]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1239]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1392]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3392]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1392 a r:Inference; r:gives { - 2392 :kaprekar (0 3). + 3393 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2392 math:notEqualTo 0}] - skolem:lemma2716 - [ a r:Fact; r:gives {((2 3 9 2) "=<") list:sort (2 2 3 9)}] - [ a r:Fact; r:gives {((2 3 9 2) ">=") list:sort (9 3 2 2)}] - skolem:lemma2466 - skolem:lemma2467 - [ a r:Fact; r:gives {(9322 2239) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1393}] + [ a r:Fact; r:gives {(1393 2000) math:sum 3393}] + skolem:lemma3391 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2392]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2239]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1393]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3393]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1393 a r:Inference; r:gives { - 2393 :kaprekar (0 4). + 3394 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2393 math:notEqualTo 0}] - skolem:lemma2717 - [ a r:Fact; r:gives {((2 3 9 3) "=<") list:sort (2 3 3 9)}] - [ a r:Fact; r:gives {((2 3 9 3) ">=") list:sort (9 3 3 2)}] - skolem:lemma2622 - skolem:lemma2623 - [ a r:Fact; r:gives {(9332 2339) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1394}] + [ a r:Fact; r:gives {(1394 2000) math:sum 3394}] + skolem:lemma3392 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2393]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2339]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1394]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3394]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1394 a r:Inference; r:gives { - 2394 :kaprekar (0 3). + 3395 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2394 math:notEqualTo 0}] - skolem:lemma2718 - [ a r:Fact; r:gives {((2 3 9 4) "=<") list:sort (2 3 4 9)}] - [ a r:Fact; r:gives {((2 3 9 4) ">=") list:sort (9 4 3 2)}] - skolem:lemma2644 - skolem:lemma2645 - [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1395}] + [ a r:Fact; r:gives {(1395 2000) math:sum 3395}] + skolem:lemma3393 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2394]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2349]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1395]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3395]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1395 a r:Inference; r:gives { - 2395 :kaprekar (0 5). + 3396 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2395 math:notEqualTo 0}] - skolem:lemma2719 - [ a r:Fact; r:gives {((2 3 9 5) "=<") list:sort (2 3 5 9)}] - [ a r:Fact; r:gives {((2 3 9 5) ">=") list:sort (9 5 3 2)}] - skolem:lemma2664 - skolem:lemma2665 - [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1396}] + [ a r:Fact; r:gives {(1396 2000) math:sum 3396}] + skolem:lemma3394 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2395]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2359]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1396]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3396]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1396 a r:Inference; r:gives { - 2396 :kaprekar (0 6). + 3397 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2396 math:notEqualTo 0}] - skolem:lemma2720 - [ a r:Fact; r:gives {((2 3 9 6) "=<") list:sort (2 3 6 9)}] - [ a r:Fact; r:gives {((2 3 9 6) ">=") list:sort (9 6 3 2)}] - skolem:lemma2682 - skolem:lemma2683 - [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1397}] + [ a r:Fact; r:gives {(1397 2000) math:sum 3397}] + skolem:lemma3395 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2396]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2369]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1397]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3397]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1397 a r:Inference; r:gives { - 2397 :kaprekar (0 3). + 3398 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2397 math:notEqualTo 0}] - skolem:lemma2721 - [ a r:Fact; r:gives {((2 3 9 7) "=<") list:sort (2 3 7 9)}] - [ a r:Fact; r:gives {((2 3 9 7) ">=") list:sort (9 7 3 2)}] - skolem:lemma2698 - skolem:lemma2699 - [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1398}] + [ a r:Fact; r:gives {(1398 2000) math:sum 3398}] + skolem:lemma3396 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2397]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2379]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9732]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1398]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3398]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1398 a r:Inference; r:gives { - 2398 :kaprekar (0 5). + 3399 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2398 math:notEqualTo 0}] - skolem:lemma2722 - [ a r:Fact; r:gives {((2 3 9 8) "=<") list:sort (2 3 8 9)}] - [ a r:Fact; r:gives {((2 3 9 8) ">=") list:sort (9 8 3 2)}] - skolem:lemma2712 - skolem:lemma2713 - [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7443 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1399}] + [ a r:Fact; r:gives {(1399 2000) math:sum 3399}] + skolem:lemma3397 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2398]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2389]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9832]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1399 a r:Inference; r:gives { - 2399 :kaprekar (0 3). + 3400 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2399 math:notEqualTo 0}] - skolem:lemma2723 - [ a r:Fact; r:gives {((2 3 9 9) "=<") list:sort (2 3 9 9)}] - [ a r:Fact; r:gives {((2 3 9 9) ">=") list:sort (9 9 3 2)}] - skolem:lemma2724 - skolem:lemma2725 - [ a r:Fact; r:gives {(9932 2399) math:difference 7533}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7533 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7533 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1400}] + [ a r:Fact; r:gives {(1400 2000) math:sum 3400}] + skolem:lemma3398 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2399]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2399]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9932]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1400 a r:Inference; r:gives { - 2400 :kaprekar (0 2). + 3401 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2400 math:notEqualTo 0}] - skolem:lemma2726 - [ a r:Fact; r:gives {((2 4 0 0) "=<") list:sort (0 0 2 4)}] - [ a r:Fact; r:gives {((2 4 0 0) ">=") list:sort (4 2 0 0)}] - skolem:lemma2014 - skolem:lemma2015 - [ a r:Fact; r:gives {(4200 24) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1401}] + [ a r:Fact; r:gives {(1401 2000) math:sum 3401}] + skolem:lemma3399 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2400]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1401]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3401]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1401 a r:Inference; r:gives { - 2401 :kaprekar (0 7). + 3402 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2401 math:notEqualTo 0}] - skolem:lemma2727 - [ a r:Fact; r:gives {((2 4 0 1) "=<") list:sort (0 1 2 4)}] - [ a r:Fact; r:gives {((2 4 0 1) ">=") list:sort (4 2 1 0)}] - skolem:lemma2042 - skolem:lemma2043 - [ a r:Fact; r:gives {(4210 124) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1402}] + [ a r:Fact; r:gives {(1402 2000) math:sum 3402}] + skolem:lemma3400 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2401]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 124]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1402]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3402]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1402 a r:Inference; r:gives { - 2402 :kaprekar (0 4). + 3403 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2402 math:notEqualTo 0}] - skolem:lemma2728 - [ a r:Fact; r:gives {((2 4 0 2) "=<") list:sort (0 2 2 4)}] - [ a r:Fact; r:gives {((2 4 0 2) ">=") list:sort (4 2 2 0)}] - skolem:lemma2068 - skolem:lemma2069 - [ a r:Fact; r:gives {(4220 224) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1403}] + [ a r:Fact; r:gives {(1403 2000) math:sum 3403}] + skolem:lemma3401 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2402]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 224]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1403]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3403]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1403 a r:Inference; r:gives { - 2403 :kaprekar (0 7). + 3404 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2403 math:notEqualTo 0}] - skolem:lemma2729 - [ a r:Fact; r:gives {((2 4 0 3) "=<") list:sort (0 2 3 4)}] - [ a r:Fact; r:gives {((2 4 0 3) ">=") list:sort (4 3 2 0)}] - skolem:lemma2092 - skolem:lemma2093 - [ a r:Fact; r:gives {(4320 234) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1404}] + [ a r:Fact; r:gives {(1404 2000) math:sum 3404}] + skolem:lemma3402 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2403]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 234]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1404]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3404]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1404 a r:Inference; r:gives { - 2404 :kaprekar (0 2). + 3405 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2404 math:notEqualTo 0}] - skolem:lemma2730 - [ a r:Fact; r:gives {((2 4 0 4) "=<") list:sort (0 2 4 4)}] - [ a r:Fact; r:gives {((2 4 0 4) ">=") list:sort (4 4 2 0)}] - skolem:lemma2114 - skolem:lemma2115 - [ a r:Fact; r:gives {(4420 244) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1405}] + [ a r:Fact; r:gives {(1405 2000) math:sum 3405}] + skolem:lemma3403 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2404]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 244]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1405]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3405]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1405 a r:Inference; r:gives { - 2405 :kaprekar (0 7). + 3406 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2405 math:notEqualTo 0}] - skolem:lemma2731 - [ a r:Fact; r:gives {((2 4 0 5) "=<") list:sort (0 2 4 5)}] - [ a r:Fact; r:gives {((2 4 0 5) ">=") list:sort (5 4 2 0)}] - skolem:lemma2117 - skolem:lemma2118 - [ a r:Fact; r:gives {(5420 245) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1406}] + [ a r:Fact; r:gives {(1406 2000) math:sum 3406}] + skolem:lemma3404 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2405]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 245]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1406]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3406]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1406 a r:Inference; r:gives { - 2406 :kaprekar (0 1). + 3407 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2406 math:notEqualTo 0}] - skolem:lemma2732 - [ a r:Fact; r:gives {((2 4 0 6) "=<") list:sort (0 2 4 6)}] - [ a r:Fact; r:gives {((2 4 0 6) ">=") list:sort (6 4 2 0)}] - skolem:lemma2120 - skolem:lemma2121 - [ a r:Fact; r:gives {(6420 246) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1407}] + [ a r:Fact; r:gives {(1407 2000) math:sum 3407}] + skolem:lemma3405 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2406]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 246]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1407]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3407]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1407 a r:Inference; r:gives { - 2407 :kaprekar (0 5). + 3408 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2407 math:notEqualTo 0}] - skolem:lemma2733 - [ a r:Fact; r:gives {((2 4 0 7) "=<") list:sort (0 2 4 7)}] - [ a r:Fact; r:gives {((2 4 0 7) ">=") list:sort (7 4 2 0)}] - skolem:lemma2123 - skolem:lemma2124 - [ a r:Fact; r:gives {(7420 247) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1408}] + [ a r:Fact; r:gives {(1408 2000) math:sum 3408}] + skolem:lemma3406 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2407]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 247]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1408]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3408]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1408 a r:Inference; r:gives { - 2408 :kaprekar (0 6). + 3409 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2408 math:notEqualTo 0}] - skolem:lemma2734 - [ a r:Fact; r:gives {((2 4 0 8) "=<") list:sort (0 2 4 8)}] - [ a r:Fact; r:gives {((2 4 0 8) ">=") list:sort (8 4 2 0)}] - skolem:lemma2126 - skolem:lemma2127 - [ a r:Fact; r:gives {(8420 248) math:difference 8172}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8172 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 8172 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1409}] + [ a r:Fact; r:gives {(1409 2000) math:sum 3409}] + skolem:lemma3407 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2408]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 248]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1409]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3409]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1409 a r:Inference; r:gives { - 2409 :kaprekar (0 3). + 3410 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2409 math:notEqualTo 0}] - skolem:lemma2735 - [ a r:Fact; r:gives {((2 4 0 9) "=<") list:sort (0 2 4 9)}] - [ a r:Fact; r:gives {((2 4 0 9) ">=") list:sort (9 4 2 0)}] - skolem:lemma2129 - skolem:lemma2130 - [ a r:Fact; r:gives {(9420 249) math:difference 9171}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9171 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 9171 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1410}] + [ a r:Fact; r:gives {(1410 2000) math:sum 3410}] + skolem:lemma3408 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2409]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 249]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1410]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3410]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1410 a r:Inference; r:gives { - 2410 :kaprekar (0 7). + 3411 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2410 math:notEqualTo 0}] - skolem:lemma2736 - [ a r:Fact; r:gives {((2 4 1 0) "=<") list:sort (0 1 2 4)}] - [ a r:Fact; r:gives {((2 4 1 0) ">=") list:sort (4 2 1 0)}] - skolem:lemma2042 - skolem:lemma2043 - [ a r:Fact; r:gives {(4210 124) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1411}] + [ a r:Fact; r:gives {(1411 2000) math:sum 3411}] + skolem:lemma3409 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2410]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 124]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1411]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3411]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1411 a r:Inference; r:gives { - 2411 :kaprekar (0 3). + 3412 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2411 math:notEqualTo 0}] - skolem:lemma2737 - [ a r:Fact; r:gives {((2 4 1 1) "=<") list:sort (1 1 2 4)}] - [ a r:Fact; r:gives {((2 4 1 1) ">=") list:sort (4 2 1 1)}] - skolem:lemma2232 - skolem:lemma2233 - [ a r:Fact; r:gives {(4211 1124) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1412}] + [ a r:Fact; r:gives {(1412 2000) math:sum 3412}] + skolem:lemma3410 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2411]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1124]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1412]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3412]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1412 a r:Inference; r:gives { - 2412 :kaprekar (0 6). + 3413 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2412 math:notEqualTo 0}] - skolem:lemma2738 - [ a r:Fact; r:gives {((2 4 1 2) "=<") list:sort (1 2 2 4)}] - [ a r:Fact; r:gives {((2 4 1 2) ">=") list:sort (4 2 2 1)}] - skolem:lemma2258 - skolem:lemma2259 - [ a r:Fact; r:gives {(4221 1224) math:difference 2997}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2997 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2997 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1413}] + [ a r:Fact; r:gives {(1413 2000) math:sum 3413}] + skolem:lemma3411 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2412]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1224]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1413]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3413]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1413 a r:Inference; r:gives { - 2413 :kaprekar (0 3). + 3414 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2413 math:notEqualTo 0}] - skolem:lemma2739 - [ a r:Fact; r:gives {((2 4 1 3) "=<") list:sort (1 2 3 4)}] - [ a r:Fact; r:gives {((2 4 1 3) ">=") list:sort (4 3 2 1)}] - skolem:lemma2282 - skolem:lemma2283 - [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1414}] + [ a r:Fact; r:gives {(1414 2000) math:sum 3414}] + skolem:lemma3412 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2413]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1234]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1414]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3414]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1414 a r:Inference; r:gives { - 2414 :kaprekar (0 5). + 3415 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2414 math:notEqualTo 0}] - skolem:lemma2740 - [ a r:Fact; r:gives {((2 4 1 4) "=<") list:sort (1 2 4 4)}] - [ a r:Fact; r:gives {((2 4 1 4) ">=") list:sort (4 4 2 1)}] - skolem:lemma2304 - skolem:lemma2305 - [ a r:Fact; r:gives {(4421 1244) math:difference 3177}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3177 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 3177 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1415}] + [ a r:Fact; r:gives {(1415 2000) math:sum 3415}] + skolem:lemma3413 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2414]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1244]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1415]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3415]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1415 a r:Inference; r:gives { - 2415 :kaprekar (0 2). + 3416 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2415 math:notEqualTo 0}] - skolem:lemma2741 - [ a r:Fact; r:gives {((2 4 1 5) "=<") list:sort (1 2 4 5)}] - [ a r:Fact; r:gives {((2 4 1 5) ">=") list:sort (5 4 2 1)}] - skolem:lemma2307 - skolem:lemma2308 - [ a r:Fact; r:gives {(5421 1245) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1416}] + [ a r:Fact; r:gives {(1416 2000) math:sum 3416}] + skolem:lemma3414 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2415]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1245]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1416]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3416]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1416 a r:Inference; r:gives { - 2416 :kaprekar (0 7). + 3417 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2416 math:notEqualTo 0}] - skolem:lemma2742 - [ a r:Fact; r:gives {((2 4 1 6) "=<") list:sort (1 2 4 6)}] - [ a r:Fact; r:gives {((2 4 1 6) ">=") list:sort (6 4 2 1)}] - skolem:lemma2310 - skolem:lemma2311 - [ a r:Fact; r:gives {(6421 1246) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1417}] + [ a r:Fact; r:gives {(1417 2000) math:sum 3417}] + skolem:lemma3415 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2416]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1246]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1417]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3417]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1417 a r:Inference; r:gives { - 2417 :kaprekar (0 1). + 3418 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2417 math:notEqualTo 0}] - skolem:lemma2743 - [ a r:Fact; r:gives {((2 4 1 7) "=<") list:sort (1 2 4 7)}] - [ a r:Fact; r:gives {((2 4 1 7) ">=") list:sort (7 4 2 1)}] - skolem:lemma2313 - skolem:lemma2314 - [ a r:Fact; r:gives {(7421 1247) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1418}] + [ a r:Fact; r:gives {(1418 2000) math:sum 3418}] + skolem:lemma3416 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2417]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1247]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1418]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3418]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1418 a r:Inference; r:gives { - 2418 :kaprekar (0 5). + 3419 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2418 math:notEqualTo 0}] - skolem:lemma2744 - [ a r:Fact; r:gives {((2 4 1 8) "=<") list:sort (1 2 4 8)}] - [ a r:Fact; r:gives {((2 4 1 8) ">=") list:sort (8 4 2 1)}] - skolem:lemma2316 - skolem:lemma2317 - [ a r:Fact; r:gives {(8421 1248) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1419}] + [ a r:Fact; r:gives {(1419 2000) math:sum 3419}] + skolem:lemma3417 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2418]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1248]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1419]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3419]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1419 a r:Inference; r:gives { - 2419 :kaprekar (0 6). + 3420 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2419 math:notEqualTo 0}] - skolem:lemma2745 - [ a r:Fact; r:gives {((2 4 1 9) "=<") list:sort (1 2 4 9)}] - [ a r:Fact; r:gives {((2 4 1 9) ">=") list:sort (9 4 2 1)}] - skolem:lemma2319 - skolem:lemma2320 - [ a r:Fact; r:gives {(9421 1249) math:difference 8172}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8172 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 8172 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1420}] + [ a r:Fact; r:gives {(1420 2000) math:sum 3420}] + skolem:lemma3418 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2419]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1249]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1420 a r:Inference; r:gives { - 2420 :kaprekar (0 4). + 3421 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2420 math:notEqualTo 0}] - skolem:lemma2746 - [ a r:Fact; r:gives {((2 4 2 0) "=<") list:sort (0 2 2 4)}] - [ a r:Fact; r:gives {((2 4 2 0) ">=") list:sort (4 2 2 0)}] - skolem:lemma2068 - skolem:lemma2069 - [ a r:Fact; r:gives {(4220 224) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1421}] + [ a r:Fact; r:gives {(1421 2000) math:sum 3421}] + skolem:lemma3419 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 224]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1421 a r:Inference; r:gives { - 2421 :kaprekar (0 6). + 3422 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2421 math:notEqualTo 0}] - skolem:lemma2747 - [ a r:Fact; r:gives {((2 4 2 1) "=<") list:sort (1 2 2 4)}] - [ a r:Fact; r:gives {((2 4 2 1) ">=") list:sort (4 2 2 1)}] - skolem:lemma2258 - skolem:lemma2259 - [ a r:Fact; r:gives {(4221 1224) math:difference 2997}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2997 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2997 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1422}] + [ a r:Fact; r:gives {(1422 2000) math:sum 3422}] + skolem:lemma3420 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1224]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1422 a r:Inference; r:gives { - 2422 :kaprekar (0 4). + 3423 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2422 math:notEqualTo 0}] - skolem:lemma2748 - [ a r:Fact; r:gives {((2 4 2 2) "=<") list:sort (2 2 2 4)}] - [ a r:Fact; r:gives {((2 4 2 2) ">=") list:sort (4 2 2 2)}] - skolem:lemma2427 - skolem:lemma2428 - [ a r:Fact; r:gives {(4222 2224) math:difference 1998}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1998 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1998 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1423}] + [ a r:Fact; r:gives {(1423 2000) math:sum 3423}] + skolem:lemma3421 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2224]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1423]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3423]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1423 a r:Inference; r:gives { - 2423 :kaprekar (0 3). + 3424 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2423 math:notEqualTo 0}] - skolem:lemma2749 - [ a r:Fact; r:gives {((2 4 2 3) "=<") list:sort (2 2 3 4)}] - [ a r:Fact; r:gives {((2 4 2 3) ">=") list:sort (4 3 2 2)}] - skolem:lemma2451 - skolem:lemma2452 - [ a r:Fact; r:gives {(4322 2234) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1424}] + [ a r:Fact; r:gives {(1424 2000) math:sum 3424}] + skolem:lemma3422 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2423]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2234]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1424]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3424]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1424 a r:Inference; r:gives { - 2424 :kaprekar (0 6). + 3425 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2424 math:notEqualTo 0}] - skolem:lemma2750 - [ a r:Fact; r:gives {((2 4 2 4) "=<") list:sort (2 2 4 4)}] - [ a r:Fact; r:gives {((2 4 2 4) ">=") list:sort (4 4 2 2)}] - skolem:lemma2473 - skolem:lemma2474 - [ a r:Fact; r:gives {(4422 2244) math:difference 2178}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2178 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2178 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1425}] + [ a r:Fact; r:gives {(1425 2000) math:sum 3425}] + skolem:lemma3423 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2424]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2244]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2178]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1425]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3425]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1425 a r:Inference; r:gives { - 2425 :kaprekar (0 5). + 3426 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2425 math:notEqualTo 0}] - skolem:lemma2751 - [ a r:Fact; r:gives {((2 4 2 5) "=<") list:sort (2 2 4 5)}] - [ a r:Fact; r:gives {((2 4 2 5) ">=") list:sort (5 4 2 2)}] - skolem:lemma2476 - skolem:lemma2477 - [ a r:Fact; r:gives {(5422 2245) math:difference 3177}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3177 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 3177 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1426}] + [ a r:Fact; r:gives {(1426 2000) math:sum 3426}] + skolem:lemma3424 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2425]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2245]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1426]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3426]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1426 a r:Inference; r:gives { - 2426 :kaprekar (0 2). + 3427 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2426 math:notEqualTo 0}] - skolem:lemma2752 - [ a r:Fact; r:gives {((2 4 2 6) "=<") list:sort (2 2 4 6)}] - [ a r:Fact; r:gives {((2 4 2 6) ">=") list:sort (6 4 2 2)}] - skolem:lemma2479 - skolem:lemma2480 - [ a r:Fact; r:gives {(6422 2246) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1427}] + [ a r:Fact; r:gives {(1427 2000) math:sum 3427}] + skolem:lemma3425 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2426]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2246]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1427]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3427]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1427 a r:Inference; r:gives { - 2427 :kaprekar (0 7). + 3428 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2427 math:notEqualTo 0}] - skolem:lemma2753 - [ a r:Fact; r:gives {((2 4 2 7) "=<") list:sort (2 2 4 7)}] - [ a r:Fact; r:gives {((2 4 2 7) ">=") list:sort (7 4 2 2)}] - skolem:lemma2482 - skolem:lemma2483 - [ a r:Fact; r:gives {(7422 2247) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1428}] + [ a r:Fact; r:gives {(1428 2000) math:sum 3428}] + skolem:lemma3426 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2427]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2247]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1428]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3428]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1428 a r:Inference; r:gives { - 2428 :kaprekar (0 1). + 3429 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2428 math:notEqualTo 0}] - skolem:lemma2754 - [ a r:Fact; r:gives {((2 4 2 8) "=<") list:sort (2 2 4 8)}] - [ a r:Fact; r:gives {((2 4 2 8) ">=") list:sort (8 4 2 2)}] - skolem:lemma2485 - skolem:lemma2486 - [ a r:Fact; r:gives {(8422 2248) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1429}] + [ a r:Fact; r:gives {(1429 2000) math:sum 3429}] + skolem:lemma3427 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2428]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2248]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1429]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3429]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1429 a r:Inference; r:gives { - 2429 :kaprekar (0 5). + 3430 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2429 math:notEqualTo 0}] - skolem:lemma2755 - [ a r:Fact; r:gives {((2 4 2 9) "=<") list:sort (2 2 4 9)}] - [ a r:Fact; r:gives {((2 4 2 9) ">=") list:sort (9 4 2 2)}] - skolem:lemma2488 - skolem:lemma2489 - [ a r:Fact; r:gives {(9422 2249) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1430}] + [ a r:Fact; r:gives {(1430 2000) math:sum 3430}] + skolem:lemma3428 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2429]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2249]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1430 a r:Inference; r:gives { - 2430 :kaprekar (0 7). + 3431 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2430 math:notEqualTo 0}] - skolem:lemma2756 - [ a r:Fact; r:gives {((2 4 3 0) "=<") list:sort (0 2 3 4)}] - [ a r:Fact; r:gives {((2 4 3 0) ">=") list:sort (4 3 2 0)}] - skolem:lemma2092 - skolem:lemma2093 - [ a r:Fact; r:gives {(4320 234) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1431}] + [ a r:Fact; r:gives {(1431 2000) math:sum 3431}] + skolem:lemma3429 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2430]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 234]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1431 a r:Inference; r:gives { - 2431 :kaprekar (0 3). + 3432 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2431 math:notEqualTo 0}] - skolem:lemma2757 - [ a r:Fact; r:gives {((2 4 3 1) "=<") list:sort (1 2 3 4)}] - [ a r:Fact; r:gives {((2 4 3 1) ">=") list:sort (4 3 2 1)}] - skolem:lemma2282 - skolem:lemma2283 - [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1432}] + [ a r:Fact; r:gives {(1432 2000) math:sum 3432}] + skolem:lemma3430 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2431]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1234]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1432 a r:Inference; r:gives { - 2432 :kaprekar (0 3). + 3433 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2432 math:notEqualTo 0}] - skolem:lemma2758 - [ a r:Fact; r:gives {((2 4 3 2) "=<") list:sort (2 2 3 4)}] - [ a r:Fact; r:gives {((2 4 3 2) ">=") list:sort (4 3 2 2)}] - skolem:lemma2451 - skolem:lemma2452 - [ a r:Fact; r:gives {(4322 2234) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1433}] + [ a r:Fact; r:gives {(1433 2000) math:sum 3433}] + skolem:lemma3431 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2234]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1433 a r:Inference; r:gives { - 2433 :kaprekar (0 4). + 3434 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2433 math:notEqualTo 0}] - skolem:lemma2759 - [ a r:Fact; r:gives {((2 4 3 3) "=<") list:sort (2 3 3 4)}] - [ a r:Fact; r:gives {((2 4 3 3) ">=") list:sort (4 3 3 2)}] - skolem:lemma2607 - skolem:lemma2608 - [ a r:Fact; r:gives {(4332 2334) math:difference 1998}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1998 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1998 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1434}] + [ a r:Fact; r:gives {(1434 2000) math:sum 3434}] + skolem:lemma3432 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2433]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2334]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1434]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3434]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1434 a r:Inference; r:gives { - 2434 :kaprekar (0 3). + 3435 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2434 math:notEqualTo 0}] - skolem:lemma2760 - [ a r:Fact; r:gives {((2 4 3 4) "=<") list:sort (2 3 4 4)}] - [ a r:Fact; r:gives {((2 4 3 4) ">=") list:sort (4 4 3 2)}] - skolem:lemma2629 - skolem:lemma2630 - [ a r:Fact; r:gives {(4432 2344) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1435}] + [ a r:Fact; r:gives {(1435 2000) math:sum 3435}] + skolem:lemma3433 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2434]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2344]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1435]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3435]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1435 a r:Inference; r:gives { - 2435 :kaprekar (0 3). + 3436 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2435 math:notEqualTo 0}] - skolem:lemma2761 - [ a r:Fact; r:gives {((2 4 3 5) "=<") list:sort (2 3 4 5)}] - [ a r:Fact; r:gives {((2 4 3 5) ">=") list:sort (5 4 3 2)}] - skolem:lemma2632 - skolem:lemma2633 - [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1436}] + [ a r:Fact; r:gives {(1436 2000) math:sum 3436}] + skolem:lemma3434 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2435]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2345]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1436]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3436]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1436 a r:Inference; r:gives { - 2436 :kaprekar (0 7). + 3437 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2436 math:notEqualTo 0}] - skolem:lemma2762 - [ a r:Fact; r:gives {((2 4 3 6) "=<") list:sort (2 3 4 6)}] - [ a r:Fact; r:gives {((2 4 3 6) ">=") list:sort (6 4 3 2)}] - skolem:lemma2635 - skolem:lemma2636 - [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1437}] + [ a r:Fact; r:gives {(1437 2000) math:sum 3437}] + skolem:lemma3435 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2436]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2346]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1437]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3437]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1437 a r:Inference; r:gives { - 2437 :kaprekar (0 7). + 3438 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2437 math:notEqualTo 0}] - skolem:lemma2763 - [ a r:Fact; r:gives {((2 4 3 7) "=<") list:sort (2 3 4 7)}] - [ a r:Fact; r:gives {((2 4 3 7) ">=") list:sort (7 4 3 2)}] - skolem:lemma2638 - skolem:lemma2639 - [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1438}] + [ a r:Fact; r:gives {(1438 2000) math:sum 3438}] + skolem:lemma3436 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2437]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2347]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1438]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3438]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1438 a r:Inference; r:gives { - 2438 :kaprekar (0 7). + 3439 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2438 math:notEqualTo 0}] - skolem:lemma2764 - [ a r:Fact; r:gives {((2 4 3 8) "=<") list:sort (2 3 4 8)}] - [ a r:Fact; r:gives {((2 4 3 8) ">=") list:sort (8 4 3 2)}] - skolem:lemma2641 - skolem:lemma2642 - [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1439}] + [ a r:Fact; r:gives {(1439 2000) math:sum 3439}] + skolem:lemma3437 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2438]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2348]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1439]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3439]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1439 a r:Inference; r:gives { - 2439 :kaprekar (0 3). + 3440 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2439 math:notEqualTo 0}] - skolem:lemma2765 - [ a r:Fact; r:gives {((2 4 3 9) "=<") list:sort (2 3 4 9)}] - [ a r:Fact; r:gives {((2 4 3 9) ">=") list:sort (9 4 3 2)}] - skolem:lemma2644 - skolem:lemma2645 - [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1440}] + [ a r:Fact; r:gives {(1440 2000) math:sum 3440}] + skolem:lemma3438 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2439]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2349]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1440]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3440]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1440 a r:Inference; r:gives { - 2440 :kaprekar (0 2). + 3441 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2440 math:notEqualTo 0}] - skolem:lemma2766 - [ a r:Fact; r:gives {((2 4 4 0) "=<") list:sort (0 2 4 4)}] - [ a r:Fact; r:gives {((2 4 4 0) ">=") list:sort (4 4 2 0)}] - skolem:lemma2114 - skolem:lemma2115 - [ a r:Fact; r:gives {(4420 244) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1441}] + [ a r:Fact; r:gives {(1441 2000) math:sum 3441}] + skolem:lemma3439 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2440]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 244]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1441]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3441]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1441 a r:Inference; r:gives { - 2441 :kaprekar (0 5). + 3442 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2441 math:notEqualTo 0}] - skolem:lemma2767 - [ a r:Fact; r:gives {((2 4 4 1) "=<") list:sort (1 2 4 4)}] - [ a r:Fact; r:gives {((2 4 4 1) ">=") list:sort (4 4 2 1)}] - skolem:lemma2304 - skolem:lemma2305 - [ a r:Fact; r:gives {(4421 1244) math:difference 3177}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3177 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 3177 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1442}] + [ a r:Fact; r:gives {(1442 2000) math:sum 3442}] + skolem:lemma3440 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2441]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1244]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1442 a r:Inference; r:gives { - 2442 :kaprekar (0 6). + 3443 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2442 math:notEqualTo 0}] - skolem:lemma2768 - [ a r:Fact; r:gives {((2 4 4 2) "=<") list:sort (2 2 4 4)}] - [ a r:Fact; r:gives {((2 4 4 2) ">=") list:sort (4 4 2 2)}] - skolem:lemma2473 - skolem:lemma2474 - [ a r:Fact; r:gives {(4422 2244) math:difference 2178}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2178 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2178 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1443}] + [ a r:Fact; r:gives {(1443 2000) math:sum 3443}] + skolem:lemma3441 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2244]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2178]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1443 a r:Inference; r:gives { - 2443 :kaprekar (0 3). + 3444 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2443 math:notEqualTo 0}] - skolem:lemma2769 - [ a r:Fact; r:gives {((2 4 4 3) "=<") list:sort (2 3 4 4)}] - [ a r:Fact; r:gives {((2 4 4 3) ">=") list:sort (4 4 3 2)}] - skolem:lemma2629 - skolem:lemma2630 - [ a r:Fact; r:gives {(4432 2344) math:difference 2088}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2088 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 2088 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1444}] + [ a r:Fact; r:gives {(1444 2000) math:sum 3444}] + skolem:lemma3442 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2344]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1444 a r:Inference; r:gives { - 2444 :kaprekar (0 4). + 3445 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2444 math:notEqualTo 0}] - skolem:lemma2770 - [ a r:Fact; r:gives {((2 4 4 4) "=<") list:sort (2 4 4 4)}] - [ a r:Fact; r:gives {((2 4 4 4) ">=") list:sort (4 4 4 2)}] - skolem:lemma2771 - skolem:lemma2772 - [ a r:Fact; r:gives {(4442 2444) math:difference 1998}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 1998 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 1998 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1445}] + [ a r:Fact; r:gives {(1445 2000) math:sum 3445}] + skolem:lemma3443 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1445]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3445]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1445 a r:Inference; r:gives { - 2445 :kaprekar (0 6). + 3446 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2445 math:notEqualTo 0}] - skolem:lemma2773 - [ a r:Fact; r:gives {((2 4 4 5) "=<") list:sort (2 4 4 5)}] - [ a r:Fact; r:gives {((2 4 4 5) ">=") list:sort (5 4 4 2)}] - skolem:lemma2774 - skolem:lemma2775 - [ a r:Fact; r:gives {(5442 2445) math:difference 2997}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2997 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2997 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1446}] + [ a r:Fact; r:gives {(1446 2000) math:sum 3446}] + skolem:lemma3444 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2445]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2445]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1446]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3446]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1446 a r:Inference; r:gives { - 2446 :kaprekar (0 4). + 3447 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2446 math:notEqualTo 0}] - skolem:lemma2776 - [ a r:Fact; r:gives {((2 4 4 6) "=<") list:sort (2 4 4 6)}] - [ a r:Fact; r:gives {((2 4 4 6) ">=") list:sort (6 4 4 2)}] - skolem:lemma2777 - skolem:lemma2778 - [ a r:Fact; r:gives {(6442 2446) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1447}] + [ a r:Fact; r:gives {(1447 2000) math:sum 3447}] + skolem:lemma3445 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2446]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2446]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1447]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3447]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1447 a r:Inference; r:gives { - 2447 :kaprekar (0 6). + 3448 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2447 math:notEqualTo 0}] - skolem:lemma2779 - [ a r:Fact; r:gives {((2 4 4 7) "=<") list:sort (2 4 4 7)}] - [ a r:Fact; r:gives {((2 4 4 7) ">=") list:sort (7 4 4 2)}] - skolem:lemma2780 - skolem:lemma2781 - [ a r:Fact; r:gives {(7442 2447) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1448}] + [ a r:Fact; r:gives {(1448 2000) math:sum 3448}] + skolem:lemma3446 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2447]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2447]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1448]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3448]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1448 a r:Inference; r:gives { - 2448 :kaprekar (0 6). + 3449 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2448 math:notEqualTo 0}] - skolem:lemma2782 - [ a r:Fact; r:gives {((2 4 4 8) "=<") list:sort (2 4 4 8)}] - [ a r:Fact; r:gives {((2 4 4 8) ">=") list:sort (8 4 4 2)}] - skolem:lemma2783 - skolem:lemma2784 - [ a r:Fact; r:gives {(8442 2448) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1449}] + [ a r:Fact; r:gives {(1449 2000) math:sum 3449}] + skolem:lemma3447 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2448]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2448]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1449]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3449]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1449 a r:Inference; r:gives { - 2449 :kaprekar (0 4). + 3450 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2449 math:notEqualTo 0}] - skolem:lemma2785 - [ a r:Fact; r:gives {((2 4 4 9) "=<") list:sort (2 4 4 9)}] - [ a r:Fact; r:gives {((2 4 4 9) ">=") list:sort (9 4 4 2)}] - skolem:lemma2786 - skolem:lemma2787 - [ a r:Fact; r:gives {(9442 2449) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1450}] + [ a r:Fact; r:gives {(1450 2000) math:sum 3450}] + skolem:lemma3448 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2449]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2449]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1450]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3450]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1450 a r:Inference; r:gives { - 2450 :kaprekar (0 7). + 3451 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2450 math:notEqualTo 0}] - skolem:lemma2788 - [ a r:Fact; r:gives {((2 4 5 0) "=<") list:sort (0 2 4 5)}] - [ a r:Fact; r:gives {((2 4 5 0) ">=") list:sort (5 4 2 0)}] - skolem:lemma2117 - skolem:lemma2118 - [ a r:Fact; r:gives {(5420 245) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1451}] + [ a r:Fact; r:gives {(1451 2000) math:sum 3451}] + skolem:lemma3449 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2450]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 245]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1451]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3451]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1451 a r:Inference; r:gives { - 2451 :kaprekar (0 2). + 3452 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2451 math:notEqualTo 0}] - skolem:lemma2789 - [ a r:Fact; r:gives {((2 4 5 1) "=<") list:sort (1 2 4 5)}] - [ a r:Fact; r:gives {((2 4 5 1) ">=") list:sort (5 4 2 1)}] - skolem:lemma2307 - skolem:lemma2308 - [ a r:Fact; r:gives {(5421 1245) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1452}] + [ a r:Fact; r:gives {(1452 2000) math:sum 3452}] + skolem:lemma3450 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2451]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1245]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1452]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3452]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1452 a r:Inference; r:gives { - 2452 :kaprekar (0 5). + 3453 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2452 math:notEqualTo 0}] - skolem:lemma2790 - [ a r:Fact; r:gives {((2 4 5 2) "=<") list:sort (2 2 4 5)}] - [ a r:Fact; r:gives {((2 4 5 2) ">=") list:sort (5 4 2 2)}] - skolem:lemma2476 - skolem:lemma2477 - [ a r:Fact; r:gives {(5422 2245) math:difference 3177}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3177 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 3177 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1453}] + [ a r:Fact; r:gives {(1453 2000) math:sum 3453}] + skolem:lemma3451 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2452]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2245]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1453]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3453]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1453 a r:Inference; r:gives { - 2453 :kaprekar (0 3). + 3454 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2453 math:notEqualTo 0}] - skolem:lemma2791 - [ a r:Fact; r:gives {((2 4 5 3) "=<") list:sort (2 3 4 5)}] - [ a r:Fact; r:gives {((2 4 5 3) ">=") list:sort (5 4 3 2)}] - skolem:lemma2632 - skolem:lemma2633 - [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1454}] + [ a r:Fact; r:gives {(1454 2000) math:sum 3454}] + skolem:lemma3452 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2453]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2345]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1454]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3454]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1454 a r:Inference; r:gives { - 2454 :kaprekar (0 6). + 3455 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2454 math:notEqualTo 0}] - skolem:lemma2792 - [ a r:Fact; r:gives {((2 4 5 4) "=<") list:sort (2 4 4 5)}] - [ a r:Fact; r:gives {((2 4 5 4) ">=") list:sort (5 4 4 2)}] - skolem:lemma2774 - skolem:lemma2775 - [ a r:Fact; r:gives {(5442 2445) math:difference 2997}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2997 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2997 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1455}] + [ a r:Fact; r:gives {(1455 2000) math:sum 3455}] + skolem:lemma3453 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2454]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2445]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1455]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3455]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1455 a r:Inference; r:gives { - 2455 :kaprekar (0 3). + 3456 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2455 math:notEqualTo 0}] - skolem:lemma2793 - [ a r:Fact; r:gives {((2 4 5 5) "=<") list:sort (2 4 5 5)}] - [ a r:Fact; r:gives {((2 4 5 5) ">=") list:sort (5 5 4 2)}] - skolem:lemma2794 - skolem:lemma2795 - [ a r:Fact; r:gives {(5542 2455) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1456}] + [ a r:Fact; r:gives {(1456 2000) math:sum 3456}] + skolem:lemma3454 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2455]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2455]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1456 a r:Inference; r:gives { - 2456 :kaprekar (0 7). + 3457 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2456 math:notEqualTo 0}] - skolem:lemma2796 - [ a r:Fact; r:gives {((2 4 5 6) "=<") list:sort (2 4 5 6)}] - [ a r:Fact; r:gives {((2 4 5 6) ">=") list:sort (6 5 4 2)}] - skolem:lemma2797 - skolem:lemma2798 - [ a r:Fact; r:gives {(6542 2456) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1457}] + [ a r:Fact; r:gives {(1457 2000) math:sum 3457}] + skolem:lemma3455 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2456]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2456]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1457]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3457]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1457 a r:Inference; r:gives { - 2457 :kaprekar (0 7). + 3458 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2457 math:notEqualTo 0}] - skolem:lemma2799 - [ a r:Fact; r:gives {((2 4 5 7) "=<") list:sort (2 4 5 7)}] - [ a r:Fact; r:gives {((2 4 5 7) ">=") list:sort (7 5 4 2)}] - skolem:lemma2800 - skolem:lemma2801 - [ a r:Fact; r:gives {(7542 2457) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1458}] + [ a r:Fact; r:gives {(1458 2000) math:sum 3458}] + skolem:lemma3456 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2457]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2457]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1458]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3458]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1458 a r:Inference; r:gives { - 2458 :kaprekar (0 7). + 3459 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2458 math:notEqualTo 0}] - skolem:lemma2802 - [ a r:Fact; r:gives {((2 4 5 8) "=<") list:sort (2 4 5 8)}] - [ a r:Fact; r:gives {((2 4 5 8) ">=") list:sort (8 5 4 2)}] - skolem:lemma2803 - skolem:lemma2804 - [ a r:Fact; r:gives {(8542 2458) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1459}] + [ a r:Fact; r:gives {(1459 2000) math:sum 3459}] + skolem:lemma3457 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2458]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2458]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1459]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3459]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1459 a r:Inference; r:gives { - 2459 :kaprekar (0 3). + 3460 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2459 math:notEqualTo 0}] - skolem:lemma2805 - [ a r:Fact; r:gives {((2 4 5 9) "=<") list:sort (2 4 5 9)}] - [ a r:Fact; r:gives {((2 4 5 9) ">=") list:sort (9 5 4 2)}] - skolem:lemma2806 - skolem:lemma2807 - [ a r:Fact; r:gives {(9542 2459) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1460}] + [ a r:Fact; r:gives {(1460 2000) math:sum 3460}] + skolem:lemma3458 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2459]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2459]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1460]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3460]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1460 a r:Inference; r:gives { - 2460 :kaprekar (0 1). + 3461 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2460 math:notEqualTo 0}] - skolem:lemma2808 - [ a r:Fact; r:gives {((2 4 6 0) "=<") list:sort (0 2 4 6)}] - [ a r:Fact; r:gives {((2 4 6 0) ">=") list:sort (6 4 2 0)}] - skolem:lemma2120 - skolem:lemma2121 - [ a r:Fact; r:gives {(6420 246) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1461}] + [ a r:Fact; r:gives {(1461 2000) math:sum 3461}] + skolem:lemma3459 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2460]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 246]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1461]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3461]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1461 a r:Inference; r:gives { - 2461 :kaprekar (0 7). + 3462 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2461 math:notEqualTo 0}] - skolem:lemma2809 - [ a r:Fact; r:gives {((2 4 6 1) "=<") list:sort (1 2 4 6)}] - [ a r:Fact; r:gives {((2 4 6 1) ">=") list:sort (6 4 2 1)}] - skolem:lemma2310 - skolem:lemma2311 - [ a r:Fact; r:gives {(6421 1246) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1462}] + [ a r:Fact; r:gives {(1462 2000) math:sum 3462}] + skolem:lemma3460 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2461]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1246]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1462]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3462]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1462 a r:Inference; r:gives { - 2462 :kaprekar (0 2). + 3463 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2462 math:notEqualTo 0}] - skolem:lemma2810 - [ a r:Fact; r:gives {((2 4 6 2) "=<") list:sort (2 2 4 6)}] - [ a r:Fact; r:gives {((2 4 6 2) ">=") list:sort (6 4 2 2)}] - skolem:lemma2479 - skolem:lemma2480 - [ a r:Fact; r:gives {(6422 2246) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1463}] + [ a r:Fact; r:gives {(1463 2000) math:sum 3463}] + skolem:lemma3461 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2462]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2246]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1463]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3463]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1463 a r:Inference; r:gives { - 2463 :kaprekar (0 7). + 3464 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2463 math:notEqualTo 0}] - skolem:lemma2811 - [ a r:Fact; r:gives {((2 4 6 3) "=<") list:sort (2 3 4 6)}] - [ a r:Fact; r:gives {((2 4 6 3) ">=") list:sort (6 4 3 2)}] - skolem:lemma2635 - skolem:lemma2636 - [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1464}] + [ a r:Fact; r:gives {(1464 2000) math:sum 3464}] + skolem:lemma3462 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2463]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2346]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1464]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3464]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1464 a r:Inference; r:gives { - 2464 :kaprekar (0 4). + 3465 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2464 math:notEqualTo 0}] - skolem:lemma2812 - [ a r:Fact; r:gives {((2 4 6 4) "=<") list:sort (2 4 4 6)}] - [ a r:Fact; r:gives {((2 4 6 4) ">=") list:sort (6 4 4 2)}] - skolem:lemma2777 - skolem:lemma2778 - [ a r:Fact; r:gives {(6442 2446) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1465}] + [ a r:Fact; r:gives {(1465 2000) math:sum 3465}] + skolem:lemma3463 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2464]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2446]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1465]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3465]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1465 a r:Inference; r:gives { - 2465 :kaprekar (0 7). + 3466 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2465 math:notEqualTo 0}] - skolem:lemma2813 - [ a r:Fact; r:gives {((2 4 6 5) "=<") list:sort (2 4 5 6)}] - [ a r:Fact; r:gives {((2 4 6 5) ">=") list:sort (6 5 4 2)}] - skolem:lemma2797 - skolem:lemma2798 - [ a r:Fact; r:gives {(6542 2456) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1466}] + [ a r:Fact; r:gives {(1466 2000) math:sum 3466}] + skolem:lemma3464 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2465]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2456]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1466]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3466]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1466 a r:Inference; r:gives { - 2466 :kaprekar (0 2). + 3467 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2466 math:notEqualTo 0}] - skolem:lemma2814 - [ a r:Fact; r:gives {((2 4 6 6) "=<") list:sort (2 4 6 6)}] - [ a r:Fact; r:gives {((2 4 6 6) ">=") list:sort (6 6 4 2)}] - skolem:lemma2815 - skolem:lemma2816 - [ a r:Fact; r:gives {(6642 2466) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1467}] + [ a r:Fact; r:gives {(1467 2000) math:sum 3467}] + skolem:lemma3465 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2466]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2466]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1467]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3467]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1467 a r:Inference; r:gives { - 2467 :kaprekar (0 7). + 3468 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2467 math:notEqualTo 0}] - skolem:lemma2817 - [ a r:Fact; r:gives {((2 4 6 7) "=<") list:sort (2 4 6 7)}] - [ a r:Fact; r:gives {((2 4 6 7) ">=") list:sort (7 6 4 2)}] - skolem:lemma2818 - skolem:lemma2819 - [ a r:Fact; r:gives {(7642 2467) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1468}] + [ a r:Fact; r:gives {(1468 2000) math:sum 3468}] + skolem:lemma3466 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2467]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2467]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1468]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3468]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1468 a r:Inference; r:gives { - 2468 :kaprekar (0 1). + 3469 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2468 math:notEqualTo 0}] - skolem:lemma2820 - [ a r:Fact; r:gives {((2 4 6 8) "=<") list:sort (2 4 6 8)}] - [ a r:Fact; r:gives {((2 4 6 8) ">=") list:sort (8 6 4 2)}] - skolem:lemma2821 - skolem:lemma2822 - [ a r:Fact; r:gives {(8642 2468) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1469}] + [ a r:Fact; r:gives {(1469 2000) math:sum 3469}] + skolem:lemma3467 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2468]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2468]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1469]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3469]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1469 a r:Inference; r:gives { - 2469 :kaprekar (0 5). + 3470 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2469 math:notEqualTo 0}] - skolem:lemma2823 - [ a r:Fact; r:gives {((2 4 6 9) "=<") list:sort (2 4 6 9)}] - [ a r:Fact; r:gives {((2 4 6 9) ">=") list:sort (9 6 4 2)}] - skolem:lemma2824 - skolem:lemma2825 - [ a r:Fact; r:gives {(9642 2469) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1470}] + [ a r:Fact; r:gives {(1470 2000) math:sum 3470}] + skolem:lemma3468 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2469]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2469]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1470]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3470]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1470 a r:Inference; r:gives { - 2470 :kaprekar (0 5). + 3471 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2470 math:notEqualTo 0}] - skolem:lemma2826 - [ a r:Fact; r:gives {((2 4 7 0) "=<") list:sort (0 2 4 7)}] - [ a r:Fact; r:gives {((2 4 7 0) ">=") list:sort (7 4 2 0)}] - skolem:lemma2123 - skolem:lemma2124 - [ a r:Fact; r:gives {(7420 247) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1471}] + [ a r:Fact; r:gives {(1471 2000) math:sum 3471}] + skolem:lemma3469 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2470]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 247]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1471]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3471]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1471 a r:Inference; r:gives { - 2471 :kaprekar (0 1). + 3472 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2471 math:notEqualTo 0}] - skolem:lemma2827 - [ a r:Fact; r:gives {((2 4 7 1) "=<") list:sort (1 2 4 7)}] - [ a r:Fact; r:gives {((2 4 7 1) ">=") list:sort (7 4 2 1)}] - skolem:lemma2313 - skolem:lemma2314 - [ a r:Fact; r:gives {(7421 1247) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1472}] + [ a r:Fact; r:gives {(1472 2000) math:sum 3472}] + skolem:lemma3470 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2471]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1247]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1472]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3472]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1472 a r:Inference; r:gives { - 2472 :kaprekar (0 7). + 3473 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2472 math:notEqualTo 0}] - skolem:lemma2828 - [ a r:Fact; r:gives {((2 4 7 2) "=<") list:sort (2 2 4 7)}] - [ a r:Fact; r:gives {((2 4 7 2) ">=") list:sort (7 4 2 2)}] - skolem:lemma2482 - skolem:lemma2483 - [ a r:Fact; r:gives {(7422 2247) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1473}] + [ a r:Fact; r:gives {(1473 2000) math:sum 3473}] + skolem:lemma3471 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2472]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2247]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1473]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3473]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1473 a r:Inference; r:gives { - 2473 :kaprekar (0 7). + 3474 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2473 math:notEqualTo 0}] - skolem:lemma2829 - [ a r:Fact; r:gives {((2 4 7 3) "=<") list:sort (2 3 4 7)}] - [ a r:Fact; r:gives {((2 4 7 3) ">=") list:sort (7 4 3 2)}] - skolem:lemma2638 - skolem:lemma2639 - [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1474}] + [ a r:Fact; r:gives {(1474 2000) math:sum 3474}] + skolem:lemma3472 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2473]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2347]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1474]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3474]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1474 a r:Inference; r:gives { - 2474 :kaprekar (0 6). + 3475 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2474 math:notEqualTo 0}] - skolem:lemma2830 - [ a r:Fact; r:gives {((2 4 7 4) "=<") list:sort (2 4 4 7)}] - [ a r:Fact; r:gives {((2 4 7 4) ">=") list:sort (7 4 4 2)}] - skolem:lemma2780 - skolem:lemma2781 - [ a r:Fact; r:gives {(7442 2447) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1475}] + [ a r:Fact; r:gives {(1475 2000) math:sum 3475}] + skolem:lemma3473 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2474]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2447]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1475]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3475]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1475 a r:Inference; r:gives { - 2475 :kaprekar (0 7). + 3476 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2475 math:notEqualTo 0}] - skolem:lemma2831 - [ a r:Fact; r:gives {((2 4 7 5) "=<") list:sort (2 4 5 7)}] - [ a r:Fact; r:gives {((2 4 7 5) ">=") list:sort (7 5 4 2)}] - skolem:lemma2800 - skolem:lemma2801 - [ a r:Fact; r:gives {(7542 2457) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1476}] + [ a r:Fact; r:gives {(1476 2000) math:sum 3476}] + skolem:lemma3474 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2475]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2457]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1476]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3476]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1476 a r:Inference; r:gives { - 2476 :kaprekar (0 7). + 3477 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2476 math:notEqualTo 0}] - skolem:lemma2832 - [ a r:Fact; r:gives {((2 4 7 6) "=<") list:sort (2 4 6 7)}] - [ a r:Fact; r:gives {((2 4 7 6) ">=") list:sort (7 6 4 2)}] - skolem:lemma2818 - skolem:lemma2819 - [ a r:Fact; r:gives {(7642 2467) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1477}] + [ a r:Fact; r:gives {(1477 2000) math:sum 3477}] + skolem:lemma3475 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2476]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2467]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1477]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3477]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1477 a r:Inference; r:gives { - 2477 :kaprekar (0 5). + 3478 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2477 math:notEqualTo 0}] - skolem:lemma2833 - [ a r:Fact; r:gives {((2 4 7 7) "=<") list:sort (2 4 7 7)}] - [ a r:Fact; r:gives {((2 4 7 7) ">=") list:sort (7 7 4 2)}] - skolem:lemma2834 - skolem:lemma2835 - [ a r:Fact; r:gives {(7742 2477) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1478}] + [ a r:Fact; r:gives {(1478 2000) math:sum 3478}] + skolem:lemma3476 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2477]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2477]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7742]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1478]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3478]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1478 a r:Inference; r:gives { - 2478 :kaprekar (0 3). + 3479 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2478 math:notEqualTo 0}] - skolem:lemma2836 - [ a r:Fact; r:gives {((2 4 7 8) "=<") list:sort (2 4 7 8)}] - [ a r:Fact; r:gives {((2 4 7 8) ">=") list:sort (8 7 4 2)}] - skolem:lemma2837 - skolem:lemma2838 - [ a r:Fact; r:gives {(8742 2478) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1479}] + [ a r:Fact; r:gives {(1479 2000) math:sum 3479}] + skolem:lemma3477 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2478]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2478]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8742]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1479]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3479]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1479 a r:Inference; r:gives { - 2479 :kaprekar (0 6). + 3480 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2479 math:notEqualTo 0}] - skolem:lemma2839 - [ a r:Fact; r:gives {((2 4 7 9) "=<") list:sort (2 4 7 9)}] - [ a r:Fact; r:gives {((2 4 7 9) ">=") list:sort (9 7 4 2)}] - skolem:lemma2840 - skolem:lemma2841 - [ a r:Fact; r:gives {(9742 2479) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1480}] + [ a r:Fact; r:gives {(1480 2000) math:sum 3480}] + skolem:lemma3478 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2479]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2479]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9742]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1480]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3480]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1480 a r:Inference; r:gives { - 2480 :kaprekar (0 6). + 3481 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2480 math:notEqualTo 0}] - skolem:lemma2842 - [ a r:Fact; r:gives {((2 4 8 0) "=<") list:sort (0 2 4 8)}] - [ a r:Fact; r:gives {((2 4 8 0) ">=") list:sort (8 4 2 0)}] - skolem:lemma2126 - skolem:lemma2127 - [ a r:Fact; r:gives {(8420 248) math:difference 8172}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8172 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 8172 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1481}] + [ a r:Fact; r:gives {(1481 2000) math:sum 3481}] + skolem:lemma3479 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2480]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 248]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1481]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3481]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1481 a r:Inference; r:gives { - 2481 :kaprekar (0 5). + 3482 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2481 math:notEqualTo 0}] - skolem:lemma2843 - [ a r:Fact; r:gives {((2 4 8 1) "=<") list:sort (1 2 4 8)}] - [ a r:Fact; r:gives {((2 4 8 1) ">=") list:sort (8 4 2 1)}] - skolem:lemma2316 - skolem:lemma2317 - [ a r:Fact; r:gives {(8421 1248) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1482}] + [ a r:Fact; r:gives {(1482 2000) math:sum 3482}] + skolem:lemma3480 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2481]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1248]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1482]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3482]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1482 a r:Inference; r:gives { - 2482 :kaprekar (0 1). + 3483 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2482 math:notEqualTo 0}] - skolem:lemma2844 - [ a r:Fact; r:gives {((2 4 8 2) "=<") list:sort (2 2 4 8)}] - [ a r:Fact; r:gives {((2 4 8 2) ">=") list:sort (8 4 2 2)}] - skolem:lemma2485 - skolem:lemma2486 - [ a r:Fact; r:gives {(8422 2248) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1483}] + [ a r:Fact; r:gives {(1483 2000) math:sum 3483}] + skolem:lemma3481 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2482]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2248]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1483]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3483]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1483 a r:Inference; r:gives { - 2483 :kaprekar (0 7). + 3484 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2483 math:notEqualTo 0}] - skolem:lemma2845 - [ a r:Fact; r:gives {((2 4 8 3) "=<") list:sort (2 3 4 8)}] - [ a r:Fact; r:gives {((2 4 8 3) ">=") list:sort (8 4 3 2)}] - skolem:lemma2641 - skolem:lemma2642 - [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1484}] + [ a r:Fact; r:gives {(1484 2000) math:sum 3484}] + skolem:lemma3482 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2483]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2348]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1484]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3484]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1484 a r:Inference; r:gives { - 2484 :kaprekar (0 6). + 3485 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2484 math:notEqualTo 0}] - skolem:lemma2846 - [ a r:Fact; r:gives {((2 4 8 4) "=<") list:sort (2 4 4 8)}] - [ a r:Fact; r:gives {((2 4 8 4) ">=") list:sort (8 4 4 2)}] - skolem:lemma2783 - skolem:lemma2784 - [ a r:Fact; r:gives {(8442 2448) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1485}] + [ a r:Fact; r:gives {(1485 2000) math:sum 3485}] + skolem:lemma3483 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2484]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2448]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1485]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3485]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1485 a r:Inference; r:gives { - 2485 :kaprekar (0 7). + 3486 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2485 math:notEqualTo 0}] - skolem:lemma2847 - [ a r:Fact; r:gives {((2 4 8 5) "=<") list:sort (2 4 5 8)}] - [ a r:Fact; r:gives {((2 4 8 5) ">=") list:sort (8 5 4 2)}] - skolem:lemma2803 - skolem:lemma2804 - [ a r:Fact; r:gives {(8542 2458) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1486}] + [ a r:Fact; r:gives {(1486 2000) math:sum 3486}] + skolem:lemma3484 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2485]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2458]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1486]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3486]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1486 a r:Inference; r:gives { - 2486 :kaprekar (0 1). + 3487 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2486 math:notEqualTo 0}] - skolem:lemma2848 - [ a r:Fact; r:gives {((2 4 8 6) "=<") list:sort (2 4 6 8)}] - [ a r:Fact; r:gives {((2 4 8 6) ">=") list:sort (8 6 4 2)}] - skolem:lemma2821 - skolem:lemma2822 - [ a r:Fact; r:gives {(8642 2468) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1487}] + [ a r:Fact; r:gives {(1487 2000) math:sum 3487}] + skolem:lemma3485 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2486]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2468]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1487]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3487]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1487 a r:Inference; r:gives { - 2487 :kaprekar (0 3). + 3488 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2487 math:notEqualTo 0}] - skolem:lemma2849 - [ a r:Fact; r:gives {((2 4 8 7) "=<") list:sort (2 4 7 8)}] - [ a r:Fact; r:gives {((2 4 8 7) ">=") list:sort (8 7 4 2)}] - skolem:lemma2837 - skolem:lemma2838 - [ a r:Fact; r:gives {(8742 2478) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1488}] + [ a r:Fact; r:gives {(1488 2000) math:sum 3488}] + skolem:lemma3486 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2487]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2478]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8742]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1488]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3488]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1488 a r:Inference; r:gives { - 2488 :kaprekar (0 4). + 3489 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2488 math:notEqualTo 0}] - skolem:lemma2850 - [ a r:Fact; r:gives {((2 4 8 8) "=<") list:sort (2 4 8 8)}] - [ a r:Fact; r:gives {((2 4 8 8) ">=") list:sort (8 8 4 2)}] - skolem:lemma2851 - skolem:lemma2852 - [ a r:Fact; r:gives {(8842 2488) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1489}] + [ a r:Fact; r:gives {(1489 2000) math:sum 3489}] + skolem:lemma3487 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2488]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2488]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8842]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1489]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3489]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1489 a r:Inference; r:gives { - 2489 :kaprekar (0 3). + 3490 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2489 math:notEqualTo 0}] - skolem:lemma2853 - [ a r:Fact; r:gives {((2 4 8 9) "=<") list:sort (2 4 8 9)}] - [ a r:Fact; r:gives {((2 4 8 9) ">=") list:sort (9 8 4 2)}] - skolem:lemma2854 - skolem:lemma2855 - [ a r:Fact; r:gives {(9842 2489) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1490}] + [ a r:Fact; r:gives {(1490 2000) math:sum 3490}] + skolem:lemma3488 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2489]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2489]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9842]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1490]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3490]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1490 a r:Inference; r:gives { - 2490 :kaprekar (0 3). + 3491 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2490 math:notEqualTo 0}] - skolem:lemma2856 - [ a r:Fact; r:gives {((2 4 9 0) "=<") list:sort (0 2 4 9)}] - [ a r:Fact; r:gives {((2 4 9 0) ">=") list:sort (9 4 2 0)}] - skolem:lemma2129 - skolem:lemma2130 - [ a r:Fact; r:gives {(9420 249) math:difference 9171}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9171 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 9171 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1491}] + [ a r:Fact; r:gives {(1491 2000) math:sum 3491}] + skolem:lemma3489 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2490]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 249]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1491]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3491]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1491 a r:Inference; r:gives { - 2491 :kaprekar (0 6). + 3492 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2491 math:notEqualTo 0}] - skolem:lemma2857 - [ a r:Fact; r:gives {((2 4 9 1) "=<") list:sort (1 2 4 9)}] - [ a r:Fact; r:gives {((2 4 9 1) ">=") list:sort (9 4 2 1)}] - skolem:lemma2319 - skolem:lemma2320 - [ a r:Fact; r:gives {(9421 1249) math:difference 8172}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8172 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 8172 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1492}] + [ a r:Fact; r:gives {(1492 2000) math:sum 3492}] + skolem:lemma3490 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2491]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1249]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1492]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3492]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1492 a r:Inference; r:gives { - 2492 :kaprekar (0 5). + 3493 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2492 math:notEqualTo 0}] - skolem:lemma2858 - [ a r:Fact; r:gives {((2 4 9 2) "=<") list:sort (2 2 4 9)}] - [ a r:Fact; r:gives {((2 4 9 2) ">=") list:sort (9 4 2 2)}] - skolem:lemma2488 - skolem:lemma2489 - [ a r:Fact; r:gives {(9422 2249) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1493}] + [ a r:Fact; r:gives {(1493 2000) math:sum 3493}] + skolem:lemma3491 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2492]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2249]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1493]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3493]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1493 a r:Inference; r:gives { - 2493 :kaprekar (0 3). + 3494 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2493 math:notEqualTo 0}] - skolem:lemma2859 - [ a r:Fact; r:gives {((2 4 9 3) "=<") list:sort (2 3 4 9)}] - [ a r:Fact; r:gives {((2 4 9 3) ">=") list:sort (9 4 3 2)}] - skolem:lemma2644 - skolem:lemma2645 - [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1494}] + [ a r:Fact; r:gives {(1494 2000) math:sum 3494}] + skolem:lemma3492 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2493]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2349]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1494]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3494]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1494 a r:Inference; r:gives { - 2494 :kaprekar (0 4). + 3495 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2494 math:notEqualTo 0}] - skolem:lemma2860 - [ a r:Fact; r:gives {((2 4 9 4) "=<") list:sort (2 4 4 9)}] - [ a r:Fact; r:gives {((2 4 9 4) ">=") list:sort (9 4 4 2)}] - skolem:lemma2786 - skolem:lemma2787 - [ a r:Fact; r:gives {(9442 2449) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1495}] + [ a r:Fact; r:gives {(1495 2000) math:sum 3495}] + skolem:lemma3493 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2494]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2449]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1495]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3495]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1495 a r:Inference; r:gives { - 2495 :kaprekar (0 3). + 3496 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2495 math:notEqualTo 0}] - skolem:lemma2861 - [ a r:Fact; r:gives {((2 4 9 5) "=<") list:sort (2 4 5 9)}] - [ a r:Fact; r:gives {((2 4 9 5) ">=") list:sort (9 5 4 2)}] - skolem:lemma2806 - skolem:lemma2807 - [ a r:Fact; r:gives {(9542 2459) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1496}] + [ a r:Fact; r:gives {(1496 2000) math:sum 3496}] + skolem:lemma3494 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2495]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2459]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1496]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3496]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1496 a r:Inference; r:gives { - 2496 :kaprekar (0 5). + 3497 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2496 math:notEqualTo 0}] - skolem:lemma2862 - [ a r:Fact; r:gives {((2 4 9 6) "=<") list:sort (2 4 6 9)}] - [ a r:Fact; r:gives {((2 4 9 6) ">=") list:sort (9 6 4 2)}] - skolem:lemma2824 - skolem:lemma2825 - [ a r:Fact; r:gives {(9642 2469) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1497}] + [ a r:Fact; r:gives {(1497 2000) math:sum 3497}] + skolem:lemma3495 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2496]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2469]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1497]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3497]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1497 a r:Inference; r:gives { - 2497 :kaprekar (0 6). + 3498 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2497 math:notEqualTo 0}] - skolem:lemma2863 - [ a r:Fact; r:gives {((2 4 9 7) "=<") list:sort (2 4 7 9)}] - [ a r:Fact; r:gives {((2 4 9 7) ">=") list:sort (9 7 4 2)}] - skolem:lemma2840 - skolem:lemma2841 - [ a r:Fact; r:gives {(9742 2479) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1498}] + [ a r:Fact; r:gives {(1498 2000) math:sum 3498}] + skolem:lemma3496 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2497]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2479]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9742]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1498]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3498]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1498 a r:Inference; r:gives { - 2498 :kaprekar (0 3). + 3499 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2498 math:notEqualTo 0}] - skolem:lemma2864 - [ a r:Fact; r:gives {((2 4 9 8) "=<") list:sort (2 4 8 9)}] - [ a r:Fact; r:gives {((2 4 9 8) ">=") list:sort (9 8 4 2)}] - skolem:lemma2854 - skolem:lemma2855 - [ a r:Fact; r:gives {(9842 2489) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1499}] + [ a r:Fact; r:gives {(1499 2000) math:sum 3499}] + skolem:lemma3497 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2498]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2489]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9842]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1499]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3499]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1499 a r:Inference; r:gives { - 2499 :kaprekar (0 5). + 3500 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2499 math:notEqualTo 0}] - skolem:lemma2865 - [ a r:Fact; r:gives {((2 4 9 9) "=<") list:sort (2 4 9 9)}] - [ a r:Fact; r:gives {((2 4 9 9) ">=") list:sort (9 9 4 2)}] - skolem:lemma2866 - skolem:lemma2867 - [ a r:Fact; r:gives {(9942 2499) math:difference 7443}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7443 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1500}] + [ a r:Fact; r:gives {(1500 2000) math:sum 3500}] + skolem:lemma3498 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2499]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2499]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9942]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1500 a r:Inference; r:gives { - 2500 :kaprekar (0 7). + 3501 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2500 math:notEqualTo 0}] - skolem:lemma2868 - [ a r:Fact; r:gives {((2 5 0 0) "=<") list:sort (0 0 2 5)}] - [ a r:Fact; r:gives {((2 5 0 0) ">=") list:sort (5 2 0 0)}] - skolem:lemma2017 - skolem:lemma2018 - [ a r:Fact; r:gives {(5200 25) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1501}] + [ a r:Fact; r:gives {(1501 2000) math:sum 3501}] + skolem:lemma3499 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2500]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1501]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3501]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1501 a r:Inference; r:gives { - 2501 :kaprekar (0 7). + 3502 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2501 math:notEqualTo 0}] - skolem:lemma2869 - [ a r:Fact; r:gives {((2 5 0 1) "=<") list:sort (0 1 2 5)}] - [ a r:Fact; r:gives {((2 5 0 1) ">=") list:sort (5 2 1 0)}] - skolem:lemma2045 - skolem:lemma2046 - [ a r:Fact; r:gives {(5210 125) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1502}] + [ a r:Fact; r:gives {(1502 2000) math:sum 3502}] + skolem:lemma3500 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2501]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 125]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1502]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3502]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1502 a r:Inference; r:gives { - 2502 :kaprekar (0 6). + 3503 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2502 math:notEqualTo 0}] - skolem:lemma2870 - [ a r:Fact; r:gives {((2 5 0 2) "=<") list:sort (0 2 2 5)}] - [ a r:Fact; r:gives {((2 5 0 2) ">=") list:sort (5 2 2 0)}] - skolem:lemma2071 - skolem:lemma2072 - [ a r:Fact; r:gives {(5220 225) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1503}] + [ a r:Fact; r:gives {(1503 2000) math:sum 3503}] + skolem:lemma3501 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2502]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 225]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1503]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3503]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1503 a r:Inference; r:gives { - 2503 :kaprekar (0 7). + 3504 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2503 math:notEqualTo 0}] - skolem:lemma2871 - [ a r:Fact; r:gives {((2 5 0 3) "=<") list:sort (0 2 3 5)}] - [ a r:Fact; r:gives {((2 5 0 3) ">=") list:sort (5 3 2 0)}] - skolem:lemma2095 - skolem:lemma2096 - [ a r:Fact; r:gives {(5320 235) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1504}] + [ a r:Fact; r:gives {(1504 2000) math:sum 3504}] + skolem:lemma3502 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2503]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 235]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1504]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3504]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1504 a r:Inference; r:gives { - 2504 :kaprekar (0 7). + 3505 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2504 math:notEqualTo 0}] - skolem:lemma2872 - [ a r:Fact; r:gives {((2 5 0 4) "=<") list:sort (0 2 4 5)}] - [ a r:Fact; r:gives {((2 5 0 4) ">=") list:sort (5 4 2 0)}] - skolem:lemma2117 - skolem:lemma2118 - [ a r:Fact; r:gives {(5420 245) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1505}] + [ a r:Fact; r:gives {(1505 2000) math:sum 3505}] + skolem:lemma3503 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2504]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 245]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1505]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3505]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1505 a r:Inference; r:gives { - 2505 :kaprekar (0 5). + 3506 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2505 math:notEqualTo 0}] - skolem:lemma2873 - [ a r:Fact; r:gives {((2 5 0 5) "=<") list:sort (0 2 5 5)}] - [ a r:Fact; r:gives {((2 5 0 5) ">=") list:sort (5 5 2 0)}] - skolem:lemma2137 - skolem:lemma2138 - [ a r:Fact; r:gives {(5520 255) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1506}] + [ a r:Fact; r:gives {(1506 2000) math:sum 3506}] + skolem:lemma3504 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2505]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 255]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1506]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3506]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1506 a r:Inference; r:gives { - 2506 :kaprekar (0 3). + 3507 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2506 math:notEqualTo 0}] - skolem:lemma2874 - [ a r:Fact; r:gives {((2 5 0 6) "=<") list:sort (0 2 5 6)}] - [ a r:Fact; r:gives {((2 5 0 6) ">=") list:sort (6 5 2 0)}] - skolem:lemma2140 - skolem:lemma2141 - [ a r:Fact; r:gives {(6520 256) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1507}] + [ a r:Fact; r:gives {(1507 2000) math:sum 3507}] + skolem:lemma3505 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2506]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 256]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1507]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3507]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1507 a r:Inference; r:gives { - 2507 :kaprekar (0 6). + 3508 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2507 math:notEqualTo 0}] - skolem:lemma2875 - [ a r:Fact; r:gives {((2 5 0 7) "=<") list:sort (0 2 5 7)}] - [ a r:Fact; r:gives {((2 5 0 7) ">=") list:sort (7 5 2 0)}] - skolem:lemma2143 - skolem:lemma2144 - [ a r:Fact; r:gives {(7520 257) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1508}] + [ a r:Fact; r:gives {(1508 2000) math:sum 3508}] + skolem:lemma3506 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2507]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 257]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1508]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3508]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1508 a r:Inference; r:gives { - 2508 :kaprekar (0 5). + 3509 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2508 math:notEqualTo 0}] - skolem:lemma2876 - [ a r:Fact; r:gives {((2 5 0 8) "=<") list:sort (0 2 5 8)}] - [ a r:Fact; r:gives {((2 5 0 8) ">=") list:sort (8 5 2 0)}] - skolem:lemma2146 - skolem:lemma2147 - [ a r:Fact; r:gives {(8520 258) math:difference 8262}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8262 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 8262 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1509}] + [ a r:Fact; r:gives {(1509 2000) math:sum 3509}] + skolem:lemma3507 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2508]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 258]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1509]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3509]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1509 a r:Inference; r:gives { - 2509 :kaprekar (0 3). + 3510 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2509 math:notEqualTo 0}] - skolem:lemma2877 - [ a r:Fact; r:gives {((2 5 0 9) "=<") list:sort (0 2 5 9)}] - [ a r:Fact; r:gives {((2 5 0 9) ">=") list:sort (9 5 2 0)}] - skolem:lemma2149 - skolem:lemma2150 - [ a r:Fact; r:gives {(9520 259) math:difference 9261}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9261 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 9261 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1510}] + [ a r:Fact; r:gives {(1510 2000) math:sum 3510}] + skolem:lemma3508 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2509]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 259]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9261]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1510]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3510]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1510 a r:Inference; r:gives { - 2510 :kaprekar (0 7). + 3511 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2510 math:notEqualTo 0}] - skolem:lemma2878 - [ a r:Fact; r:gives {((2 5 1 0) "=<") list:sort (0 1 2 5)}] - [ a r:Fact; r:gives {((2 5 1 0) ">=") list:sort (5 2 1 0)}] - skolem:lemma2045 - skolem:lemma2046 - [ a r:Fact; r:gives {(5210 125) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1511}] + [ a r:Fact; r:gives {(1511 2000) math:sum 3511}] + skolem:lemma3509 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2510]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 125]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1511]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3511]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1511 a r:Inference; r:gives { - 2511 :kaprekar (0 7). + 3512 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2511 math:notEqualTo 0}] - skolem:lemma2879 - [ a r:Fact; r:gives {((2 5 1 1) "=<") list:sort (1 1 2 5)}] - [ a r:Fact; r:gives {((2 5 1 1) ">=") list:sort (5 2 1 1)}] - skolem:lemma2235 - skolem:lemma2236 - [ a r:Fact; r:gives {(5211 1125) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1512}] + [ a r:Fact; r:gives {(1512 2000) math:sum 3512}] + skolem:lemma3510 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2511]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1125]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1512]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3512]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1512 a r:Inference; r:gives { - 2512 :kaprekar (0 4). + 3513 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2512 math:notEqualTo 0}] - skolem:lemma2880 - [ a r:Fact; r:gives {((2 5 1 2) "=<") list:sort (1 2 2 5)}] - [ a r:Fact; r:gives {((2 5 1 2) ">=") list:sort (5 2 2 1)}] - skolem:lemma2261 - skolem:lemma2262 - [ a r:Fact; r:gives {(5221 1225) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1513}] + [ a r:Fact; r:gives {(1513 2000) math:sum 3513}] + skolem:lemma3511 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2512]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1225]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1513]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3513]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1513 a r:Inference; r:gives { - 2513 :kaprekar (0 7). + 3514 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2513 math:notEqualTo 0}] - skolem:lemma2881 - [ a r:Fact; r:gives {((2 5 1 3) "=<") list:sort (1 2 3 5)}] - [ a r:Fact; r:gives {((2 5 1 3) ">=") list:sort (5 3 2 1)}] - skolem:lemma2285 - skolem:lemma2286 - [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1514}] + [ a r:Fact; r:gives {(1514 2000) math:sum 3514}] + skolem:lemma3512 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2513]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1235]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1514]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3514]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1514 a r:Inference; r:gives { - 2514 :kaprekar (0 2). + 3515 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2514 math:notEqualTo 0}] - skolem:lemma2882 - [ a r:Fact; r:gives {((2 5 1 4) "=<") list:sort (1 2 4 5)}] - [ a r:Fact; r:gives {((2 5 1 4) ">=") list:sort (5 4 2 1)}] - skolem:lemma2307 - skolem:lemma2308 - [ a r:Fact; r:gives {(5421 1245) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1515}] + [ a r:Fact; r:gives {(1515 2000) math:sum 3515}] + skolem:lemma3513 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2514]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1245]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1515]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3515]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1515 a r:Inference; r:gives { - 2515 :kaprekar (0 3). + 3516 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2515 math:notEqualTo 0}] - skolem:lemma2883 - [ a r:Fact; r:gives {((2 5 1 5) "=<") list:sort (1 2 5 5)}] - [ a r:Fact; r:gives {((2 5 1 5) ">=") list:sort (5 5 2 1)}] - skolem:lemma2327 - skolem:lemma2328 - [ a r:Fact; r:gives {(5521 1255) math:difference 4266}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4266 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 4266 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1516}] + [ a r:Fact; r:gives {(1516 2000) math:sum 3516}] + skolem:lemma3514 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2515]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1255]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1516]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3516]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1516 a r:Inference; r:gives { - 2516 :kaprekar (0 5). + 3517 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2516 math:notEqualTo 0}] - skolem:lemma2884 - [ a r:Fact; r:gives {((2 5 1 6) "=<") list:sort (1 2 5 6)}] - [ a r:Fact; r:gives {((2 5 1 6) ">=") list:sort (6 5 2 1)}] - skolem:lemma2330 - skolem:lemma2331 - [ a r:Fact; r:gives {(6521 1256) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1517}] + [ a r:Fact; r:gives {(1517 2000) math:sum 3517}] + skolem:lemma3515 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2516]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1256]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1517]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3517]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1517 a r:Inference; r:gives { - 2517 :kaprekar (0 3). + 3518 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2517 math:notEqualTo 0}] - skolem:lemma2885 - [ a r:Fact; r:gives {((2 5 1 7) "=<") list:sort (1 2 5 7)}] - [ a r:Fact; r:gives {((2 5 1 7) ">=") list:sort (7 5 2 1)}] - skolem:lemma2333 - skolem:lemma2334 - [ a r:Fact; r:gives {(7521 1257) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1518}] + [ a r:Fact; r:gives {(1518 2000) math:sum 3518}] + skolem:lemma3516 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2517]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1257]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1518]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3518]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1518 a r:Inference; r:gives { - 2518 :kaprekar (0 6). + 3519 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2518 math:notEqualTo 0}] - skolem:lemma2886 - [ a r:Fact; r:gives {((2 5 1 8) "=<") list:sort (1 2 5 8)}] - [ a r:Fact; r:gives {((2 5 1 8) ">=") list:sort (8 5 2 1)}] - skolem:lemma2336 - skolem:lemma2337 - [ a r:Fact; r:gives {(8521 1258) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1519}] + [ a r:Fact; r:gives {(1519 2000) math:sum 3519}] + skolem:lemma3517 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2518]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1258]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1519]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3519]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1519 a r:Inference; r:gives { - 2519 :kaprekar (0 5). + 3520 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2519 math:notEqualTo 0}] - skolem:lemma2887 - [ a r:Fact; r:gives {((2 5 1 9) "=<") list:sort (1 2 5 9)}] - [ a r:Fact; r:gives {((2 5 1 9) ">=") list:sort (9 5 2 1)}] - skolem:lemma2339 - skolem:lemma2340 - [ a r:Fact; r:gives {(9521 1259) math:difference 8262}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8262 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 8262 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1520}] + [ a r:Fact; r:gives {(1520 2000) math:sum 3520}] + skolem:lemma3518 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2519]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1259]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1520 a r:Inference; r:gives { - 2520 :kaprekar (0 6). + 3521 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2520 math:notEqualTo 0}] - skolem:lemma2888 - [ a r:Fact; r:gives {((2 5 2 0) "=<") list:sort (0 2 2 5)}] - [ a r:Fact; r:gives {((2 5 2 0) ">=") list:sort (5 2 2 0)}] - skolem:lemma2071 - skolem:lemma2072 - [ a r:Fact; r:gives {(5220 225) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1521}] + [ a r:Fact; r:gives {(1521 2000) math:sum 3521}] + skolem:lemma3519 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 225]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1521 a r:Inference; r:gives { - 2521 :kaprekar (0 4). + 3522 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2521 math:notEqualTo 0}] - skolem:lemma2889 - [ a r:Fact; r:gives {((2 5 2 1) "=<") list:sort (1 2 2 5)}] - [ a r:Fact; r:gives {((2 5 2 1) ">=") list:sort (5 2 2 1)}] - skolem:lemma2261 - skolem:lemma2262 - [ a r:Fact; r:gives {(5221 1225) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1522}] + [ a r:Fact; r:gives {(1522 2000) math:sum 3522}] + skolem:lemma3520 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1225]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1522 a r:Inference; r:gives { - 2522 :kaprekar (0 6). + 3523 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2522 math:notEqualTo 0}] - skolem:lemma2890 - [ a r:Fact; r:gives {((2 5 2 2) "=<") list:sort (2 2 2 5)}] - [ a r:Fact; r:gives {((2 5 2 2) ">=") list:sort (5 2 2 2)}] - skolem:lemma2430 - skolem:lemma2431 - [ a r:Fact; r:gives {(5222 2225) math:difference 2997}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2997 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2997 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1523}] + [ a r:Fact; r:gives {(1523 2000) math:sum 3523}] + skolem:lemma3521 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2225]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1523]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3523]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1523 a r:Inference; r:gives { - 2523 :kaprekar (0 3). + 3524 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2523 math:notEqualTo 0}] - skolem:lemma2891 - [ a r:Fact; r:gives {((2 5 2 3) "=<") list:sort (2 2 3 5)}] - [ a r:Fact; r:gives {((2 5 2 3) ">=") list:sort (5 3 2 2)}] - skolem:lemma2454 - skolem:lemma2455 - [ a r:Fact; r:gives {(5322 2235) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1524}] + [ a r:Fact; r:gives {(1524 2000) math:sum 3524}] + skolem:lemma3522 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2523]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2235]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1524]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3524]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1524 a r:Inference; r:gives { - 2524 :kaprekar (0 5). + 3525 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2524 math:notEqualTo 0}] - skolem:lemma2892 - [ a r:Fact; r:gives {((2 5 2 4) "=<") list:sort (2 2 4 5)}] - [ a r:Fact; r:gives {((2 5 2 4) ">=") list:sort (5 4 2 2)}] - skolem:lemma2476 - skolem:lemma2477 - [ a r:Fact; r:gives {(5422 2245) math:difference 3177}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3177 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 3177 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1525}] + [ a r:Fact; r:gives {(1525 2000) math:sum 3525}] + skolem:lemma3523 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2524]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2245]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1525]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3525]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1525 a r:Inference; r:gives { - 2525 :kaprekar (0 6). + 3526 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2525 math:notEqualTo 0}] - skolem:lemma2893 - [ a r:Fact; r:gives {((2 5 2 5) "=<") list:sort (2 2 5 5)}] - [ a r:Fact; r:gives {((2 5 2 5) ">=") list:sort (5 5 2 2)}] - skolem:lemma2496 - skolem:lemma2497 - [ a r:Fact; r:gives {(5522 2255) math:difference 3267}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3267 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 3267 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1526}] + [ a r:Fact; r:gives {(1526 2000) math:sum 3526}] + skolem:lemma3524 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2525]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2255]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1526]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3526]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1526 a r:Inference; r:gives { - 2526 :kaprekar (0 3). + 3527 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2526 math:notEqualTo 0}] - skolem:lemma2894 - [ a r:Fact; r:gives {((2 5 2 6) "=<") list:sort (2 2 5 6)}] - [ a r:Fact; r:gives {((2 5 2 6) ">=") list:sort (6 5 2 2)}] - skolem:lemma2499 - skolem:lemma2500 - [ a r:Fact; r:gives {(6522 2256) math:difference 4266}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4266 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 4266 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1527}] + [ a r:Fact; r:gives {(1527 2000) math:sum 3527}] + skolem:lemma3525 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2526]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2256]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1527]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3527]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1527 a r:Inference; r:gives { - 2527 :kaprekar (0 5). + 3528 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2527 math:notEqualTo 0}] - skolem:lemma2895 - [ a r:Fact; r:gives {((2 5 2 7) "=<") list:sort (2 2 5 7)}] - [ a r:Fact; r:gives {((2 5 2 7) ">=") list:sort (7 5 2 2)}] - skolem:lemma2502 - skolem:lemma2503 - [ a r:Fact; r:gives {(7522 2257) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1528}] + [ a r:Fact; r:gives {(1528 2000) math:sum 3528}] + skolem:lemma3526 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2527]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2257]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1528]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3528]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1528 a r:Inference; r:gives { - 2528 :kaprekar (0 3). + 3529 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2528 math:notEqualTo 0}] - skolem:lemma2896 - [ a r:Fact; r:gives {((2 5 2 8) "=<") list:sort (2 2 5 8)}] - [ a r:Fact; r:gives {((2 5 2 8) ">=") list:sort (8 5 2 2)}] - skolem:lemma2505 - skolem:lemma2506 - [ a r:Fact; r:gives {(8522 2258) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1529}] + [ a r:Fact; r:gives {(1529 2000) math:sum 3529}] + skolem:lemma3527 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2528]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2258]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1529]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3529]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1529 a r:Inference; r:gives { - 2529 :kaprekar (0 6). + 3530 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2529 math:notEqualTo 0}] - skolem:lemma2897 - [ a r:Fact; r:gives {((2 5 2 9) "=<") list:sort (2 2 5 9)}] - [ a r:Fact; r:gives {((2 5 2 9) ">=") list:sort (9 5 2 2)}] - skolem:lemma2508 - skolem:lemma2509 - [ a r:Fact; r:gives {(9522 2259) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1530}] + [ a r:Fact; r:gives {(1530 2000) math:sum 3530}] + skolem:lemma3528 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2529]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2259]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1530 a r:Inference; r:gives { - 2530 :kaprekar (0 7). + 3531 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2530 math:notEqualTo 0}] - skolem:lemma2898 - [ a r:Fact; r:gives {((2 5 3 0) "=<") list:sort (0 2 3 5)}] - [ a r:Fact; r:gives {((2 5 3 0) ">=") list:sort (5 3 2 0)}] - skolem:lemma2095 - skolem:lemma2096 - [ a r:Fact; r:gives {(5320 235) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1531}] + [ a r:Fact; r:gives {(1531 2000) math:sum 3531}] + skolem:lemma3529 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2530]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 235]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1531 a r:Inference; r:gives { - 2531 :kaprekar (0 7). + 3532 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2531 math:notEqualTo 0}] - skolem:lemma2899 - [ a r:Fact; r:gives {((2 5 3 1) "=<") list:sort (1 2 3 5)}] - [ a r:Fact; r:gives {((2 5 3 1) ">=") list:sort (5 3 2 1)}] - skolem:lemma2285 - skolem:lemma2286 - [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1532}] + [ a r:Fact; r:gives {(1532 2000) math:sum 3532}] + skolem:lemma3530 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2531]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1235]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1532 a r:Inference; r:gives { - 2532 :kaprekar (0 3). + 3533 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2532 math:notEqualTo 0}] - skolem:lemma2900 - [ a r:Fact; r:gives {((2 5 3 2) "=<") list:sort (2 2 3 5)}] - [ a r:Fact; r:gives {((2 5 3 2) ">=") list:sort (5 3 2 2)}] - skolem:lemma2454 - skolem:lemma2455 - [ a r:Fact; r:gives {(5322 2235) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1533}] + [ a r:Fact; r:gives {(1533 2000) math:sum 3533}] + skolem:lemma3531 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2235]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1533 a r:Inference; r:gives { - 2533 :kaprekar (0 6). + 3534 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2533 math:notEqualTo 0}] - skolem:lemma2901 - [ a r:Fact; r:gives {((2 5 3 3) "=<") list:sort (2 3 3 5)}] - [ a r:Fact; r:gives {((2 5 3 3) ">=") list:sort (5 3 3 2)}] - skolem:lemma2610 - skolem:lemma2611 - [ a r:Fact; r:gives {(5332 2335) math:difference 2997}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2997 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2997 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1534}] + [ a r:Fact; r:gives {(1534 2000) math:sum 3534}] + skolem:lemma3532 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2335]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1534]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3534]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1534 a r:Inference; r:gives { - 2534 :kaprekar (0 3). + 3535 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2534 math:notEqualTo 0}] - skolem:lemma2902 - [ a r:Fact; r:gives {((2 5 3 4) "=<") list:sort (2 3 4 5)}] - [ a r:Fact; r:gives {((2 5 3 4) ">=") list:sort (5 4 3 2)}] - skolem:lemma2632 - skolem:lemma2633 - [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1535}] + [ a r:Fact; r:gives {(1535 2000) math:sum 3535}] + skolem:lemma3533 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2534]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2345]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1535]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3535]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1535 a r:Inference; r:gives { - 2535 :kaprekar (0 5). + 3536 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2535 math:notEqualTo 0}] - skolem:lemma2903 - [ a r:Fact; r:gives {((2 5 3 5) "=<") list:sort (2 3 5 5)}] - [ a r:Fact; r:gives {((2 5 3 5) ">=") list:sort (5 5 3 2)}] - skolem:lemma2652 - skolem:lemma2653 - [ a r:Fact; r:gives {(5532 2355) math:difference 3177}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3177 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 3177 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1536}] + [ a r:Fact; r:gives {(1536 2000) math:sum 3536}] + skolem:lemma3534 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2535]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1536]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3536]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1536 a r:Inference; r:gives { - 2536 :kaprekar (0 2). + 3537 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2536 math:notEqualTo 0}] - skolem:lemma2904 - [ a r:Fact; r:gives {((2 5 3 6) "=<") list:sort (2 3 5 6)}] - [ a r:Fact; r:gives {((2 5 3 6) ">=") list:sort (6 5 3 2)}] - skolem:lemma2655 - skolem:lemma2656 - [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1537}] + [ a r:Fact; r:gives {(1537 2000) math:sum 3537}] + skolem:lemma3535 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2536]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2356]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1537]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3537]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1537 a r:Inference; r:gives { - 2537 :kaprekar (0 7). + 3538 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2537 math:notEqualTo 0}] - skolem:lemma2905 - [ a r:Fact; r:gives {((2 5 3 7) "=<") list:sort (2 3 5 7)}] - [ a r:Fact; r:gives {((2 5 3 7) ">=") list:sort (7 5 3 2)}] - skolem:lemma2658 - skolem:lemma2659 - [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1538}] + [ a r:Fact; r:gives {(1538 2000) math:sum 3538}] + skolem:lemma3536 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2537]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2357]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1538]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3538]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1538 a r:Inference; r:gives { - 2538 :kaprekar (0 1). + 3539 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2538 math:notEqualTo 0}] - skolem:lemma2906 - [ a r:Fact; r:gives {((2 5 3 8) "=<") list:sort (2 3 5 8)}] - [ a r:Fact; r:gives {((2 5 3 8) ">=") list:sort (8 5 3 2)}] - skolem:lemma2661 - skolem:lemma2662 - [ a r:Fact; r:gives {(8532 2358) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1539}] + [ a r:Fact; r:gives {(1539 2000) math:sum 3539}] + skolem:lemma3537 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2538]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2358]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1539]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3539]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1539 a r:Inference; r:gives { - 2539 :kaprekar (0 5). + 3540 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2539 math:notEqualTo 0}] - skolem:lemma2907 - [ a r:Fact; r:gives {((2 5 3 9) "=<") list:sort (2 3 5 9)}] - [ a r:Fact; r:gives {((2 5 3 9) ">=") list:sort (9 5 3 2)}] - skolem:lemma2664 - skolem:lemma2665 - [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1540}] + [ a r:Fact; r:gives {(1540 2000) math:sum 3540}] + skolem:lemma3538 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2539]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2359]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1540]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3540]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1540 a r:Inference; r:gives { - 2540 :kaprekar (0 7). + 3541 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2540 math:notEqualTo 0}] - skolem:lemma2908 - [ a r:Fact; r:gives {((2 5 4 0) "=<") list:sort (0 2 4 5)}] - [ a r:Fact; r:gives {((2 5 4 0) ">=") list:sort (5 4 2 0)}] - skolem:lemma2117 - skolem:lemma2118 - [ a r:Fact; r:gives {(5420 245) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1541}] + [ a r:Fact; r:gives {(1541 2000) math:sum 3541}] + skolem:lemma3539 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2540]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 245]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1541]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3541]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1541 a r:Inference; r:gives { - 2541 :kaprekar (0 2). + 3542 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2541 math:notEqualTo 0}] - skolem:lemma2909 - [ a r:Fact; r:gives {((2 5 4 1) "=<") list:sort (1 2 4 5)}] - [ a r:Fact; r:gives {((2 5 4 1) ">=") list:sort (5 4 2 1)}] - skolem:lemma2307 - skolem:lemma2308 - [ a r:Fact; r:gives {(5421 1245) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1542}] + [ a r:Fact; r:gives {(1542 2000) math:sum 3542}] + skolem:lemma3540 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2541]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1245]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1542 a r:Inference; r:gives { - 2542 :kaprekar (0 5). + 3543 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2542 math:notEqualTo 0}] - skolem:lemma2910 - [ a r:Fact; r:gives {((2 5 4 2) "=<") list:sort (2 2 4 5)}] - [ a r:Fact; r:gives {((2 5 4 2) ">=") list:sort (5 4 2 2)}] - skolem:lemma2476 - skolem:lemma2477 - [ a r:Fact; r:gives {(5422 2245) math:difference 3177}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3177 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 3177 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1543}] + [ a r:Fact; r:gives {(1543 2000) math:sum 3543}] + skolem:lemma3541 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2245]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1543 a r:Inference; r:gives { - 2543 :kaprekar (0 3). + 3544 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2543 math:notEqualTo 0}] - skolem:lemma2911 - [ a r:Fact; r:gives {((2 5 4 3) "=<") list:sort (2 3 4 5)}] - [ a r:Fact; r:gives {((2 5 4 3) ">=") list:sort (5 4 3 2)}] - skolem:lemma2632 - skolem:lemma2633 - [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1544}] + [ a r:Fact; r:gives {(1544 2000) math:sum 3544}] + skolem:lemma3542 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2543]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2345]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1544]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3544]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1544 a r:Inference; r:gives { - 2544 :kaprekar (0 6). + 3545 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2544 math:notEqualTo 0}] - skolem:lemma2912 - [ a r:Fact; r:gives {((2 5 4 4) "=<") list:sort (2 4 4 5)}] - [ a r:Fact; r:gives {((2 5 4 4) ">=") list:sort (5 4 4 2)}] - skolem:lemma2774 - skolem:lemma2775 - [ a r:Fact; r:gives {(5442 2445) math:difference 2997}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2997 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2997 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1545}] + [ a r:Fact; r:gives {(1545 2000) math:sum 3545}] + skolem:lemma3543 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2544]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2445]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1545]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3545]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1545 a r:Inference; r:gives { - 2545 :kaprekar (0 3). + 3546 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2545 math:notEqualTo 0}] - skolem:lemma2913 - [ a r:Fact; r:gives {((2 5 4 5) "=<") list:sort (2 4 5 5)}] - [ a r:Fact; r:gives {((2 5 4 5) ">=") list:sort (5 5 4 2)}] - skolem:lemma2794 - skolem:lemma2795 - [ a r:Fact; r:gives {(5542 2455) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1546}] + [ a r:Fact; r:gives {(1546 2000) math:sum 3546}] + skolem:lemma3544 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2545]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2455]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1546]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3546]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1546 a r:Inference; r:gives { - 2546 :kaprekar (0 7). + 3547 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2546 math:notEqualTo 0}] - skolem:lemma2914 - [ a r:Fact; r:gives {((2 5 4 6) "=<") list:sort (2 4 5 6)}] - [ a r:Fact; r:gives {((2 5 4 6) ">=") list:sort (6 5 4 2)}] - skolem:lemma2797 - skolem:lemma2798 - [ a r:Fact; r:gives {(6542 2456) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1547}] + [ a r:Fact; r:gives {(1547 2000) math:sum 3547}] + skolem:lemma3545 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2546]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2456]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1547]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3547]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1547 a r:Inference; r:gives { - 2547 :kaprekar (0 7). + 3548 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2547 math:notEqualTo 0}] - skolem:lemma2915 - [ a r:Fact; r:gives {((2 5 4 7) "=<") list:sort (2 4 5 7)}] - [ a r:Fact; r:gives {((2 5 4 7) ">=") list:sort (7 5 4 2)}] - skolem:lemma2800 - skolem:lemma2801 - [ a r:Fact; r:gives {(7542 2457) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1548}] + [ a r:Fact; r:gives {(1548 2000) math:sum 3548}] + skolem:lemma3546 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2547]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2457]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1548]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3548]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1548 a r:Inference; r:gives { - 2548 :kaprekar (0 7). + 3549 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2548 math:notEqualTo 0}] - skolem:lemma2916 - [ a r:Fact; r:gives {((2 5 4 8) "=<") list:sort (2 4 5 8)}] - [ a r:Fact; r:gives {((2 5 4 8) ">=") list:sort (8 5 4 2)}] - skolem:lemma2803 - skolem:lemma2804 - [ a r:Fact; r:gives {(8542 2458) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1549}] + [ a r:Fact; r:gives {(1549 2000) math:sum 3549}] + skolem:lemma3547 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2548]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2458]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1549]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3549]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1549 a r:Inference; r:gives { - 2549 :kaprekar (0 3). + 3550 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2549 math:notEqualTo 0}] - skolem:lemma2917 - [ a r:Fact; r:gives {((2 5 4 9) "=<") list:sort (2 4 5 9)}] - [ a r:Fact; r:gives {((2 5 4 9) ">=") list:sort (9 5 4 2)}] - skolem:lemma2806 - skolem:lemma2807 - [ a r:Fact; r:gives {(9542 2459) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1550}] + [ a r:Fact; r:gives {(1550 2000) math:sum 3550}] + skolem:lemma3548 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2549]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2459]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1550]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3550]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1550 a r:Inference; r:gives { - 2550 :kaprekar (0 5). + 3551 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2550 math:notEqualTo 0}] - skolem:lemma2918 - [ a r:Fact; r:gives {((2 5 5 0) "=<") list:sort (0 2 5 5)}] - [ a r:Fact; r:gives {((2 5 5 0) ">=") list:sort (5 5 2 0)}] - skolem:lemma2137 - skolem:lemma2138 - [ a r:Fact; r:gives {(5520 255) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1551}] + [ a r:Fact; r:gives {(1551 2000) math:sum 3551}] + skolem:lemma3549 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2550]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 255]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1551]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3551]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1551 a r:Inference; r:gives { - 2551 :kaprekar (0 3). + 3552 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2551 math:notEqualTo 0}] - skolem:lemma2919 - [ a r:Fact; r:gives {((2 5 5 1) "=<") list:sort (1 2 5 5)}] - [ a r:Fact; r:gives {((2 5 5 1) ">=") list:sort (5 5 2 1)}] - skolem:lemma2327 - skolem:lemma2328 - [ a r:Fact; r:gives {(5521 1255) math:difference 4266}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4266 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 4266 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1552}] + [ a r:Fact; r:gives {(1552 2000) math:sum 3552}] + skolem:lemma3550 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2551]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1255]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1552 a r:Inference; r:gives { - 2552 :kaprekar (0 6). + 3553 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2552 math:notEqualTo 0}] - skolem:lemma2920 - [ a r:Fact; r:gives {((2 5 5 2) "=<") list:sort (2 2 5 5)}] - [ a r:Fact; r:gives {((2 5 5 2) ">=") list:sort (5 5 2 2)}] - skolem:lemma2496 - skolem:lemma2497 - [ a r:Fact; r:gives {(5522 2255) math:difference 3267}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3267 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 3267 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1553}] + [ a r:Fact; r:gives {(1553 2000) math:sum 3553}] + skolem:lemma3551 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2552]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2255]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1553 a r:Inference; r:gives { - 2553 :kaprekar (0 5). + 3554 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2553 math:notEqualTo 0}] - skolem:lemma2921 - [ a r:Fact; r:gives {((2 5 5 3) "=<") list:sort (2 3 5 5)}] - [ a r:Fact; r:gives {((2 5 5 3) ">=") list:sort (5 5 3 2)}] - skolem:lemma2652 - skolem:lemma2653 - [ a r:Fact; r:gives {(5532 2355) math:difference 3177}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3177 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 3177 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1554}] + [ a r:Fact; r:gives {(1554 2000) math:sum 3554}] + skolem:lemma3552 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2553]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1554]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3554]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1554 a r:Inference; r:gives { - 2554 :kaprekar (0 3). + 3555 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2554 math:notEqualTo 0}] - skolem:lemma2922 - [ a r:Fact; r:gives {((2 5 5 4) "=<") list:sort (2 4 5 5)}] - [ a r:Fact; r:gives {((2 5 5 4) ">=") list:sort (5 5 4 2)}] - skolem:lemma2794 - skolem:lemma2795 - [ a r:Fact; r:gives {(5542 2455) math:difference 3087}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3087 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 3087 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1555}] + [ a r:Fact; r:gives {(1555 2000) math:sum 3555}] + skolem:lemma3553 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2554]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2455]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1555]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3555]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1555 a r:Inference; r:gives { - 2555 :kaprekar (0 6). + 3556 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2555 math:notEqualTo 0}] - skolem:lemma2923 - [ a r:Fact; r:gives {((2 5 5 5) "=<") list:sort (2 5 5 5)}] - [ a r:Fact; r:gives {((2 5 5 5) ">=") list:sort (5 5 5 2)}] - skolem:lemma2924 - skolem:lemma2925 - [ a r:Fact; r:gives {(5552 2555) math:difference 2997}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 2997 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 2997 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1556}] + [ a r:Fact; r:gives {(1556 2000) math:sum 3556}] + skolem:lemma3554 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2555]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2555]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5552]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1556]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3556]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1556 a r:Inference; r:gives { - 2556 :kaprekar (0 4). + 3557 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2556 math:notEqualTo 0}] - skolem:lemma2926 - [ a r:Fact; r:gives {((2 5 5 6) "=<") list:sort (2 5 5 6)}] - [ a r:Fact; r:gives {((2 5 5 6) ">=") list:sort (6 5 5 2)}] - skolem:lemma2927 - skolem:lemma2928 - [ a r:Fact; r:gives {(6552 2556) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1557}] + [ a r:Fact; r:gives {(1557 2000) math:sum 3557}] + skolem:lemma3555 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2556]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2556]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6552]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1557]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3557]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1557 a r:Inference; r:gives { - 2557 :kaprekar (0 6). + 3558 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2557 math:notEqualTo 0}] - skolem:lemma2929 - [ a r:Fact; r:gives {((2 5 5 7) "=<") list:sort (2 5 5 7)}] - [ a r:Fact; r:gives {((2 5 5 7) ">=") list:sort (7 5 5 2)}] - skolem:lemma2930 - skolem:lemma2931 - [ a r:Fact; r:gives {(7552 2557) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1558}] + [ a r:Fact; r:gives {(1558 2000) math:sum 3558}] + skolem:lemma3556 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2557]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2557]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7552]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1558]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3558]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1558 a r:Inference; r:gives { - 2558 :kaprekar (0 6). + 3559 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2558 math:notEqualTo 0}] - skolem:lemma2932 - [ a r:Fact; r:gives {((2 5 5 8) "=<") list:sort (2 5 5 8)}] - [ a r:Fact; r:gives {((2 5 5 8) ">=") list:sort (8 5 5 2)}] - skolem:lemma2933 - skolem:lemma2934 - [ a r:Fact; r:gives {(8552 2558) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1559}] + [ a r:Fact; r:gives {(1559 2000) math:sum 3559}] + skolem:lemma3557 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2558]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2558]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8552]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1559]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3559]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1559 a r:Inference; r:gives { - 2559 :kaprekar (0 4). + 3560 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2559 math:notEqualTo 0}] - skolem:lemma2935 - [ a r:Fact; r:gives {((2 5 5 9) "=<") list:sort (2 5 5 9)}] - [ a r:Fact; r:gives {((2 5 5 9) ">=") list:sort (9 5 5 2)}] - skolem:lemma2936 - skolem:lemma2937 - [ a r:Fact; r:gives {(9552 2559) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1560}] + [ a r:Fact; r:gives {(1560 2000) math:sum 3560}] + skolem:lemma3558 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2559]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2559]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9552]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1560]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3560]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1560 a r:Inference; r:gives { - 2560 :kaprekar (0 3). + 3561 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2560 math:notEqualTo 0}] - skolem:lemma2938 - [ a r:Fact; r:gives {((2 5 6 0) "=<") list:sort (0 2 5 6)}] - [ a r:Fact; r:gives {((2 5 6 0) ">=") list:sort (6 5 2 0)}] - skolem:lemma2140 - skolem:lemma2141 - [ a r:Fact; r:gives {(6520 256) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1561}] + [ a r:Fact; r:gives {(1561 2000) math:sum 3561}] + skolem:lemma3559 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2560]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 256]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1561]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3561]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1561 a r:Inference; r:gives { - 2561 :kaprekar (0 5). + 3562 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2561 math:notEqualTo 0}] - skolem:lemma2939 - [ a r:Fact; r:gives {((2 5 6 1) "=<") list:sort (1 2 5 6)}] - [ a r:Fact; r:gives {((2 5 6 1) ">=") list:sort (6 5 2 1)}] - skolem:lemma2330 - skolem:lemma2331 - [ a r:Fact; r:gives {(6521 1256) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1562}] + [ a r:Fact; r:gives {(1562 2000) math:sum 3562}] + skolem:lemma3560 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2561]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1256]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1562]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3562]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1562 a r:Inference; r:gives { - 2562 :kaprekar (0 3). + 3563 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2562 math:notEqualTo 0}] - skolem:lemma2940 - [ a r:Fact; r:gives {((2 5 6 2) "=<") list:sort (2 2 5 6)}] - [ a r:Fact; r:gives {((2 5 6 2) ">=") list:sort (6 5 2 2)}] - skolem:lemma2499 - skolem:lemma2500 - [ a r:Fact; r:gives {(6522 2256) math:difference 4266}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4266 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 4266 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1563}] + [ a r:Fact; r:gives {(1563 2000) math:sum 3563}] + skolem:lemma3561 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2562]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2256]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1563]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3563]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1563 a r:Inference; r:gives { - 2563 :kaprekar (0 2). + 3564 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2563 math:notEqualTo 0}] - skolem:lemma2941 - [ a r:Fact; r:gives {((2 5 6 3) "=<") list:sort (2 3 5 6)}] - [ a r:Fact; r:gives {((2 5 6 3) ">=") list:sort (6 5 3 2)}] - skolem:lemma2655 - skolem:lemma2656 - [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1564}] + [ a r:Fact; r:gives {(1564 2000) math:sum 3564}] + skolem:lemma3562 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2563]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2356]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1564]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3564]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1564 a r:Inference; r:gives { - 2564 :kaprekar (0 7). + 3565 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2564 math:notEqualTo 0}] - skolem:lemma2942 - [ a r:Fact; r:gives {((2 5 6 4) "=<") list:sort (2 4 5 6)}] - [ a r:Fact; r:gives {((2 5 6 4) ">=") list:sort (6 5 4 2)}] - skolem:lemma2797 - skolem:lemma2798 - [ a r:Fact; r:gives {(6542 2456) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1565}] + [ a r:Fact; r:gives {(1565 2000) math:sum 3565}] + skolem:lemma3563 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2564]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2456]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1565]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3565]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1565 a r:Inference; r:gives { - 2565 :kaprekar (0 4). + 3566 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2565 math:notEqualTo 0}] - skolem:lemma2943 - [ a r:Fact; r:gives {((2 5 6 5) "=<") list:sort (2 5 5 6)}] - [ a r:Fact; r:gives {((2 5 6 5) ">=") list:sort (6 5 5 2)}] - skolem:lemma2927 - skolem:lemma2928 - [ a r:Fact; r:gives {(6552 2556) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1566}] + [ a r:Fact; r:gives {(1566 2000) math:sum 3566}] + skolem:lemma3564 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2565]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2556]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6552]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1566]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3566]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1566 a r:Inference; r:gives { - 2566 :kaprekar (0 7). + 3567 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2566 math:notEqualTo 0}] - skolem:lemma2944 - [ a r:Fact; r:gives {((2 5 6 6) "=<") list:sort (2 5 6 6)}] - [ a r:Fact; r:gives {((2 5 6 6) ">=") list:sort (6 6 5 2)}] - skolem:lemma2945 - skolem:lemma2946 - [ a r:Fact; r:gives {(6652 2566) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1567}] + [ a r:Fact; r:gives {(1567 2000) math:sum 3567}] + skolem:lemma3565 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2566]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2566]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1567]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3567]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1567 a r:Inference; r:gives { - 2567 :kaprekar (0 7). + 3568 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2567 math:notEqualTo 0}] - skolem:lemma2947 - [ a r:Fact; r:gives {((2 5 6 7) "=<") list:sort (2 5 6 7)}] - [ a r:Fact; r:gives {((2 5 6 7) ">=") list:sort (7 6 5 2)}] - skolem:lemma2948 - skolem:lemma2949 - [ a r:Fact; r:gives {(7652 2567) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1568}] + [ a r:Fact; r:gives {(1568 2000) math:sum 3568}] + skolem:lemma3566 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2567]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2567]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1568]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3568]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1568 a r:Inference; r:gives { - 2568 :kaprekar (0 7). + 3569 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2568 math:notEqualTo 0}] - skolem:lemma2950 - [ a r:Fact; r:gives {((2 5 6 8) "=<") list:sort (2 5 6 8)}] - [ a r:Fact; r:gives {((2 5 6 8) ">=") list:sort (8 6 5 2)}] - skolem:lemma2951 - skolem:lemma2952 - [ a r:Fact; r:gives {(8652 2568) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1569}] + [ a r:Fact; r:gives {(1569 2000) math:sum 3569}] + skolem:lemma3567 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2568]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2568]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1569]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3569]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1569 a r:Inference; r:gives { - 2569 :kaprekar (0 3). + 3570 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2569 math:notEqualTo 0}] - skolem:lemma2953 - [ a r:Fact; r:gives {((2 5 6 9) "=<") list:sort (2 5 6 9)}] - [ a r:Fact; r:gives {((2 5 6 9) ">=") list:sort (9 6 5 2)}] - skolem:lemma2954 - skolem:lemma2955 - [ a r:Fact; r:gives {(9652 2569) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1570}] + [ a r:Fact; r:gives {(1570 2000) math:sum 3570}] + skolem:lemma3568 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2569]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2569]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1570]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3570]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1570 a r:Inference; r:gives { - 2570 :kaprekar (0 6). + 3571 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2570 math:notEqualTo 0}] - skolem:lemma2956 - [ a r:Fact; r:gives {((2 5 7 0) "=<") list:sort (0 2 5 7)}] - [ a r:Fact; r:gives {((2 5 7 0) ">=") list:sort (7 5 2 0)}] - skolem:lemma2143 - skolem:lemma2144 - [ a r:Fact; r:gives {(7520 257) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1571}] + [ a r:Fact; r:gives {(1571 2000) math:sum 3571}] + skolem:lemma3569 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2570]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 257]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1571]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3571]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1571 a r:Inference; r:gives { - 2571 :kaprekar (0 3). + 3572 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2571 math:notEqualTo 0}] - skolem:lemma2957 - [ a r:Fact; r:gives {((2 5 7 1) "=<") list:sort (1 2 5 7)}] - [ a r:Fact; r:gives {((2 5 7 1) ">=") list:sort (7 5 2 1)}] - skolem:lemma2333 - skolem:lemma2334 - [ a r:Fact; r:gives {(7521 1257) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1572}] + [ a r:Fact; r:gives {(1572 2000) math:sum 3572}] + skolem:lemma3570 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2571]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1257]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1572]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3572]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1572 a r:Inference; r:gives { - 2572 :kaprekar (0 5). + 3573 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2572 math:notEqualTo 0}] - skolem:lemma2958 - [ a r:Fact; r:gives {((2 5 7 2) "=<") list:sort (2 2 5 7)}] - [ a r:Fact; r:gives {((2 5 7 2) ">=") list:sort (7 5 2 2)}] - skolem:lemma2502 - skolem:lemma2503 - [ a r:Fact; r:gives {(7522 2257) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1573}] + [ a r:Fact; r:gives {(1573 2000) math:sum 3573}] + skolem:lemma3571 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2572]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2257]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1573]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3573]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1573 a r:Inference; r:gives { - 2573 :kaprekar (0 7). + 3574 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2573 math:notEqualTo 0}] - skolem:lemma2959 - [ a r:Fact; r:gives {((2 5 7 3) "=<") list:sort (2 3 5 7)}] - [ a r:Fact; r:gives {((2 5 7 3) ">=") list:sort (7 5 3 2)}] - skolem:lemma2658 - skolem:lemma2659 - [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1574}] + [ a r:Fact; r:gives {(1574 2000) math:sum 3574}] + skolem:lemma3572 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2573]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2357]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1574]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3574]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1574 a r:Inference; r:gives { - 2574 :kaprekar (0 7). + 3575 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2574 math:notEqualTo 0}] - skolem:lemma2960 - [ a r:Fact; r:gives {((2 5 7 4) "=<") list:sort (2 4 5 7)}] - [ a r:Fact; r:gives {((2 5 7 4) ">=") list:sort (7 5 4 2)}] - skolem:lemma2800 - skolem:lemma2801 - [ a r:Fact; r:gives {(7542 2457) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1575}] + [ a r:Fact; r:gives {(1575 2000) math:sum 3575}] + skolem:lemma3573 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2574]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2457]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1575]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3575]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1575 a r:Inference; r:gives { - 2575 :kaprekar (0 6). + 3576 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2575 math:notEqualTo 0}] - skolem:lemma2961 - [ a r:Fact; r:gives {((2 5 7 5) "=<") list:sort (2 5 5 7)}] - [ a r:Fact; r:gives {((2 5 7 5) ">=") list:sort (7 5 5 2)}] - skolem:lemma2930 - skolem:lemma2931 - [ a r:Fact; r:gives {(7552 2557) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1576}] + [ a r:Fact; r:gives {(1576 2000) math:sum 3576}] + skolem:lemma3574 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2575]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2557]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7552]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1576]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3576]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1576 a r:Inference; r:gives { - 2576 :kaprekar (0 7). + 3577 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2576 math:notEqualTo 0}] - skolem:lemma2962 - [ a r:Fact; r:gives {((2 5 7 6) "=<") list:sort (2 5 6 7)}] - [ a r:Fact; r:gives {((2 5 7 6) ">=") list:sort (7 6 5 2)}] - skolem:lemma2948 - skolem:lemma2949 - [ a r:Fact; r:gives {(7652 2567) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1577}] + [ a r:Fact; r:gives {(1577 2000) math:sum 3577}] + skolem:lemma3575 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2576]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2567]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1577]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3577]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1577 a r:Inference; r:gives { - 2577 :kaprekar (0 7). + 3578 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2577 math:notEqualTo 0}] - skolem:lemma2963 - [ a r:Fact; r:gives {((2 5 7 7) "=<") list:sort (2 5 7 7)}] - [ a r:Fact; r:gives {((2 5 7 7) ">=") list:sort (7 7 5 2)}] - skolem:lemma2964 - skolem:lemma2965 - [ a r:Fact; r:gives {(7752 2577) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1578}] + [ a r:Fact; r:gives {(1578 2000) math:sum 3578}] + skolem:lemma3576 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2577]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2577]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7752]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1578]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3578]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1578 a r:Inference; r:gives { - 2578 :kaprekar (0 1). + 3579 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2578 math:notEqualTo 0}] - skolem:lemma2966 - [ a r:Fact; r:gives {((2 5 7 8) "=<") list:sort (2 5 7 8)}] - [ a r:Fact; r:gives {((2 5 7 8) ">=") list:sort (8 7 5 2)}] - skolem:lemma2967 - skolem:lemma2968 - [ a r:Fact; r:gives {(8752 2578) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1579}] + [ a r:Fact; r:gives {(1579 2000) math:sum 3579}] + skolem:lemma3577 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2578]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2578]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8752]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1579]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3579]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1579 a r:Inference; r:gives { - 2579 :kaprekar (0 5). + 3580 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2579 math:notEqualTo 0}] - skolem:lemma2969 - [ a r:Fact; r:gives {((2 5 7 9) "=<") list:sort (2 5 7 9)}] - [ a r:Fact; r:gives {((2 5 7 9) ">=") list:sort (9 7 5 2)}] - skolem:lemma2970 - skolem:lemma2971 - [ a r:Fact; r:gives {(9752 2579) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1580}] + [ a r:Fact; r:gives {(1580 2000) math:sum 3580}] + skolem:lemma3578 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2579]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2579]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9752]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1580]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3580]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1580 a r:Inference; r:gives { - 2580 :kaprekar (0 5). + 3581 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2580 math:notEqualTo 0}] - skolem:lemma2972 - [ a r:Fact; r:gives {((2 5 8 0) "=<") list:sort (0 2 5 8)}] - [ a r:Fact; r:gives {((2 5 8 0) ">=") list:sort (8 5 2 0)}] - skolem:lemma2146 - skolem:lemma2147 - [ a r:Fact; r:gives {(8520 258) math:difference 8262}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8262 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 8262 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1581}] + [ a r:Fact; r:gives {(1581 2000) math:sum 3581}] + skolem:lemma3579 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2580]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 258]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1581]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3581]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1581 a r:Inference; r:gives { - 2581 :kaprekar (0 6). + 3582 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2581 math:notEqualTo 0}] - skolem:lemma2973 - [ a r:Fact; r:gives {((2 5 8 1) "=<") list:sort (1 2 5 8)}] - [ a r:Fact; r:gives {((2 5 8 1) ">=") list:sort (8 5 2 1)}] - skolem:lemma2336 - skolem:lemma2337 - [ a r:Fact; r:gives {(8521 1258) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1582}] + [ a r:Fact; r:gives {(1582 2000) math:sum 3582}] + skolem:lemma3580 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2581]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1258]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1582]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3582]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1582 a r:Inference; r:gives { - 2582 :kaprekar (0 3). + 3583 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2582 math:notEqualTo 0}] - skolem:lemma2974 - [ a r:Fact; r:gives {((2 5 8 2) "=<") list:sort (2 2 5 8)}] - [ a r:Fact; r:gives {((2 5 8 2) ">=") list:sort (8 5 2 2)}] - skolem:lemma2505 - skolem:lemma2506 - [ a r:Fact; r:gives {(8522 2258) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1583}] + [ a r:Fact; r:gives {(1583 2000) math:sum 3583}] + skolem:lemma3581 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2582]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2258]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1583]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3583]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1583 a r:Inference; r:gives { - 2583 :kaprekar (0 1). + 3584 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2583 math:notEqualTo 0}] - skolem:lemma2975 - [ a r:Fact; r:gives {((2 5 8 3) "=<") list:sort (2 3 5 8)}] - [ a r:Fact; r:gives {((2 5 8 3) ">=") list:sort (8 5 3 2)}] - skolem:lemma2661 - skolem:lemma2662 - [ a r:Fact; r:gives {(8532 2358) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1584}] + [ a r:Fact; r:gives {(1584 2000) math:sum 3584}] + skolem:lemma3582 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2583]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2358]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1584]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3584]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1584 a r:Inference; r:gives { - 2584 :kaprekar (0 7). + 3585 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2584 math:notEqualTo 0}] - skolem:lemma2976 - [ a r:Fact; r:gives {((2 5 8 4) "=<") list:sort (2 4 5 8)}] - [ a r:Fact; r:gives {((2 5 8 4) ">=") list:sort (8 5 4 2)}] - skolem:lemma2803 - skolem:lemma2804 - [ a r:Fact; r:gives {(8542 2458) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1585}] + [ a r:Fact; r:gives {(1585 2000) math:sum 3585}] + skolem:lemma3583 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2584]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2458]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1585]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3585]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1585 a r:Inference; r:gives { - 2585 :kaprekar (0 6). + 3586 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2585 math:notEqualTo 0}] - skolem:lemma2977 - [ a r:Fact; r:gives {((2 5 8 5) "=<") list:sort (2 5 5 8)}] - [ a r:Fact; r:gives {((2 5 8 5) ">=") list:sort (8 5 5 2)}] - skolem:lemma2933 - skolem:lemma2934 - [ a r:Fact; r:gives {(8552 2558) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1586}] + [ a r:Fact; r:gives {(1586 2000) math:sum 3586}] + skolem:lemma3584 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2585]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2558]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8552]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1586]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3586]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1586 a r:Inference; r:gives { - 2586 :kaprekar (0 7). + 3587 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2586 math:notEqualTo 0}] - skolem:lemma2978 - [ a r:Fact; r:gives {((2 5 8 6) "=<") list:sort (2 5 6 8)}] - [ a r:Fact; r:gives {((2 5 8 6) ">=") list:sort (8 6 5 2)}] - skolem:lemma2951 - skolem:lemma2952 - [ a r:Fact; r:gives {(8652 2568) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1587}] + [ a r:Fact; r:gives {(1587 2000) math:sum 3587}] + skolem:lemma3585 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2586]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2568]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1587]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3587]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1587 a r:Inference; r:gives { - 2587 :kaprekar (0 1). + 3588 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2587 math:notEqualTo 0}] - skolem:lemma2979 - [ a r:Fact; r:gives {((2 5 8 7) "=<") list:sort (2 5 7 8)}] - [ a r:Fact; r:gives {((2 5 8 7) ">=") list:sort (8 7 5 2)}] - skolem:lemma2967 - skolem:lemma2968 - [ a r:Fact; r:gives {(8752 2578) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1588}] + [ a r:Fact; r:gives {(1588 2000) math:sum 3588}] + skolem:lemma3586 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2587]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2578]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8752]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1588]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3588]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1588 a r:Inference; r:gives { - 2588 :kaprekar (0 3). + 3589 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2588 math:notEqualTo 0}] - skolem:lemma2980 - [ a r:Fact; r:gives {((2 5 8 8) "=<") list:sort (2 5 8 8)}] - [ a r:Fact; r:gives {((2 5 8 8) ">=") list:sort (8 8 5 2)}] - skolem:lemma2981 - skolem:lemma2982 - [ a r:Fact; r:gives {(8852 2588) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1589}] + [ a r:Fact; r:gives {(1589 2000) math:sum 3589}] + skolem:lemma3587 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2588]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2588]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8852]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1589]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3589]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1589 a r:Inference; r:gives { - 2589 :kaprekar (0 6). + 3590 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2589 math:notEqualTo 0}] - skolem:lemma2983 - [ a r:Fact; r:gives {((2 5 8 9) "=<") list:sort (2 5 8 9)}] - [ a r:Fact; r:gives {((2 5 8 9) ">=") list:sort (9 8 5 2)}] - skolem:lemma2984 - skolem:lemma2985 - [ a r:Fact; r:gives {(9852 2589) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1590}] + [ a r:Fact; r:gives {(1590 2000) math:sum 3590}] + skolem:lemma3588 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2589]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2589]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9852]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1590]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3590]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1590 a r:Inference; r:gives { - 2590 :kaprekar (0 3). + 3591 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2590 math:notEqualTo 0}] - skolem:lemma2986 - [ a r:Fact; r:gives {((2 5 9 0) "=<") list:sort (0 2 5 9)}] - [ a r:Fact; r:gives {((2 5 9 0) ">=") list:sort (9 5 2 0)}] - skolem:lemma2149 - skolem:lemma2150 - [ a r:Fact; r:gives {(9520 259) math:difference 9261}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9261 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 9261 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1591}] + [ a r:Fact; r:gives {(1591 2000) math:sum 3591}] + skolem:lemma3589 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2590]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 259]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9261]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1591]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3591]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1591 a r:Inference; r:gives { - 2591 :kaprekar (0 5). + 3592 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2591 math:notEqualTo 0}] - skolem:lemma2987 - [ a r:Fact; r:gives {((2 5 9 1) "=<") list:sort (1 2 5 9)}] - [ a r:Fact; r:gives {((2 5 9 1) ">=") list:sort (9 5 2 1)}] - skolem:lemma2339 - skolem:lemma2340 - [ a r:Fact; r:gives {(9521 1259) math:difference 8262}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8262 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 8262 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1592}] + [ a r:Fact; r:gives {(1592 2000) math:sum 3592}] + skolem:lemma3590 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2591]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1259]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1592]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3592]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1592 a r:Inference; r:gives { - 2592 :kaprekar (0 6). + 3593 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2592 math:notEqualTo 0}] - skolem:lemma2988 - [ a r:Fact; r:gives {((2 5 9 2) "=<") list:sort (2 2 5 9)}] - [ a r:Fact; r:gives {((2 5 9 2) ">=") list:sort (9 5 2 2)}] - skolem:lemma2508 - skolem:lemma2509 - [ a r:Fact; r:gives {(9522 2259) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1593}] + [ a r:Fact; r:gives {(1593 2000) math:sum 3593}] + skolem:lemma3591 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2592]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2259]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1593]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3593]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1593 a r:Inference; r:gives { - 2593 :kaprekar (0 5). + 3594 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2593 math:notEqualTo 0}] - skolem:lemma2989 - [ a r:Fact; r:gives {((2 5 9 3) "=<") list:sort (2 3 5 9)}] - [ a r:Fact; r:gives {((2 5 9 3) ">=") list:sort (9 5 3 2)}] - skolem:lemma2664 - skolem:lemma2665 - [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1594}] + [ a r:Fact; r:gives {(1594 2000) math:sum 3594}] + skolem:lemma3592 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2593]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2359]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1594]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3594]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1594 a r:Inference; r:gives { - 2594 :kaprekar (0 3). + 3595 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2594 math:notEqualTo 0}] - skolem:lemma2990 - [ a r:Fact; r:gives {((2 5 9 4) "=<") list:sort (2 4 5 9)}] - [ a r:Fact; r:gives {((2 5 9 4) ">=") list:sort (9 5 4 2)}] - skolem:lemma2806 - skolem:lemma2807 - [ a r:Fact; r:gives {(9542 2459) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1595}] + [ a r:Fact; r:gives {(1595 2000) math:sum 3595}] + skolem:lemma3593 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2594]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2459]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1595]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3595]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1595 a r:Inference; r:gives { - 2595 :kaprekar (0 4). + 3596 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2595 math:notEqualTo 0}] - skolem:lemma2991 - [ a r:Fact; r:gives {((2 5 9 5) "=<") list:sort (2 5 5 9)}] - [ a r:Fact; r:gives {((2 5 9 5) ">=") list:sort (9 5 5 2)}] - skolem:lemma2936 - skolem:lemma2937 - [ a r:Fact; r:gives {(9552 2559) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1596}] + [ a r:Fact; r:gives {(1596 2000) math:sum 3596}] + skolem:lemma3594 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2595]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2559]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9552]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1596]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3596]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1596 a r:Inference; r:gives { - 2596 :kaprekar (0 3). + 3597 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2596 math:notEqualTo 0}] - skolem:lemma2992 - [ a r:Fact; r:gives {((2 5 9 6) "=<") list:sort (2 5 6 9)}] - [ a r:Fact; r:gives {((2 5 9 6) ">=") list:sort (9 6 5 2)}] - skolem:lemma2954 - skolem:lemma2955 - [ a r:Fact; r:gives {(9652 2569) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1597}] + [ a r:Fact; r:gives {(1597 2000) math:sum 3597}] + skolem:lemma3595 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2596]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2569]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1597]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3597]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1597 a r:Inference; r:gives { - 2597 :kaprekar (0 5). + 3598 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2597 math:notEqualTo 0}] - skolem:lemma2993 - [ a r:Fact; r:gives {((2 5 9 7) "=<") list:sort (2 5 7 9)}] - [ a r:Fact; r:gives {((2 5 9 7) ">=") list:sort (9 7 5 2)}] - skolem:lemma2970 - skolem:lemma2971 - [ a r:Fact; r:gives {(9752 2579) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1598}] + [ a r:Fact; r:gives {(1598 2000) math:sum 3598}] + skolem:lemma3596 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2597]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2579]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9752]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1598]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3598]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1598 a r:Inference; r:gives { - 2598 :kaprekar (0 6). + 3599 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2598 math:notEqualTo 0}] - skolem:lemma2994 - [ a r:Fact; r:gives {((2 5 9 8) "=<") list:sort (2 5 8 9)}] - [ a r:Fact; r:gives {((2 5 9 8) ">=") list:sort (9 8 5 2)}] - skolem:lemma2984 - skolem:lemma2985 - [ a r:Fact; r:gives {(9852 2589) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1599}] + [ a r:Fact; r:gives {(1599 2000) math:sum 3599}] + skolem:lemma3597 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2598]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2589]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9852]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1599]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3599]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1599 a r:Inference; r:gives { - 2599 :kaprekar (0 3). + 3600 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2599 math:notEqualTo 0}] - skolem:lemma2995 - [ a r:Fact; r:gives {((2 5 9 9) "=<") list:sort (2 5 9 9)}] - [ a r:Fact; r:gives {((2 5 9 9) ">=") list:sort (9 9 5 2)}] - skolem:lemma2996 - skolem:lemma2997 - [ a r:Fact; r:gives {(9952 2599) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1600}] + [ a r:Fact; r:gives {(1600 2000) math:sum 3600}] + skolem:lemma3598 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2599]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2599]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9952]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1600 a r:Inference; r:gives { - 2600 :kaprekar (0 1). + 3601 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2600 math:notEqualTo 0}] - skolem:lemma2998 - [ a r:Fact; r:gives {((2 6 0 0) "=<") list:sort (0 0 2 6)}] - [ a r:Fact; r:gives {((2 6 0 0) ">=") list:sort (6 2 0 0)}] - skolem:lemma2020 - skolem:lemma2021 - [ a r:Fact; r:gives {(6200 26) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1601}] + [ a r:Fact; r:gives {(1601 2000) math:sum 3601}] + skolem:lemma3599 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2600]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1601]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3601]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1601 a r:Inference; r:gives { - 2601 :kaprekar (0 7). + 3602 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2601 math:notEqualTo 0}] - skolem:lemma2999 - [ a r:Fact; r:gives {((2 6 0 1) "=<") list:sort (0 1 2 6)}] - [ a r:Fact; r:gives {((2 6 0 1) ">=") list:sort (6 2 1 0)}] - skolem:lemma2048 - skolem:lemma2049 - [ a r:Fact; r:gives {(6210 126) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1602}] + [ a r:Fact; r:gives {(1602 2000) math:sum 3602}] + skolem:lemma3600 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2601]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 126]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1602]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3602]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1602 a r:Inference; r:gives { - 2602 :kaprekar (0 6). + 3603 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2602 math:notEqualTo 0}] - skolem:lemma3000 - [ a r:Fact; r:gives {((2 6 0 2) "=<") list:sort (0 2 2 6)}] - [ a r:Fact; r:gives {((2 6 0 2) ">=") list:sort (6 2 2 0)}] - skolem:lemma2074 - skolem:lemma2075 - [ a r:Fact; r:gives {(6220 226) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1603}] + [ a r:Fact; r:gives {(1603 2000) math:sum 3603}] + skolem:lemma3601 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2602]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 226]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1603]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3603]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1603 a r:Inference; r:gives { - 2603 :kaprekar (0 7). + 3604 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2603 math:notEqualTo 0}] - skolem:lemma3001 - [ a r:Fact; r:gives {((2 6 0 3) "=<") list:sort (0 2 3 6)}] - [ a r:Fact; r:gives {((2 6 0 3) ">=") list:sort (6 3 2 0)}] - skolem:lemma2098 - skolem:lemma2099 - [ a r:Fact; r:gives {(6320 236) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1604}] + [ a r:Fact; r:gives {(1604 2000) math:sum 3604}] + skolem:lemma3602 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2603]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 236]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1604]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3604]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1604 a r:Inference; r:gives { - 2604 :kaprekar (0 1). + 3605 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2604 math:notEqualTo 0}] - skolem:lemma3002 - [ a r:Fact; r:gives {((2 6 0 4) "=<") list:sort (0 2 4 6)}] - [ a r:Fact; r:gives {((2 6 0 4) ">=") list:sort (6 4 2 0)}] - skolem:lemma2120 - skolem:lemma2121 - [ a r:Fact; r:gives {(6420 246) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1605}] + [ a r:Fact; r:gives {(1605 2000) math:sum 3605}] + skolem:lemma3603 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2604]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 246]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1605]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3605]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1605 a r:Inference; r:gives { - 2605 :kaprekar (0 3). + 3606 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2605 math:notEqualTo 0}] - skolem:lemma3003 - [ a r:Fact; r:gives {((2 6 0 5) "=<") list:sort (0 2 5 6)}] - [ a r:Fact; r:gives {((2 6 0 5) ">=") list:sort (6 5 2 0)}] - skolem:lemma2140 - skolem:lemma2141 - [ a r:Fact; r:gives {(6520 256) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1606}] + [ a r:Fact; r:gives {(1606 2000) math:sum 3606}] + skolem:lemma3604 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2605]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 256]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1606]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3606]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1606 a r:Inference; r:gives { - 2606 :kaprekar (0 4). + 3607 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2606 math:notEqualTo 0}] - skolem:lemma3004 - [ a r:Fact; r:gives {((2 6 0 6) "=<") list:sort (0 2 6 6)}] - [ a r:Fact; r:gives {((2 6 0 6) ">=") list:sort (6 6 2 0)}] - skolem:lemma2158 - skolem:lemma2159 - [ a r:Fact; r:gives {(6620 266) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1607}] + [ a r:Fact; r:gives {(1607 2000) math:sum 3607}] + skolem:lemma3605 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2606]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6620]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1607]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3607]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1607 a r:Inference; r:gives { - 2607 :kaprekar (0 3). + 3608 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2607 math:notEqualTo 0}] - skolem:lemma3005 - [ a r:Fact; r:gives {((2 6 0 7) "=<") list:sort (0 2 6 7)}] - [ a r:Fact; r:gives {((2 6 0 7) ">=") list:sort (7 6 2 0)}] - skolem:lemma2161 - skolem:lemma2162 - [ a r:Fact; r:gives {(7620 267) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1608}] + [ a r:Fact; r:gives {(1608 2000) math:sum 3608}] + skolem:lemma3606 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2607]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7620]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1608]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3608]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1608 a r:Inference; r:gives { - 2608 :kaprekar (0 2). + 3609 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2608 math:notEqualTo 0}] - skolem:lemma3006 - [ a r:Fact; r:gives {((2 6 0 8) "=<") list:sort (0 2 6 8)}] - [ a r:Fact; r:gives {((2 6 0 8) ">=") list:sort (8 6 2 0)}] - skolem:lemma2164 - skolem:lemma2165 - [ a r:Fact; r:gives {(8620 268) math:difference 8352}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8352 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 8352 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1609}] + [ a r:Fact; r:gives {(1609 2000) math:sum 3609}] + skolem:lemma3607 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2608]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 268]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8620]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1609]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3609]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1609 a r:Inference; r:gives { - 2609 :kaprekar (0 7). + 3610 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2609 math:notEqualTo 0}] - skolem:lemma3007 - [ a r:Fact; r:gives {((2 6 0 9) "=<") list:sort (0 2 6 9)}] - [ a r:Fact; r:gives {((2 6 0 9) ">=") list:sort (9 6 2 0)}] - skolem:lemma2167 - skolem:lemma2168 - [ a r:Fact; r:gives {(9620 269) math:difference 9351}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9351 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 9351 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1610}] + [ a r:Fact; r:gives {(1610 2000) math:sum 3610}] + skolem:lemma3608 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2609]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 269]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9620]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9351]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1610]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3610]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1610 a r:Inference; r:gives { - 2610 :kaprekar (0 7). + 3611 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2610 math:notEqualTo 0}] - skolem:lemma3008 - [ a r:Fact; r:gives {((2 6 1 0) "=<") list:sort (0 1 2 6)}] - [ a r:Fact; r:gives {((2 6 1 0) ">=") list:sort (6 2 1 0)}] - skolem:lemma2048 - skolem:lemma2049 - [ a r:Fact; r:gives {(6210 126) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1611}] + [ a r:Fact; r:gives {(1611 2000) math:sum 3611}] + skolem:lemma3609 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2610]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 126]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1611]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3611]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1611 a r:Inference; r:gives { - 2611 :kaprekar (0 7). + 3612 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2611 math:notEqualTo 0}] - skolem:lemma3009 - [ a r:Fact; r:gives {((2 6 1 1) "=<") list:sort (1 1 2 6)}] - [ a r:Fact; r:gives {((2 6 1 1) ">=") list:sort (6 2 1 1)}] - skolem:lemma2238 - skolem:lemma2239 - [ a r:Fact; r:gives {(6211 1126) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1612}] + [ a r:Fact; r:gives {(1612 2000) math:sum 3612}] + skolem:lemma3610 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2611]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1126]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1612]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3612]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1612 a r:Inference; r:gives { - 2612 :kaprekar (0 6). + 3613 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2612 math:notEqualTo 0}] - skolem:lemma3010 - [ a r:Fact; r:gives {((2 6 1 2) "=<") list:sort (1 2 2 6)}] - [ a r:Fact; r:gives {((2 6 1 2) ">=") list:sort (6 2 2 1)}] - skolem:lemma2264 - skolem:lemma2265 - [ a r:Fact; r:gives {(6221 1226) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1613}] + [ a r:Fact; r:gives {(1613 2000) math:sum 3613}] + skolem:lemma3611 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2612]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1226]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1613]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3613]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1613 a r:Inference; r:gives { - 2613 :kaprekar (0 7). + 3614 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2613 math:notEqualTo 0}] - skolem:lemma3011 - [ a r:Fact; r:gives {((2 6 1 3) "=<") list:sort (1 2 3 6)}] - [ a r:Fact; r:gives {((2 6 1 3) ">=") list:sort (6 3 2 1)}] - skolem:lemma2288 - skolem:lemma2289 - [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1614}] + [ a r:Fact; r:gives {(1614 2000) math:sum 3614}] + skolem:lemma3612 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2613]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1236]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1614]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3614]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1614 a r:Inference; r:gives { - 2614 :kaprekar (0 7). + 3615 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2614 math:notEqualTo 0}] - skolem:lemma3012 - [ a r:Fact; r:gives {((2 6 1 4) "=<") list:sort (1 2 4 6)}] - [ a r:Fact; r:gives {((2 6 1 4) ">=") list:sort (6 4 2 1)}] - skolem:lemma2310 - skolem:lemma2311 - [ a r:Fact; r:gives {(6421 1246) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1615}] + [ a r:Fact; r:gives {(1615 2000) math:sum 3615}] + skolem:lemma3613 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2614]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1246]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1615]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3615]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1615 a r:Inference; r:gives { - 2615 :kaprekar (0 5). + 3616 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2615 math:notEqualTo 0}] - skolem:lemma3013 - [ a r:Fact; r:gives {((2 6 1 5) "=<") list:sort (1 2 5 6)}] - [ a r:Fact; r:gives {((2 6 1 5) ">=") list:sort (6 5 2 1)}] - skolem:lemma2330 - skolem:lemma2331 - [ a r:Fact; r:gives {(6521 1256) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1616}] + [ a r:Fact; r:gives {(1616 2000) math:sum 3616}] + skolem:lemma3614 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2615]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1256]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1616]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3616]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1616 a r:Inference; r:gives { - 2616 :kaprekar (0 5). + 3617 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2616 math:notEqualTo 0}] - skolem:lemma3014 - [ a r:Fact; r:gives {((2 6 1 6) "=<") list:sort (1 2 6 6)}] - [ a r:Fact; r:gives {((2 6 1 6) ">=") list:sort (6 6 2 1)}] - skolem:lemma2348 - skolem:lemma2349 - [ a r:Fact; r:gives {(6621 1266) math:difference 5355}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5355 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5355 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1617}] + [ a r:Fact; r:gives {(1617 2000) math:sum 3617}] + skolem:lemma3615 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2616]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1617]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3617]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1617 a r:Inference; r:gives { - 2617 :kaprekar (0 4). + 3618 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2617 math:notEqualTo 0}] - skolem:lemma3015 - [ a r:Fact; r:gives {((2 6 1 7) "=<") list:sort (1 2 6 7)}] - [ a r:Fact; r:gives {((2 6 1 7) ">=") list:sort (7 6 2 1)}] - skolem:lemma2351 - skolem:lemma2352 - [ a r:Fact; r:gives {(7621 1267) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1618}] + [ a r:Fact; r:gives {(1618 2000) math:sum 3618}] + skolem:lemma3616 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2617]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1618]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3618]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1618 a r:Inference; r:gives { - 2618 :kaprekar (0 3). + 3619 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2618 math:notEqualTo 0}] - skolem:lemma3016 - [ a r:Fact; r:gives {((2 6 1 8) "=<") list:sort (1 2 6 8)}] - [ a r:Fact; r:gives {((2 6 1 8) ">=") list:sort (8 6 2 1)}] - skolem:lemma2354 - skolem:lemma2355 - [ a r:Fact; r:gives {(8621 1268) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1619}] + [ a r:Fact; r:gives {(1619 2000) math:sum 3619}] + skolem:lemma3617 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2618]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1268]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1619]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3619]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1619 a r:Inference; r:gives { - 2619 :kaprekar (0 2). + 3620 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2619 math:notEqualTo 0}] - skolem:lemma3017 - [ a r:Fact; r:gives {((2 6 1 9) "=<") list:sort (1 2 6 9)}] - [ a r:Fact; r:gives {((2 6 1 9) ">=") list:sort (9 6 2 1)}] - skolem:lemma2357 - skolem:lemma2358 - [ a r:Fact; r:gives {(9621 1269) math:difference 8352}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8352 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 8352 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1620}] + [ a r:Fact; r:gives {(1620 2000) math:sum 3620}] + skolem:lemma3618 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2619]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1269]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1620 a r:Inference; r:gives { - 2620 :kaprekar (0 6). + 3621 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2620 math:notEqualTo 0}] - skolem:lemma3018 - [ a r:Fact; r:gives {((2 6 2 0) "=<") list:sort (0 2 2 6)}] - [ a r:Fact; r:gives {((2 6 2 0) ">=") list:sort (6 2 2 0)}] - skolem:lemma2074 - skolem:lemma2075 - [ a r:Fact; r:gives {(6220 226) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1621}] + [ a r:Fact; r:gives {(1621 2000) math:sum 3621}] + skolem:lemma3619 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2620]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 226]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1621 a r:Inference; r:gives { - 2621 :kaprekar (0 6). + 3622 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2621 math:notEqualTo 0}] - skolem:lemma3019 - [ a r:Fact; r:gives {((2 6 2 1) "=<") list:sort (1 2 2 6)}] - [ a r:Fact; r:gives {((2 6 2 1) ">=") list:sort (6 2 2 1)}] - skolem:lemma2264 - skolem:lemma2265 - [ a r:Fact; r:gives {(6221 1226) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1622}] + [ a r:Fact; r:gives {(1622 2000) math:sum 3622}] + skolem:lemma3620 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1226]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1622 a r:Inference; r:gives { - 2622 :kaprekar (0 4). + 3623 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2622 math:notEqualTo 0}] - skolem:lemma3020 - [ a r:Fact; r:gives {((2 6 2 2) "=<") list:sort (2 2 2 6)}] - [ a r:Fact; r:gives {((2 6 2 2) ">=") list:sort (6 2 2 2)}] - skolem:lemma2433 - skolem:lemma2434 - [ a r:Fact; r:gives {(6222 2226) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1623}] + [ a r:Fact; r:gives {(1623 2000) math:sum 3623}] + skolem:lemma3621 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2226]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1623]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3623]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1623 a r:Inference; r:gives { - 2623 :kaprekar (0 7). + 3624 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2623 math:notEqualTo 0}] - skolem:lemma3021 - [ a r:Fact; r:gives {((2 6 2 3) "=<") list:sort (2 2 3 6)}] - [ a r:Fact; r:gives {((2 6 2 3) ">=") list:sort (6 3 2 2)}] - skolem:lemma2457 - skolem:lemma2458 - [ a r:Fact; r:gives {(6322 2236) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1624}] + [ a r:Fact; r:gives {(1624 2000) math:sum 3624}] + skolem:lemma3622 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2623]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2236]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1624]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3624]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1624 a r:Inference; r:gives { - 2624 :kaprekar (0 2). + 3625 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2624 math:notEqualTo 0}] - skolem:lemma3022 - [ a r:Fact; r:gives {((2 6 2 4) "=<") list:sort (2 2 4 6)}] - [ a r:Fact; r:gives {((2 6 2 4) ">=") list:sort (6 4 2 2)}] - skolem:lemma2479 - skolem:lemma2480 - [ a r:Fact; r:gives {(6422 2246) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1625}] + [ a r:Fact; r:gives {(1625 2000) math:sum 3625}] + skolem:lemma3623 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2624]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2246]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1625]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3625]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1625 a r:Inference; r:gives { - 2625 :kaprekar (0 3). + 3626 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2625 math:notEqualTo 0}] - skolem:lemma3023 - [ a r:Fact; r:gives {((2 6 2 5) "=<") list:sort (2 2 5 6)}] - [ a r:Fact; r:gives {((2 6 2 5) ">=") list:sort (6 5 2 2)}] - skolem:lemma2499 - skolem:lemma2500 - [ a r:Fact; r:gives {(6522 2256) math:difference 4266}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4266 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 4266 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1626}] + [ a r:Fact; r:gives {(1626 2000) math:sum 3626}] + skolem:lemma3624 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2625]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2256]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1626]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3626]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1626 a r:Inference; r:gives { - 2626 :kaprekar (0 4). + 3627 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2626 math:notEqualTo 0}] - skolem:lemma3024 - [ a r:Fact; r:gives {((2 6 2 6) "=<") list:sort (2 2 6 6)}] - [ a r:Fact; r:gives {((2 6 2 6) ">=") list:sort (6 6 2 2)}] - skolem:lemma2517 - skolem:lemma2518 - [ a r:Fact; r:gives {(6622 2266) math:difference 4356}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4356 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 4356 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1627}] + [ a r:Fact; r:gives {(1627 2000) math:sum 3627}] + skolem:lemma3625 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2626]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4356]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1627]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3627]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1627 a r:Inference; r:gives { - 2627 :kaprekar (0 5). + 3628 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2627 math:notEqualTo 0}] - skolem:lemma3025 - [ a r:Fact; r:gives {((2 6 2 7) "=<") list:sort (2 2 6 7)}] - [ a r:Fact; r:gives {((2 6 2 7) ">=") list:sort (7 6 2 2)}] - skolem:lemma2520 - skolem:lemma2521 - [ a r:Fact; r:gives {(7622 2267) math:difference 5355}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5355 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5355 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1628}] + [ a r:Fact; r:gives {(1628 2000) math:sum 3628}] + skolem:lemma3626 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2627]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1628]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3628]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1628 a r:Inference; r:gives { - 2628 :kaprekar (0 4). + 3629 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2628 math:notEqualTo 0}] - skolem:lemma3026 - [ a r:Fact; r:gives {((2 6 2 8) "=<") list:sort (2 2 6 8)}] - [ a r:Fact; r:gives {((2 6 2 8) ">=") list:sort (8 6 2 2)}] - skolem:lemma2523 - skolem:lemma2524 - [ a r:Fact; r:gives {(8622 2268) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1629}] + [ a r:Fact; r:gives {(1629 2000) math:sum 3629}] + skolem:lemma3627 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2628]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2268]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1629]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3629]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1629 a r:Inference; r:gives { - 2629 :kaprekar (0 3). + 3630 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2629 math:notEqualTo 0}] - skolem:lemma3027 - [ a r:Fact; r:gives {((2 6 2 9) "=<") list:sort (2 2 6 9)}] - [ a r:Fact; r:gives {((2 6 2 9) ">=") list:sort (9 6 2 2)}] - skolem:lemma2526 - skolem:lemma2527 - [ a r:Fact; r:gives {(9622 2269) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1630}] + [ a r:Fact; r:gives {(1630 2000) math:sum 3630}] + skolem:lemma3628 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2629]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2269]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1630 a r:Inference; r:gives { - 2630 :kaprekar (0 7). + 3631 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2630 math:notEqualTo 0}] - skolem:lemma3028 - [ a r:Fact; r:gives {((2 6 3 0) "=<") list:sort (0 2 3 6)}] - [ a r:Fact; r:gives {((2 6 3 0) ">=") list:sort (6 3 2 0)}] - skolem:lemma2098 - skolem:lemma2099 - [ a r:Fact; r:gives {(6320 236) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1631}] + [ a r:Fact; r:gives {(1631 2000) math:sum 3631}] + skolem:lemma3629 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2630]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 236]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1631 a r:Inference; r:gives { - 2631 :kaprekar (0 7). + 3632 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2631 math:notEqualTo 0}] - skolem:lemma3029 - [ a r:Fact; r:gives {((2 6 3 1) "=<") list:sort (1 2 3 6)}] - [ a r:Fact; r:gives {((2 6 3 1) ">=") list:sort (6 3 2 1)}] - skolem:lemma2288 - skolem:lemma2289 - [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1632}] + [ a r:Fact; r:gives {(1632 2000) math:sum 3632}] + skolem:lemma3630 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2631]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1236]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1632 a r:Inference; r:gives { - 2632 :kaprekar (0 7). + 3633 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2632 math:notEqualTo 0}] - skolem:lemma3030 - [ a r:Fact; r:gives {((2 6 3 2) "=<") list:sort (2 2 3 6)}] - [ a r:Fact; r:gives {((2 6 3 2) ">=") list:sort (6 3 2 2)}] - skolem:lemma2457 - skolem:lemma2458 - [ a r:Fact; r:gives {(6322 2236) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1633}] + [ a r:Fact; r:gives {(1633 2000) math:sum 3633}] + skolem:lemma3631 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2236]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1633 a r:Inference; r:gives { - 2633 :kaprekar (0 4). + 3634 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2633 math:notEqualTo 0}] - skolem:lemma3031 - [ a r:Fact; r:gives {((2 6 3 3) "=<") list:sort (2 3 3 6)}] - [ a r:Fact; r:gives {((2 6 3 3) ">=") list:sort (6 3 3 2)}] - skolem:lemma2613 - skolem:lemma2614 - [ a r:Fact; r:gives {(6332 2336) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1634}] + [ a r:Fact; r:gives {(1634 2000) math:sum 3634}] + skolem:lemma3632 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2633]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2336]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1634]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3634]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1634 a r:Inference; r:gives { - 2634 :kaprekar (0 7). + 3635 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2634 math:notEqualTo 0}] - skolem:lemma3032 - [ a r:Fact; r:gives {((2 6 3 4) "=<") list:sort (2 3 4 6)}] - [ a r:Fact; r:gives {((2 6 3 4) ">=") list:sort (6 4 3 2)}] - skolem:lemma2635 - skolem:lemma2636 - [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1635}] + [ a r:Fact; r:gives {(1635 2000) math:sum 3635}] + skolem:lemma3633 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2634]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2346]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1635]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3635]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1635 a r:Inference; r:gives { - 2635 :kaprekar (0 2). + 3636 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2635 math:notEqualTo 0}] - skolem:lemma3033 - [ a r:Fact; r:gives {((2 6 3 5) "=<") list:sort (2 3 5 6)}] - [ a r:Fact; r:gives {((2 6 3 5) ">=") list:sort (6 5 3 2)}] - skolem:lemma2655 - skolem:lemma2656 - [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1636}] + [ a r:Fact; r:gives {(1636 2000) math:sum 3636}] + skolem:lemma3634 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2635]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2356]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1636]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3636]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1636 a r:Inference; r:gives { - 2636 :kaprekar (0 3). + 3637 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2636 math:notEqualTo 0}] - skolem:lemma3034 - [ a r:Fact; r:gives {((2 6 3 6) "=<") list:sort (2 3 6 6)}] - [ a r:Fact; r:gives {((2 6 3 6) ">=") list:sort (6 6 3 2)}] - skolem:lemma2673 - skolem:lemma2674 - [ a r:Fact; r:gives {(6632 2366) math:difference 4266}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4266 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 4266 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1637}] + [ a r:Fact; r:gives {(1637 2000) math:sum 3637}] + skolem:lemma3635 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2636]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2366]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1637]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3637]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1637 a r:Inference; r:gives { - 2637 :kaprekar (0 5). + 3638 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2637 math:notEqualTo 0}] - skolem:lemma3035 - [ a r:Fact; r:gives {((2 6 3 7) "=<") list:sort (2 3 6 7)}] - [ a r:Fact; r:gives {((2 6 3 7) ">=") list:sort (7 6 3 2)}] - skolem:lemma2676 - skolem:lemma2677 - [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1638}] + [ a r:Fact; r:gives {(1638 2000) math:sum 3638}] + skolem:lemma3636 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2637]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2367]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1638]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3638]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1638 a r:Inference; r:gives { - 2638 :kaprekar (0 3). + 3639 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2638 math:notEqualTo 0}] - skolem:lemma3036 - [ a r:Fact; r:gives {((2 6 3 8) "=<") list:sort (2 3 6 8)}] - [ a r:Fact; r:gives {((2 6 3 8) ">=") list:sort (8 6 3 2)}] - skolem:lemma2679 - skolem:lemma2680 - [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1639}] + [ a r:Fact; r:gives {(1639 2000) math:sum 3639}] + skolem:lemma3637 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2638]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2368]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1639]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3639]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1639 a r:Inference; r:gives { - 2639 :kaprekar (0 6). + 3640 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2639 math:notEqualTo 0}] - skolem:lemma3037 - [ a r:Fact; r:gives {((2 6 3 9) "=<") list:sort (2 3 6 9)}] - [ a r:Fact; r:gives {((2 6 3 9) ">=") list:sort (9 6 3 2)}] - skolem:lemma2682 - skolem:lemma2683 - [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1640}] + [ a r:Fact; r:gives {(1640 2000) math:sum 3640}] + skolem:lemma3638 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2639]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2369]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1640]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3640]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1640 a r:Inference; r:gives { - 2640 :kaprekar (0 1). + 3641 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2640 math:notEqualTo 0}] - skolem:lemma3038 - [ a r:Fact; r:gives {((2 6 4 0) "=<") list:sort (0 2 4 6)}] - [ a r:Fact; r:gives {((2 6 4 0) ">=") list:sort (6 4 2 0)}] - skolem:lemma2120 - skolem:lemma2121 - [ a r:Fact; r:gives {(6420 246) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1641}] + [ a r:Fact; r:gives {(1641 2000) math:sum 3641}] + skolem:lemma3639 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2640]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 246]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1641]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3641]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1641 a r:Inference; r:gives { - 2641 :kaprekar (0 7). + 3642 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2641 math:notEqualTo 0}] - skolem:lemma3039 - [ a r:Fact; r:gives {((2 6 4 1) "=<") list:sort (1 2 4 6)}] - [ a r:Fact; r:gives {((2 6 4 1) ">=") list:sort (6 4 2 1)}] - skolem:lemma2310 - skolem:lemma2311 - [ a r:Fact; r:gives {(6421 1246) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1642}] + [ a r:Fact; r:gives {(1642 2000) math:sum 3642}] + skolem:lemma3640 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2641]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1246]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1642 a r:Inference; r:gives { - 2642 :kaprekar (0 2). + 3643 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2642 math:notEqualTo 0}] - skolem:lemma3040 - [ a r:Fact; r:gives {((2 6 4 2) "=<") list:sort (2 2 4 6)}] - [ a r:Fact; r:gives {((2 6 4 2) ">=") list:sort (6 4 2 2)}] - skolem:lemma2479 - skolem:lemma2480 - [ a r:Fact; r:gives {(6422 2246) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1643}] + [ a r:Fact; r:gives {(1643 2000) math:sum 3643}] + skolem:lemma3641 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2246]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1643 a r:Inference; r:gives { - 2643 :kaprekar (0 7). + 3644 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2643 math:notEqualTo 0}] - skolem:lemma3041 - [ a r:Fact; r:gives {((2 6 4 3) "=<") list:sort (2 3 4 6)}] - [ a r:Fact; r:gives {((2 6 4 3) ">=") list:sort (6 4 3 2)}] - skolem:lemma2635 - skolem:lemma2636 - [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1644}] + [ a r:Fact; r:gives {(1644 2000) math:sum 3644}] + skolem:lemma3642 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2643]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2346]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1644]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3644]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1644 a r:Inference; r:gives { - 2644 :kaprekar (0 4). + 3645 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2644 math:notEqualTo 0}] - skolem:lemma3042 - [ a r:Fact; r:gives {((2 6 4 4) "=<") list:sort (2 4 4 6)}] - [ a r:Fact; r:gives {((2 6 4 4) ">=") list:sort (6 4 4 2)}] - skolem:lemma2777 - skolem:lemma2778 - [ a r:Fact; r:gives {(6442 2446) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1645}] + [ a r:Fact; r:gives {(1645 2000) math:sum 3645}] + skolem:lemma3643 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2644]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2446]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1645]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3645]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1645 a r:Inference; r:gives { - 2645 :kaprekar (0 7). + 3646 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2645 math:notEqualTo 0}] - skolem:lemma3043 - [ a r:Fact; r:gives {((2 6 4 5) "=<") list:sort (2 4 5 6)}] - [ a r:Fact; r:gives {((2 6 4 5) ">=") list:sort (6 5 4 2)}] - skolem:lemma2797 - skolem:lemma2798 - [ a r:Fact; r:gives {(6542 2456) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1646}] + [ a r:Fact; r:gives {(1646 2000) math:sum 3646}] + skolem:lemma3644 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2645]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2456]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1646]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3646]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1646 a r:Inference; r:gives { - 2646 :kaprekar (0 2). + 3647 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2646 math:notEqualTo 0}] - skolem:lemma3044 - [ a r:Fact; r:gives {((2 6 4 6) "=<") list:sort (2 4 6 6)}] - [ a r:Fact; r:gives {((2 6 4 6) ">=") list:sort (6 6 4 2)}] - skolem:lemma2815 - skolem:lemma2816 - [ a r:Fact; r:gives {(6642 2466) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1647}] + [ a r:Fact; r:gives {(1647 2000) math:sum 3647}] + skolem:lemma3645 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2646]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2466]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1647]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3647]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1647 a r:Inference; r:gives { - 2647 :kaprekar (0 7). + 3648 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2647 math:notEqualTo 0}] - skolem:lemma3045 - [ a r:Fact; r:gives {((2 6 4 7) "=<") list:sort (2 4 6 7)}] - [ a r:Fact; r:gives {((2 6 4 7) ">=") list:sort (7 6 4 2)}] - skolem:lemma2818 - skolem:lemma2819 - [ a r:Fact; r:gives {(7642 2467) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1648}] + [ a r:Fact; r:gives {(1648 2000) math:sum 3648}] + skolem:lemma3646 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2647]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2467]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1648]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3648]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1648 a r:Inference; r:gives { - 2648 :kaprekar (0 1). + 3649 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2648 math:notEqualTo 0}] - skolem:lemma3046 - [ a r:Fact; r:gives {((2 6 4 8) "=<") list:sort (2 4 6 8)}] - [ a r:Fact; r:gives {((2 6 4 8) ">=") list:sort (8 6 4 2)}] - skolem:lemma2821 - skolem:lemma2822 - [ a r:Fact; r:gives {(8642 2468) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1649}] + [ a r:Fact; r:gives {(1649 2000) math:sum 3649}] + skolem:lemma3647 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2648]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2468]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1649]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3649]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1649 a r:Inference; r:gives { - 2649 :kaprekar (0 5). + 3650 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2649 math:notEqualTo 0}] - skolem:lemma3047 - [ a r:Fact; r:gives {((2 6 4 9) "=<") list:sort (2 4 6 9)}] - [ a r:Fact; r:gives {((2 6 4 9) ">=") list:sort (9 6 4 2)}] - skolem:lemma2824 - skolem:lemma2825 - [ a r:Fact; r:gives {(9642 2469) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1650}] + [ a r:Fact; r:gives {(1650 2000) math:sum 3650}] + skolem:lemma3648 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2649]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2469]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1650]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3650]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1650 a r:Inference; r:gives { - 2650 :kaprekar (0 3). + 3651 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2650 math:notEqualTo 0}] - skolem:lemma3048 - [ a r:Fact; r:gives {((2 6 5 0) "=<") list:sort (0 2 5 6)}] - [ a r:Fact; r:gives {((2 6 5 0) ">=") list:sort (6 5 2 0)}] - skolem:lemma2140 - skolem:lemma2141 - [ a r:Fact; r:gives {(6520 256) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1651}] + [ a r:Fact; r:gives {(1651 2000) math:sum 3651}] + skolem:lemma3649 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2650]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 256]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1651]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3651]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1651 a r:Inference; r:gives { - 2651 :kaprekar (0 5). + 3652 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2651 math:notEqualTo 0}] - skolem:lemma3049 - [ a r:Fact; r:gives {((2 6 5 1) "=<") list:sort (1 2 5 6)}] - [ a r:Fact; r:gives {((2 6 5 1) ">=") list:sort (6 5 2 1)}] - skolem:lemma2330 - skolem:lemma2331 - [ a r:Fact; r:gives {(6521 1256) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1652}] + [ a r:Fact; r:gives {(1652 2000) math:sum 3652}] + skolem:lemma3650 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2651]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1256]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1652 a r:Inference; r:gives { - 2652 :kaprekar (0 3). + 3653 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2652 math:notEqualTo 0}] - skolem:lemma3050 - [ a r:Fact; r:gives {((2 6 5 2) "=<") list:sort (2 2 5 6)}] - [ a r:Fact; r:gives {((2 6 5 2) ">=") list:sort (6 5 2 2)}] - skolem:lemma2499 - skolem:lemma2500 - [ a r:Fact; r:gives {(6522 2256) math:difference 4266}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4266 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 4266 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1653}] + [ a r:Fact; r:gives {(1653 2000) math:sum 3653}] + skolem:lemma3651 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2256]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1653 a r:Inference; r:gives { - 2653 :kaprekar (0 2). + 3654 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2653 math:notEqualTo 0}] - skolem:lemma3051 - [ a r:Fact; r:gives {((2 6 5 3) "=<") list:sort (2 3 5 6)}] - [ a r:Fact; r:gives {((2 6 5 3) ">=") list:sort (6 5 3 2)}] - skolem:lemma2655 - skolem:lemma2656 - [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1654}] + [ a r:Fact; r:gives {(1654 2000) math:sum 3654}] + skolem:lemma3652 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2653]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2356]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1654]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3654]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1654 a r:Inference; r:gives { - 2654 :kaprekar (0 7). + 3655 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2654 math:notEqualTo 0}] - skolem:lemma3052 - [ a r:Fact; r:gives {((2 6 5 4) "=<") list:sort (2 4 5 6)}] - [ a r:Fact; r:gives {((2 6 5 4) ">=") list:sort (6 5 4 2)}] - skolem:lemma2797 - skolem:lemma2798 - [ a r:Fact; r:gives {(6542 2456) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1655}] + [ a r:Fact; r:gives {(1655 2000) math:sum 3655}] + skolem:lemma3653 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2654]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2456]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1655]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3655]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1655 a r:Inference; r:gives { - 2655 :kaprekar (0 4). + 3656 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2655 math:notEqualTo 0}] - skolem:lemma3053 - [ a r:Fact; r:gives {((2 6 5 5) "=<") list:sort (2 5 5 6)}] - [ a r:Fact; r:gives {((2 6 5 5) ">=") list:sort (6 5 5 2)}] - skolem:lemma2927 - skolem:lemma2928 - [ a r:Fact; r:gives {(6552 2556) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1656}] + [ a r:Fact; r:gives {(1656 2000) math:sum 3656}] + skolem:lemma3654 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2655]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2556]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6552]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1656]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3656]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1656 a r:Inference; r:gives { - 2656 :kaprekar (0 7). + 3657 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2656 math:notEqualTo 0}] - skolem:lemma3054 - [ a r:Fact; r:gives {((2 6 5 6) "=<") list:sort (2 5 6 6)}] - [ a r:Fact; r:gives {((2 6 5 6) ">=") list:sort (6 6 5 2)}] - skolem:lemma2945 - skolem:lemma2946 - [ a r:Fact; r:gives {(6652 2566) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1657}] + [ a r:Fact; r:gives {(1657 2000) math:sum 3657}] + skolem:lemma3655 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2656]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2566]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1657]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3657]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1657 a r:Inference; r:gives { - 2657 :kaprekar (0 7). + 3658 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2657 math:notEqualTo 0}] - skolem:lemma3055 - [ a r:Fact; r:gives {((2 6 5 7) "=<") list:sort (2 5 6 7)}] - [ a r:Fact; r:gives {((2 6 5 7) ">=") list:sort (7 6 5 2)}] - skolem:lemma2948 - skolem:lemma2949 - [ a r:Fact; r:gives {(7652 2567) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1658}] + [ a r:Fact; r:gives {(1658 2000) math:sum 3658}] + skolem:lemma3656 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2657]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2567]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1658]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3658]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1658 a r:Inference; r:gives { - 2658 :kaprekar (0 7). + 3659 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2658 math:notEqualTo 0}] - skolem:lemma3056 - [ a r:Fact; r:gives {((2 6 5 8) "=<") list:sort (2 5 6 8)}] - [ a r:Fact; r:gives {((2 6 5 8) ">=") list:sort (8 6 5 2)}] - skolem:lemma2951 - skolem:lemma2952 - [ a r:Fact; r:gives {(8652 2568) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1659}] + [ a r:Fact; r:gives {(1659 2000) math:sum 3659}] + skolem:lemma3657 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2658]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2568]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1659]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3659]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1659 a r:Inference; r:gives { - 2659 :kaprekar (0 3). + 3660 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2659 math:notEqualTo 0}] - skolem:lemma3057 - [ a r:Fact; r:gives {((2 6 5 9) "=<") list:sort (2 5 6 9)}] - [ a r:Fact; r:gives {((2 6 5 9) ">=") list:sort (9 6 5 2)}] - skolem:lemma2954 - skolem:lemma2955 - [ a r:Fact; r:gives {(9652 2569) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1660}] + [ a r:Fact; r:gives {(1660 2000) math:sum 3660}] + skolem:lemma3658 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2659]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2569]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1660]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3660]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1660 a r:Inference; r:gives { - 2660 :kaprekar (0 4). + 3661 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2660 math:notEqualTo 0}] - skolem:lemma3058 - [ a r:Fact; r:gives {((2 6 6 0) "=<") list:sort (0 2 6 6)}] - [ a r:Fact; r:gives {((2 6 6 0) ">=") list:sort (6 6 2 0)}] - skolem:lemma2158 - skolem:lemma2159 - [ a r:Fact; r:gives {(6620 266) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1661}] + [ a r:Fact; r:gives {(1661 2000) math:sum 3661}] + skolem:lemma3659 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2660]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6620]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1661]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3661]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1661 a r:Inference; r:gives { - 2661 :kaprekar (0 5). + 3662 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2661 math:notEqualTo 0}] - skolem:lemma3059 - [ a r:Fact; r:gives {((2 6 6 1) "=<") list:sort (1 2 6 6)}] - [ a r:Fact; r:gives {((2 6 6 1) ">=") list:sort (6 6 2 1)}] - skolem:lemma2348 - skolem:lemma2349 - [ a r:Fact; r:gives {(6621 1266) math:difference 5355}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5355 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5355 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1662}] + [ a r:Fact; r:gives {(1662 2000) math:sum 3662}] + skolem:lemma3660 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2661]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1662]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3662]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1662 a r:Inference; r:gives { - 2662 :kaprekar (0 4). + 3663 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2662 math:notEqualTo 0}] - skolem:lemma3060 - [ a r:Fact; r:gives {((2 6 6 2) "=<") list:sort (2 2 6 6)}] - [ a r:Fact; r:gives {((2 6 6 2) ">=") list:sort (6 6 2 2)}] - skolem:lemma2517 - skolem:lemma2518 - [ a r:Fact; r:gives {(6622 2266) math:difference 4356}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4356 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 4356 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1663}] + [ a r:Fact; r:gives {(1663 2000) math:sum 3663}] + skolem:lemma3661 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2662]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4356]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1663]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3663]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1663 a r:Inference; r:gives { - 2663 :kaprekar (0 3). + 3664 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2663 math:notEqualTo 0}] - skolem:lemma3061 - [ a r:Fact; r:gives {((2 6 6 3) "=<") list:sort (2 3 6 6)}] - [ a r:Fact; r:gives {((2 6 6 3) ">=") list:sort (6 6 3 2)}] - skolem:lemma2673 - skolem:lemma2674 - [ a r:Fact; r:gives {(6632 2366) math:difference 4266}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4266 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 4266 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1664}] + [ a r:Fact; r:gives {(1664 2000) math:sum 3664}] + skolem:lemma3662 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2663]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2366]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1664]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3664]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1664 a r:Inference; r:gives { - 2664 :kaprekar (0 2). + 3665 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2664 math:notEqualTo 0}] - skolem:lemma3062 - [ a r:Fact; r:gives {((2 6 6 4) "=<") list:sort (2 4 6 6)}] - [ a r:Fact; r:gives {((2 6 6 4) ">=") list:sort (6 6 4 2)}] - skolem:lemma2815 - skolem:lemma2816 - [ a r:Fact; r:gives {(6642 2466) math:difference 4176}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4176 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 4176 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1665}] + [ a r:Fact; r:gives {(1665 2000) math:sum 3665}] + skolem:lemma3663 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2664]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2466]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1665]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3665]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1665 a r:Inference; r:gives { - 2665 :kaprekar (0 7). + 3666 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2665 math:notEqualTo 0}] - skolem:lemma3063 - [ a r:Fact; r:gives {((2 6 6 5) "=<") list:sort (2 5 6 6)}] - [ a r:Fact; r:gives {((2 6 6 5) ">=") list:sort (6 6 5 2)}] - skolem:lemma2945 - skolem:lemma2946 - [ a r:Fact; r:gives {(6652 2566) math:difference 4086}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4086 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 4086 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1666}] + [ a r:Fact; r:gives {(1666 2000) math:sum 3666}] + skolem:lemma3664 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2665]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2566]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1666]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3666]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1666 a r:Inference; r:gives { - 2666 :kaprekar (0 4). + 3667 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2666 math:notEqualTo 0}] - skolem:lemma3064 - [ a r:Fact; r:gives {((2 6 6 6) "=<") list:sort (2 6 6 6)}] - [ a r:Fact; r:gives {((2 6 6 6) ">=") list:sort (6 6 6 2)}] - skolem:lemma3065 - skolem:lemma3066 - [ a r:Fact; r:gives {(6662 2666) math:difference 3996}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 3996 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 3996 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1667}] + [ a r:Fact; r:gives {(1667 2000) math:sum 3667}] + skolem:lemma3665 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2666]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2666]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6662]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1667]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3667]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1667 a r:Inference; r:gives { - 2667 :kaprekar (0 6). + 3668 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2667 math:notEqualTo 0}] - skolem:lemma3067 - [ a r:Fact; r:gives {((2 6 6 7) "=<") list:sort (2 6 6 7)}] - [ a r:Fact; r:gives {((2 6 6 7) ">=") list:sort (7 6 6 2)}] - skolem:lemma3068 - skolem:lemma3069 - [ a r:Fact; r:gives {(7662 2667) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1668}] + [ a r:Fact; r:gives {(1668 2000) math:sum 3668}] + skolem:lemma3666 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2667]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2667]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7662]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1668]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3668]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1668 a r:Inference; r:gives { - 2668 :kaprekar (0 6). + 3669 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2668 math:notEqualTo 0}] - skolem:lemma3070 - [ a r:Fact; r:gives {((2 6 6 8) "=<") list:sort (2 6 6 8)}] - [ a r:Fact; r:gives {((2 6 6 8) ">=") list:sort (8 6 6 2)}] - skolem:lemma3071 - skolem:lemma3072 - [ a r:Fact; r:gives {(8662 2668) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1669}] + [ a r:Fact; r:gives {(1669 2000) math:sum 3669}] + skolem:lemma3667 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2668]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2668]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8662]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1669]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3669]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1669 a r:Inference; r:gives { - 2669 :kaprekar (0 4). + 3670 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2669 math:notEqualTo 0}] - skolem:lemma3073 - [ a r:Fact; r:gives {((2 6 6 9) "=<") list:sort (2 6 6 9)}] - [ a r:Fact; r:gives {((2 6 6 9) ">=") list:sort (9 6 6 2)}] - skolem:lemma3074 - skolem:lemma3075 - [ a r:Fact; r:gives {(9662 2669) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1670}] + [ a r:Fact; r:gives {(1670 2000) math:sum 3670}] + skolem:lemma3668 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2669]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2669]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9662]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1670]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3670]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1670 a r:Inference; r:gives { - 2670 :kaprekar (0 3). + 3671 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2670 math:notEqualTo 0}] - skolem:lemma3076 - [ a r:Fact; r:gives {((2 6 7 0) "=<") list:sort (0 2 6 7)}] - [ a r:Fact; r:gives {((2 6 7 0) ">=") list:sort (7 6 2 0)}] - skolem:lemma2161 - skolem:lemma2162 - [ a r:Fact; r:gives {(7620 267) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1671}] + [ a r:Fact; r:gives {(1671 2000) math:sum 3671}] + skolem:lemma3669 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2670]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7620]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1671]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3671]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1671 a r:Inference; r:gives { - 2671 :kaprekar (0 4). + 3672 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2671 math:notEqualTo 0}] - skolem:lemma3077 - [ a r:Fact; r:gives {((2 6 7 1) "=<") list:sort (1 2 6 7)}] - [ a r:Fact; r:gives {((2 6 7 1) ">=") list:sort (7 6 2 1)}] - skolem:lemma2351 - skolem:lemma2352 - [ a r:Fact; r:gives {(7621 1267) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1672}] + [ a r:Fact; r:gives {(1672 2000) math:sum 3672}] + skolem:lemma3670 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2671]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1672]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3672]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1672 a r:Inference; r:gives { - 2672 :kaprekar (0 5). + 3673 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2672 math:notEqualTo 0}] - skolem:lemma3078 - [ a r:Fact; r:gives {((2 6 7 2) "=<") list:sort (2 2 6 7)}] - [ a r:Fact; r:gives {((2 6 7 2) ">=") list:sort (7 6 2 2)}] - skolem:lemma2520 - skolem:lemma2521 - [ a r:Fact; r:gives {(7622 2267) math:difference 5355}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5355 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5355 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1673}] + [ a r:Fact; r:gives {(1673 2000) math:sum 3673}] + skolem:lemma3671 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2672]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1673]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3673]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1673 a r:Inference; r:gives { - 2673 :kaprekar (0 5). + 3674 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2673 math:notEqualTo 0}] - skolem:lemma3079 - [ a r:Fact; r:gives {((2 6 7 3) "=<") list:sort (2 3 6 7)}] - [ a r:Fact; r:gives {((2 6 7 3) ">=") list:sort (7 6 3 2)}] - skolem:lemma2676 - skolem:lemma2677 - [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1674}] + [ a r:Fact; r:gives {(1674 2000) math:sum 3674}] + skolem:lemma3672 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2673]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2367]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1674]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3674]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1674 a r:Inference; r:gives { - 2674 :kaprekar (0 7). + 3675 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2674 math:notEqualTo 0}] - skolem:lemma3080 - [ a r:Fact; r:gives {((2 6 7 4) "=<") list:sort (2 4 6 7)}] - [ a r:Fact; r:gives {((2 6 7 4) ">=") list:sort (7 6 4 2)}] - skolem:lemma2818 - skolem:lemma2819 - [ a r:Fact; r:gives {(7642 2467) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1675}] + [ a r:Fact; r:gives {(1675 2000) math:sum 3675}] + skolem:lemma3673 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2674]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2467]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1675]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3675]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1675 a r:Inference; r:gives { - 2675 :kaprekar (0 7). + 3676 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2675 math:notEqualTo 0}] - skolem:lemma3081 - [ a r:Fact; r:gives {((2 6 7 5) "=<") list:sort (2 5 6 7)}] - [ a r:Fact; r:gives {((2 6 7 5) ">=") list:sort (7 6 5 2)}] - skolem:lemma2948 - skolem:lemma2949 - [ a r:Fact; r:gives {(7652 2567) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1676}] + [ a r:Fact; r:gives {(1676 2000) math:sum 3676}] + skolem:lemma3674 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2675]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2567]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1676]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3676]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1676 a r:Inference; r:gives { - 2676 :kaprekar (0 6). + 3677 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2676 math:notEqualTo 0}] - skolem:lemma3082 - [ a r:Fact; r:gives {((2 6 7 6) "=<") list:sort (2 6 6 7)}] - [ a r:Fact; r:gives {((2 6 7 6) ">=") list:sort (7 6 6 2)}] - skolem:lemma3068 - skolem:lemma3069 - [ a r:Fact; r:gives {(7662 2667) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1677}] + [ a r:Fact; r:gives {(1677 2000) math:sum 3677}] + skolem:lemma3675 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2676]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2667]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7662]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1677]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3677]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1677 a r:Inference; r:gives { - 2677 :kaprekar (0 7). + 3678 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2677 math:notEqualTo 0}] - skolem:lemma3083 - [ a r:Fact; r:gives {((2 6 7 7) "=<") list:sort (2 6 7 7)}] - [ a r:Fact; r:gives {((2 6 7 7) ">=") list:sort (7 7 6 2)}] - skolem:lemma3084 - skolem:lemma3085 - [ a r:Fact; r:gives {(7762 2677) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1678}] + [ a r:Fact; r:gives {(1678 2000) math:sum 3678}] + skolem:lemma3676 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2677]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2677]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7762]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1678]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3678]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1678 a r:Inference; r:gives { - 2678 :kaprekar (0 7). + 3679 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2678 math:notEqualTo 0}] - skolem:lemma3086 - [ a r:Fact; r:gives {((2 6 7 8) "=<") list:sort (2 6 7 8)}] - [ a r:Fact; r:gives {((2 6 7 8) ">=") list:sort (8 7 6 2)}] - skolem:lemma3087 - skolem:lemma3088 - [ a r:Fact; r:gives {(8762 2678) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1679}] + [ a r:Fact; r:gives {(1679 2000) math:sum 3679}] + skolem:lemma3677 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2678]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2678]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8762]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1679]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3679]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1679 a r:Inference; r:gives { - 2679 :kaprekar (0 3). + 3680 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2679 math:notEqualTo 0}] - skolem:lemma3089 - [ a r:Fact; r:gives {((2 6 7 9) "=<") list:sort (2 6 7 9)}] - [ a r:Fact; r:gives {((2 6 7 9) ">=") list:sort (9 7 6 2)}] - skolem:lemma3090 - skolem:lemma3091 - [ a r:Fact; r:gives {(9762 2679) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1680}] + [ a r:Fact; r:gives {(1680 2000) math:sum 3680}] + skolem:lemma3678 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2679]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2679]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9762]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1680]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3680]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1680 a r:Inference; r:gives { - 2680 :kaprekar (0 2). + 3681 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2680 math:notEqualTo 0}] - skolem:lemma3092 - [ a r:Fact; r:gives {((2 6 8 0) "=<") list:sort (0 2 6 8)}] - [ a r:Fact; r:gives {((2 6 8 0) ">=") list:sort (8 6 2 0)}] - skolem:lemma2164 - skolem:lemma2165 - [ a r:Fact; r:gives {(8620 268) math:difference 8352}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8352 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 8352 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1681}] + [ a r:Fact; r:gives {(1681 2000) math:sum 3681}] + skolem:lemma3679 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2680]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 268]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8620]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1681]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3681]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1681 a r:Inference; r:gives { - 2681 :kaprekar (0 3). + 3682 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2681 math:notEqualTo 0}] - skolem:lemma3093 - [ a r:Fact; r:gives {((2 6 8 1) "=<") list:sort (1 2 6 8)}] - [ a r:Fact; r:gives {((2 6 8 1) ">=") list:sort (8 6 2 1)}] - skolem:lemma2354 - skolem:lemma2355 - [ a r:Fact; r:gives {(8621 1268) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1682}] + [ a r:Fact; r:gives {(1682 2000) math:sum 3682}] + skolem:lemma3680 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2681]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1268]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1682]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3682]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1682 a r:Inference; r:gives { - 2682 :kaprekar (0 4). + 3683 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2682 math:notEqualTo 0}] - skolem:lemma3094 - [ a r:Fact; r:gives {((2 6 8 2) "=<") list:sort (2 2 6 8)}] - [ a r:Fact; r:gives {((2 6 8 2) ">=") list:sort (8 6 2 2)}] - skolem:lemma2523 - skolem:lemma2524 - [ a r:Fact; r:gives {(8622 2268) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1683}] + [ a r:Fact; r:gives {(1683 2000) math:sum 3683}] + skolem:lemma3681 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2682]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2268]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1683]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3683]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1683 a r:Inference; r:gives { - 2683 :kaprekar (0 3). + 3684 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2683 math:notEqualTo 0}] - skolem:lemma3095 - [ a r:Fact; r:gives {((2 6 8 3) "=<") list:sort (2 3 6 8)}] - [ a r:Fact; r:gives {((2 6 8 3) ">=") list:sort (8 6 3 2)}] - skolem:lemma2679 - skolem:lemma2680 - [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1684}] + [ a r:Fact; r:gives {(1684 2000) math:sum 3684}] + skolem:lemma3682 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2683]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2368]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1684]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3684]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1684 a r:Inference; r:gives { - 2684 :kaprekar (0 1). + 3685 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2684 math:notEqualTo 0}] - skolem:lemma3096 - [ a r:Fact; r:gives {((2 6 8 4) "=<") list:sort (2 4 6 8)}] - [ a r:Fact; r:gives {((2 6 8 4) ">=") list:sort (8 6 4 2)}] - skolem:lemma2821 - skolem:lemma2822 - [ a r:Fact; r:gives {(8642 2468) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1685}] + [ a r:Fact; r:gives {(1685 2000) math:sum 3685}] + skolem:lemma3683 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2684]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2468]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1685]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3685]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1685 a r:Inference; r:gives { - 2685 :kaprekar (0 7). + 3686 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2685 math:notEqualTo 0}] - skolem:lemma3097 - [ a r:Fact; r:gives {((2 6 8 5) "=<") list:sort (2 5 6 8)}] - [ a r:Fact; r:gives {((2 6 8 5) ">=") list:sort (8 6 5 2)}] - skolem:lemma2951 - skolem:lemma2952 - [ a r:Fact; r:gives {(8652 2568) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1686}] + [ a r:Fact; r:gives {(1686 2000) math:sum 3686}] + skolem:lemma3684 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2685]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2568]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1686]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3686]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1686 a r:Inference; r:gives { - 2686 :kaprekar (0 6). + 3687 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2686 math:notEqualTo 0}] - skolem:lemma3098 - [ a r:Fact; r:gives {((2 6 8 6) "=<") list:sort (2 6 6 8)}] - [ a r:Fact; r:gives {((2 6 8 6) ">=") list:sort (8 6 6 2)}] - skolem:lemma3071 - skolem:lemma3072 - [ a r:Fact; r:gives {(8662 2668) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1687}] + [ a r:Fact; r:gives {(1687 2000) math:sum 3687}] + skolem:lemma3685 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2686]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2668]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8662]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1687]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3687]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1687 a r:Inference; r:gives { - 2687 :kaprekar (0 7). + 3688 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2687 math:notEqualTo 0}] - skolem:lemma3099 - [ a r:Fact; r:gives {((2 6 8 7) "=<") list:sort (2 6 7 8)}] - [ a r:Fact; r:gives {((2 6 8 7) ">=") list:sort (8 7 6 2)}] - skolem:lemma3087 - skolem:lemma3088 - [ a r:Fact; r:gives {(8762 2678) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1688}] + [ a r:Fact; r:gives {(1688 2000) math:sum 3688}] + skolem:lemma3686 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2687]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2678]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8762]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1688]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3688]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1688 a r:Inference; r:gives { - 2688 :kaprekar (0 1). + 3689 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2688 math:notEqualTo 0}] - skolem:lemma3100 - [ a r:Fact; r:gives {((2 6 8 8) "=<") list:sort (2 6 8 8)}] - [ a r:Fact; r:gives {((2 6 8 8) ">=") list:sort (8 8 6 2)}] - skolem:lemma3101 - skolem:lemma3102 - [ a r:Fact; r:gives {(8862 2688) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1689}] + [ a r:Fact; r:gives {(1689 2000) math:sum 3689}] + skolem:lemma3687 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2688]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2688]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8862]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1689]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3689]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1689 a r:Inference; r:gives { - 2689 :kaprekar (0 5). + 3690 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2689 math:notEqualTo 0}] - skolem:lemma3103 - [ a r:Fact; r:gives {((2 6 8 9) "=<") list:sort (2 6 8 9)}] - [ a r:Fact; r:gives {((2 6 8 9) ">=") list:sort (9 8 6 2)}] - skolem:lemma3104 - skolem:lemma3105 - [ a r:Fact; r:gives {(9862 2689) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1690}] + [ a r:Fact; r:gives {(1690 2000) math:sum 3690}] + skolem:lemma3688 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2689]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2689]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9862]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1690]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3690]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1690 a r:Inference; r:gives { - 2690 :kaprekar (0 7). + 3691 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2690 math:notEqualTo 0}] - skolem:lemma3106 - [ a r:Fact; r:gives {((2 6 9 0) "=<") list:sort (0 2 6 9)}] - [ a r:Fact; r:gives {((2 6 9 0) ">=") list:sort (9 6 2 0)}] - skolem:lemma2167 - skolem:lemma2168 - [ a r:Fact; r:gives {(9620 269) math:difference 9351}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9351 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 9351 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1691}] + [ a r:Fact; r:gives {(1691 2000) math:sum 3691}] + skolem:lemma3689 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2690]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 269]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9620]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9351]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1691]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3691]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1691 a r:Inference; r:gives { - 2691 :kaprekar (0 2). + 3692 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2691 math:notEqualTo 0}] - skolem:lemma3107 - [ a r:Fact; r:gives {((2 6 9 1) "=<") list:sort (1 2 6 9)}] - [ a r:Fact; r:gives {((2 6 9 1) ">=") list:sort (9 6 2 1)}] - skolem:lemma2357 - skolem:lemma2358 - [ a r:Fact; r:gives {(9621 1269) math:difference 8352}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8352 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 8352 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1692}] + [ a r:Fact; r:gives {(1692 2000) math:sum 3692}] + skolem:lemma3690 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2691]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1269]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1692]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3692]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1692 a r:Inference; r:gives { - 2692 :kaprekar (0 3). + 3693 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2692 math:notEqualTo 0}] - skolem:lemma3108 - [ a r:Fact; r:gives {((2 6 9 2) "=<") list:sort (2 2 6 9)}] - [ a r:Fact; r:gives {((2 6 9 2) ">=") list:sort (9 6 2 2)}] - skolem:lemma2526 - skolem:lemma2527 - [ a r:Fact; r:gives {(9622 2269) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1693}] + [ a r:Fact; r:gives {(1693 2000) math:sum 3693}] + skolem:lemma3691 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2692]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2269]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1693]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3693]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1693 a r:Inference; r:gives { - 2693 :kaprekar (0 6). + 3694 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2693 math:notEqualTo 0}] - skolem:lemma3109 - [ a r:Fact; r:gives {((2 6 9 3) "=<") list:sort (2 3 6 9)}] - [ a r:Fact; r:gives {((2 6 9 3) ">=") list:sort (9 6 3 2)}] - skolem:lemma2682 - skolem:lemma2683 - [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1694}] + [ a r:Fact; r:gives {(1694 2000) math:sum 3694}] + skolem:lemma3692 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2693]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2369]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1694]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3694]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1694 a r:Inference; r:gives { - 2694 :kaprekar (0 5). + 3695 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2694 math:notEqualTo 0}] - skolem:lemma3110 - [ a r:Fact; r:gives {((2 6 9 4) "=<") list:sort (2 4 6 9)}] - [ a r:Fact; r:gives {((2 6 9 4) ">=") list:sort (9 6 4 2)}] - skolem:lemma2824 - skolem:lemma2825 - [ a r:Fact; r:gives {(9642 2469) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1695}] + [ a r:Fact; r:gives {(1695 2000) math:sum 3695}] + skolem:lemma3693 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2694]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2469]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1695]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3695]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1695 a r:Inference; r:gives { - 2695 :kaprekar (0 3). + 3696 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2695 math:notEqualTo 0}] - skolem:lemma3111 - [ a r:Fact; r:gives {((2 6 9 5) "=<") list:sort (2 5 6 9)}] - [ a r:Fact; r:gives {((2 6 9 5) ">=") list:sort (9 6 5 2)}] - skolem:lemma2954 - skolem:lemma2955 - [ a r:Fact; r:gives {(9652 2569) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1696}] + [ a r:Fact; r:gives {(1696 2000) math:sum 3696}] + skolem:lemma3694 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2695]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2569]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1696]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3696]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1696 a r:Inference; r:gives { - 2696 :kaprekar (0 4). + 3697 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2696 math:notEqualTo 0}] - skolem:lemma3112 - [ a r:Fact; r:gives {((2 6 9 6) "=<") list:sort (2 6 6 9)}] - [ a r:Fact; r:gives {((2 6 9 6) ">=") list:sort (9 6 6 2)}] - skolem:lemma3074 - skolem:lemma3075 - [ a r:Fact; r:gives {(9662 2669) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1697}] + [ a r:Fact; r:gives {(1697 2000) math:sum 3697}] + skolem:lemma3695 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2696]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2669]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9662]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1697]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3697]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1697 a r:Inference; r:gives { - 2697 :kaprekar (0 3). + 3698 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2697 math:notEqualTo 0}] - skolem:lemma3113 - [ a r:Fact; r:gives {((2 6 9 7) "=<") list:sort (2 6 7 9)}] - [ a r:Fact; r:gives {((2 6 9 7) ">=") list:sort (9 7 6 2)}] - skolem:lemma3090 - skolem:lemma3091 - [ a r:Fact; r:gives {(9762 2679) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1698}] + [ a r:Fact; r:gives {(1698 2000) math:sum 3698}] + skolem:lemma3696 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2697]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2679]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9762]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1698]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3698]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1698 a r:Inference; r:gives { - 2698 :kaprekar (0 5). + 3699 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2698 math:notEqualTo 0}] - skolem:lemma3114 - [ a r:Fact; r:gives {((2 6 9 8) "=<") list:sort (2 6 8 9)}] - [ a r:Fact; r:gives {((2 6 9 8) ">=") list:sort (9 8 6 2)}] - skolem:lemma3104 - skolem:lemma3105 - [ a r:Fact; r:gives {(9862 2689) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1699}] + [ a r:Fact; r:gives {(1699 2000) math:sum 3699}] + skolem:lemma3697 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2698]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2689]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9862]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1699]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3699]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1699 a r:Inference; r:gives { - 2699 :kaprekar (0 6). + 3700 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2699 math:notEqualTo 0}] - skolem:lemma3115 - [ a r:Fact; r:gives {((2 6 9 9) "=<") list:sort (2 6 9 9)}] - [ a r:Fact; r:gives {((2 6 9 9) ">=") list:sort (9 9 6 2)}] - skolem:lemma3116 - skolem:lemma3117 - [ a r:Fact; r:gives {(9962 2699) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1700}] + [ a r:Fact; r:gives {(1700 2000) math:sum 3700}] + skolem:lemma3698 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2699]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2699]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9962]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1700 a r:Inference; r:gives { - 2700 :kaprekar (0 5). + 3701 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2700 math:notEqualTo 0}] - skolem:lemma3118 - [ a r:Fact; r:gives {((2 7 0 0) "=<") list:sort (0 0 2 7)}] - [ a r:Fact; r:gives {((2 7 0 0) ">=") list:sort (7 2 0 0)}] - skolem:lemma2023 - skolem:lemma2024 - [ a r:Fact; r:gives {(7200 27) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1701}] + [ a r:Fact; r:gives {(1701 2000) math:sum 3701}] + skolem:lemma3699 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2700]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1701]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3701]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1701 a r:Inference; r:gives { - 2701 :kaprekar (0 3). + 3702 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2701 math:notEqualTo 0}] - skolem:lemma3119 - [ a r:Fact; r:gives {((2 7 0 1) "=<") list:sort (0 1 2 7)}] - [ a r:Fact; r:gives {((2 7 0 1) ">=") list:sort (7 2 1 0)}] - skolem:lemma2051 - skolem:lemma2052 - [ a r:Fact; r:gives {(7210 127) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1702}] + [ a r:Fact; r:gives {(1702 2000) math:sum 3702}] + skolem:lemma3700 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2701]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 127]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1702]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3702]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1702 a r:Inference; r:gives { - 2702 :kaprekar (0 4). + 3703 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2702 math:notEqualTo 0}] - skolem:lemma3120 - [ a r:Fact; r:gives {((2 7 0 2) "=<") list:sort (0 2 2 7)}] - [ a r:Fact; r:gives {((2 7 0 2) ">=") list:sort (7 2 2 0)}] - skolem:lemma2077 - skolem:lemma2078 - [ a r:Fact; r:gives {(7220 227) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1703}] + [ a r:Fact; r:gives {(1703 2000) math:sum 3703}] + skolem:lemma3701 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2702]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 227]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1703]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3703]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1703 a r:Inference; r:gives { - 2703 :kaprekar (0 3). + 3704 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2703 math:notEqualTo 0}] - skolem:lemma3121 - [ a r:Fact; r:gives {((2 7 0 3) "=<") list:sort (0 2 3 7)}] - [ a r:Fact; r:gives {((2 7 0 3) ">=") list:sort (7 3 2 0)}] - skolem:lemma2101 - skolem:lemma2102 - [ a r:Fact; r:gives {(7320 237) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1704}] + [ a r:Fact; r:gives {(1704 2000) math:sum 3704}] + skolem:lemma3702 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2703]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 237]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1704]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3704]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1704 a r:Inference; r:gives { - 2704 :kaprekar (0 5). + 3705 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2704 math:notEqualTo 0}] - skolem:lemma3122 - [ a r:Fact; r:gives {((2 7 0 4) "=<") list:sort (0 2 4 7)}] - [ a r:Fact; r:gives {((2 7 0 4) ">=") list:sort (7 4 2 0)}] - skolem:lemma2123 - skolem:lemma2124 - [ a r:Fact; r:gives {(7420 247) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1705}] + [ a r:Fact; r:gives {(1705 2000) math:sum 3705}] + skolem:lemma3703 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2704]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 247]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1705]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3705]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1705 a r:Inference; r:gives { - 2705 :kaprekar (0 6). + 3706 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2705 math:notEqualTo 0}] - skolem:lemma3123 - [ a r:Fact; r:gives {((2 7 0 5) "=<") list:sort (0 2 5 7)}] - [ a r:Fact; r:gives {((2 7 0 5) ">=") list:sort (7 5 2 0)}] - skolem:lemma2143 - skolem:lemma2144 - [ a r:Fact; r:gives {(7520 257) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1706}] + [ a r:Fact; r:gives {(1706 2000) math:sum 3706}] + skolem:lemma3704 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2705]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 257]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1706]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3706]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1706 a r:Inference; r:gives { - 2706 :kaprekar (0 3). + 3707 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2706 math:notEqualTo 0}] - skolem:lemma3124 - [ a r:Fact; r:gives {((2 7 0 6) "=<") list:sort (0 2 6 7)}] - [ a r:Fact; r:gives {((2 7 0 6) ">=") list:sort (7 6 2 0)}] - skolem:lemma2161 - skolem:lemma2162 - [ a r:Fact; r:gives {(7620 267) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1707}] + [ a r:Fact; r:gives {(1707 2000) math:sum 3707}] + skolem:lemma3705 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2706]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7620]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1707]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3707]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1707 a r:Inference; r:gives { - 2707 :kaprekar (0 5). + 3708 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2707 math:notEqualTo 0}] - skolem:lemma3125 - [ a r:Fact; r:gives {((2 7 0 7) "=<") list:sort (0 2 7 7)}] - [ a r:Fact; r:gives {((2 7 0 7) ">=") list:sort (7 7 2 0)}] - skolem:lemma2177 - skolem:lemma2178 - [ a r:Fact; r:gives {(7720 277) math:difference 7443}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7443 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1708}] + [ a r:Fact; r:gives {(1708 2000) math:sum 3708}] + skolem:lemma3706 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2707]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 277]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7720]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1708]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3708]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1708 a r:Inference; r:gives { - 2708 :kaprekar (0 7). + 3709 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2708 math:notEqualTo 0}] - skolem:lemma3126 - [ a r:Fact; r:gives {((2 7 0 8) "=<") list:sort (0 2 7 8)}] - [ a r:Fact; r:gives {((2 7 0 8) ">=") list:sort (8 7 2 0)}] - skolem:lemma2180 - skolem:lemma2181 - [ a r:Fact; r:gives {(8720 278) math:difference 8442}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8442 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 8442 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1709}] + [ a r:Fact; r:gives {(1709 2000) math:sum 3709}] + skolem:lemma3707 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2708]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 278]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8720]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1709]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3709]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1709 a r:Inference; r:gives { - 2709 :kaprekar (0 7). + 3710 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2709 math:notEqualTo 0}] - skolem:lemma3127 - [ a r:Fact; r:gives {((2 7 0 9) "=<") list:sort (0 2 7 9)}] - [ a r:Fact; r:gives {((2 7 0 9) ">=") list:sort (9 7 2 0)}] - skolem:lemma2183 - skolem:lemma2184 - [ a r:Fact; r:gives {(9720 279) math:difference 9441}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9441 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 9441 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1710}] + [ a r:Fact; r:gives {(1710 2000) math:sum 3710}] + skolem:lemma3708 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2709]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 279]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9720]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9441]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1710]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3710]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1710 a r:Inference; r:gives { - 2710 :kaprekar (0 3). + 3711 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2710 math:notEqualTo 0}] - skolem:lemma3128 - [ a r:Fact; r:gives {((2 7 1 0) "=<") list:sort (0 1 2 7)}] - [ a r:Fact; r:gives {((2 7 1 0) ">=") list:sort (7 2 1 0)}] - skolem:lemma2051 - skolem:lemma2052 - [ a r:Fact; r:gives {(7210 127) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1711}] + [ a r:Fact; r:gives {(1711 2000) math:sum 3711}] + skolem:lemma3709 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2710]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 127]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1711]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3711]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1711 a r:Inference; r:gives { - 2711 :kaprekar (0 7). + 3712 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2711 math:notEqualTo 0}] - skolem:lemma3129 - [ a r:Fact; r:gives {((2 7 1 1) "=<") list:sort (1 1 2 7)}] - [ a r:Fact; r:gives {((2 7 1 1) ">=") list:sort (7 2 1 1)}] - skolem:lemma2241 - skolem:lemma2242 - [ a r:Fact; r:gives {(7211 1127) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1712}] + [ a r:Fact; r:gives {(1712 2000) math:sum 3712}] + skolem:lemma3710 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2711]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1127]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1712]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3712]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1712 a r:Inference; r:gives { - 2712 :kaprekar (0 6). + 3713 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2712 math:notEqualTo 0}] - skolem:lemma3130 - [ a r:Fact; r:gives {((2 7 1 2) "=<") list:sort (1 2 2 7)}] - [ a r:Fact; r:gives {((2 7 1 2) ">=") list:sort (7 2 2 1)}] - skolem:lemma2267 - skolem:lemma2268 - [ a r:Fact; r:gives {(7221 1227) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1713}] + [ a r:Fact; r:gives {(1713 2000) math:sum 3713}] + skolem:lemma3711 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2712]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1227]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1713]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3713]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1713 a r:Inference; r:gives { - 2713 :kaprekar (0 7). + 3714 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2713 math:notEqualTo 0}] - skolem:lemma3131 - [ a r:Fact; r:gives {((2 7 1 3) "=<") list:sort (1 2 3 7)}] - [ a r:Fact; r:gives {((2 7 1 3) ">=") list:sort (7 3 2 1)}] - skolem:lemma2291 - skolem:lemma2292 - [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1714}] + [ a r:Fact; r:gives {(1714 2000) math:sum 3714}] + skolem:lemma3712 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2713]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1237]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1714]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3714]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1714 a r:Inference; r:gives { - 2714 :kaprekar (0 1). + 3715 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2714 math:notEqualTo 0}] - skolem:lemma3132 - [ a r:Fact; r:gives {((2 7 1 4) "=<") list:sort (1 2 4 7)}] - [ a r:Fact; r:gives {((2 7 1 4) ">=") list:sort (7 4 2 1)}] - skolem:lemma2313 - skolem:lemma2314 - [ a r:Fact; r:gives {(7421 1247) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1715}] + [ a r:Fact; r:gives {(1715 2000) math:sum 3715}] + skolem:lemma3713 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2714]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1247]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1715]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3715]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1715 a r:Inference; r:gives { - 2715 :kaprekar (0 3). + 3716 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2715 math:notEqualTo 0}] - skolem:lemma3133 - [ a r:Fact; r:gives {((2 7 1 5) "=<") list:sort (1 2 5 7)}] - [ a r:Fact; r:gives {((2 7 1 5) ">=") list:sort (7 5 2 1)}] - skolem:lemma2333 - skolem:lemma2334 - [ a r:Fact; r:gives {(7521 1257) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1716}] + [ a r:Fact; r:gives {(1716 2000) math:sum 3716}] + skolem:lemma3714 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2715]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1257]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1716]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3716]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1716 a r:Inference; r:gives { - 2716 :kaprekar (0 4). + 3717 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2716 math:notEqualTo 0}] - skolem:lemma3134 - [ a r:Fact; r:gives {((2 7 1 6) "=<") list:sort (1 2 6 7)}] - [ a r:Fact; r:gives {((2 7 1 6) ">=") list:sort (7 6 2 1)}] - skolem:lemma2351 - skolem:lemma2352 - [ a r:Fact; r:gives {(7621 1267) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1717}] + [ a r:Fact; r:gives {(1717 2000) math:sum 3717}] + skolem:lemma3715 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2716]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1717]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3717]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1717 a r:Inference; r:gives { - 2717 :kaprekar (0 5). + 3718 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2717 math:notEqualTo 0}] - skolem:lemma3135 - [ a r:Fact; r:gives {((2 7 1 7) "=<") list:sort (1 2 7 7)}] - [ a r:Fact; r:gives {((2 7 1 7) ">=") list:sort (7 7 2 1)}] - skolem:lemma2367 - skolem:lemma2368 - [ a r:Fact; r:gives {(7721 1277) math:difference 6444}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6444 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 6444 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1718}] + [ a r:Fact; r:gives {(1718 2000) math:sum 3718}] + skolem:lemma3716 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2717]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1277]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7721]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1718]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3718]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1718 a r:Inference; r:gives { - 2718 :kaprekar (0 5). + 3719 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2718 math:notEqualTo 0}] - skolem:lemma3136 - [ a r:Fact; r:gives {((2 7 1 8) "=<") list:sort (1 2 7 8)}] - [ a r:Fact; r:gives {((2 7 1 8) ">=") list:sort (8 7 2 1)}] - skolem:lemma2370 - skolem:lemma2371 - [ a r:Fact; r:gives {(8721 1278) math:difference 7443}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7443 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1719}] + [ a r:Fact; r:gives {(1719 2000) math:sum 3719}] + skolem:lemma3717 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2718]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1278]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8721]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1719]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3719]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1719 a r:Inference; r:gives { - 2719 :kaprekar (0 7). + 3720 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2719 math:notEqualTo 0}] - skolem:lemma3137 - [ a r:Fact; r:gives {((2 7 1 9) "=<") list:sort (1 2 7 9)}] - [ a r:Fact; r:gives {((2 7 1 9) ">=") list:sort (9 7 2 1)}] - skolem:lemma2373 - skolem:lemma2374 - [ a r:Fact; r:gives {(9721 1279) math:difference 8442}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8442 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 8442 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1720}] + [ a r:Fact; r:gives {(1720 2000) math:sum 3720}] + skolem:lemma3718 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2719]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1279]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9721]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1720 a r:Inference; r:gives { - 2720 :kaprekar (0 4). + 3721 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2720 math:notEqualTo 0}] - skolem:lemma3138 - [ a r:Fact; r:gives {((2 7 2 0) "=<") list:sort (0 2 2 7)}] - [ a r:Fact; r:gives {((2 7 2 0) ">=") list:sort (7 2 2 0)}] - skolem:lemma2077 - skolem:lemma2078 - [ a r:Fact; r:gives {(7220 227) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1721}] + [ a r:Fact; r:gives {(1721 2000) math:sum 3721}] + skolem:lemma3719 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2720]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 227]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1721 a r:Inference; r:gives { - 2721 :kaprekar (0 6). + 3722 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2721 math:notEqualTo 0}] - skolem:lemma3139 - [ a r:Fact; r:gives {((2 7 2 1) "=<") list:sort (1 2 2 7)}] - [ a r:Fact; r:gives {((2 7 2 1) ">=") list:sort (7 2 2 1)}] - skolem:lemma2267 - skolem:lemma2268 - [ a r:Fact; r:gives {(7221 1227) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1722}] + [ a r:Fact; r:gives {(1722 2000) math:sum 3722}] + skolem:lemma3720 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2721]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1227]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1722 a r:Inference; r:gives { - 2722 :kaprekar (0 6). + 3723 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2722 math:notEqualTo 0}] - skolem:lemma3140 - [ a r:Fact; r:gives {((2 7 2 2) "=<") list:sort (2 2 2 7)}] - [ a r:Fact; r:gives {((2 7 2 2) ">=") list:sort (7 2 2 2)}] - skolem:lemma2436 - skolem:lemma2437 - [ a r:Fact; r:gives {(7222 2227) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1723}] + [ a r:Fact; r:gives {(1723 2000) math:sum 3723}] + skolem:lemma3721 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2722]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2227]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1723]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3723]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1723 a r:Inference; r:gives { - 2723 :kaprekar (0 7). + 3724 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2723 math:notEqualTo 0}] - skolem:lemma3141 - [ a r:Fact; r:gives {((2 7 2 3) "=<") list:sort (2 2 3 7)}] - [ a r:Fact; r:gives {((2 7 2 3) ">=") list:sort (7 3 2 2)}] - skolem:lemma2460 - skolem:lemma2461 - [ a r:Fact; r:gives {(7322 2237) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1724}] + [ a r:Fact; r:gives {(1724 2000) math:sum 3724}] + skolem:lemma3722 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2723]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2237]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1724]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3724]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1724 a r:Inference; r:gives { - 2724 :kaprekar (0 7). + 3725 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2724 math:notEqualTo 0}] - skolem:lemma3142 - [ a r:Fact; r:gives {((2 7 2 4) "=<") list:sort (2 2 4 7)}] - [ a r:Fact; r:gives {((2 7 2 4) ">=") list:sort (7 4 2 2)}] - skolem:lemma2482 - skolem:lemma2483 - [ a r:Fact; r:gives {(7422 2247) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1725}] + [ a r:Fact; r:gives {(1725 2000) math:sum 3725}] + skolem:lemma3723 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2724]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2247]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1725]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3725]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1725 a r:Inference; r:gives { - 2725 :kaprekar (0 5). + 3726 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2725 math:notEqualTo 0}] - skolem:lemma3143 - [ a r:Fact; r:gives {((2 7 2 5) "=<") list:sort (2 2 5 7)}] - [ a r:Fact; r:gives {((2 7 2 5) ">=") list:sort (7 5 2 2)}] - skolem:lemma2502 - skolem:lemma2503 - [ a r:Fact; r:gives {(7522 2257) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1726}] + [ a r:Fact; r:gives {(1726 2000) math:sum 3726}] + skolem:lemma3724 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2725]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2257]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1726]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3726]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1726 a r:Inference; r:gives { - 2726 :kaprekar (0 5). + 3727 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2726 math:notEqualTo 0}] - skolem:lemma3144 - [ a r:Fact; r:gives {((2 7 2 6) "=<") list:sort (2 2 6 7)}] - [ a r:Fact; r:gives {((2 7 2 6) ">=") list:sort (7 6 2 2)}] - skolem:lemma2520 - skolem:lemma2521 - [ a r:Fact; r:gives {(7622 2267) math:difference 5355}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5355 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5355 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1727}] + [ a r:Fact; r:gives {(1727 2000) math:sum 3727}] + skolem:lemma3725 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2726]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1727]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3727]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1727 a r:Inference; r:gives { - 2727 :kaprekar (0 5). + 3728 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2727 math:notEqualTo 0}] - skolem:lemma3145 - [ a r:Fact; r:gives {((2 7 2 7) "=<") list:sort (2 2 7 7)}] - [ a r:Fact; r:gives {((2 7 2 7) ">=") list:sort (7 7 2 2)}] - skolem:lemma2536 - skolem:lemma2537 - [ a r:Fact; r:gives {(7722 2277) math:difference 5445}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5445 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5445 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1728}] + [ a r:Fact; r:gives {(1728 2000) math:sum 3728}] + skolem:lemma3726 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2727]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2277]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7722]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5445]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1728]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3728]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1728 a r:Inference; r:gives { - 2728 :kaprekar (0 5). + 3729 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2728 math:notEqualTo 0}] - skolem:lemma3146 - [ a r:Fact; r:gives {((2 7 2 8) "=<") list:sort (2 2 7 8)}] - [ a r:Fact; r:gives {((2 7 2 8) ">=") list:sort (8 7 2 2)}] - skolem:lemma2539 - skolem:lemma2540 - [ a r:Fact; r:gives {(8722 2278) math:difference 6444}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6444 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 6444 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1729}] + [ a r:Fact; r:gives {(1729 2000) math:sum 3729}] + skolem:lemma3727 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2728]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2278]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8722]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1729]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3729]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1729 a r:Inference; r:gives { - 2729 :kaprekar (0 5). + 3730 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2729 math:notEqualTo 0}] - skolem:lemma3147 - [ a r:Fact; r:gives {((2 7 2 9) "=<") list:sort (2 2 7 9)}] - [ a r:Fact; r:gives {((2 7 2 9) ">=") list:sort (9 7 2 2)}] - skolem:lemma2542 - skolem:lemma2543 - [ a r:Fact; r:gives {(9722 2279) math:difference 7443}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7443 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1730}] + [ a r:Fact; r:gives {(1730 2000) math:sum 3730}] + skolem:lemma3728 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2729]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2279]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9722]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1730 a r:Inference; r:gives { - 2730 :kaprekar (0 3). + 3731 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2730 math:notEqualTo 0}] - skolem:lemma3148 - [ a r:Fact; r:gives {((2 7 3 0) "=<") list:sort (0 2 3 7)}] - [ a r:Fact; r:gives {((2 7 3 0) ">=") list:sort (7 3 2 0)}] - skolem:lemma2101 - skolem:lemma2102 - [ a r:Fact; r:gives {(7320 237) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1731}] + [ a r:Fact; r:gives {(1731 2000) math:sum 3731}] + skolem:lemma3729 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2730]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 237]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1731]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3731]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1731 a r:Inference; r:gives { - 2731 :kaprekar (0 7). + 3732 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2731 math:notEqualTo 0}] - skolem:lemma3149 - [ a r:Fact; r:gives {((2 7 3 1) "=<") list:sort (1 2 3 7)}] - [ a r:Fact; r:gives {((2 7 3 1) ">=") list:sort (7 3 2 1)}] - skolem:lemma2291 - skolem:lemma2292 - [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1732}] + [ a r:Fact; r:gives {(1732 2000) math:sum 3732}] + skolem:lemma3730 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2731]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1237]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1732 a r:Inference; r:gives { - 2732 :kaprekar (0 7). + 3733 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2732 math:notEqualTo 0}] - skolem:lemma3150 - [ a r:Fact; r:gives {((2 7 3 2) "=<") list:sort (2 2 3 7)}] - [ a r:Fact; r:gives {((2 7 3 2) ">=") list:sort (7 3 2 2)}] - skolem:lemma2460 - skolem:lemma2461 - [ a r:Fact; r:gives {(7322 2237) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1733}] + [ a r:Fact; r:gives {(1733 2000) math:sum 3733}] + skolem:lemma3731 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2732]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2237]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1733 a r:Inference; r:gives { - 2733 :kaprekar (0 6). + 3734 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2733 math:notEqualTo 0}] - skolem:lemma3151 - [ a r:Fact; r:gives {((2 7 3 3) "=<") list:sort (2 3 3 7)}] - [ a r:Fact; r:gives {((2 7 3 3) ">=") list:sort (7 3 3 2)}] - skolem:lemma2616 - skolem:lemma2617 - [ a r:Fact; r:gives {(7332 2337) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1734}] + [ a r:Fact; r:gives {(1734 2000) math:sum 3734}] + skolem:lemma3732 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2733]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2337]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1734]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3734]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1734 a r:Inference; r:gives { - 2734 :kaprekar (0 7). + 3735 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2734 math:notEqualTo 0}] - skolem:lemma3152 - [ a r:Fact; r:gives {((2 7 3 4) "=<") list:sort (2 3 4 7)}] - [ a r:Fact; r:gives {((2 7 3 4) ">=") list:sort (7 4 3 2)}] - skolem:lemma2638 - skolem:lemma2639 - [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1735}] + [ a r:Fact; r:gives {(1735 2000) math:sum 3735}] + skolem:lemma3733 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2734]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2347]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1735]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3735]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1735 a r:Inference; r:gives { - 2735 :kaprekar (0 7). + 3736 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2735 math:notEqualTo 0}] - skolem:lemma3153 - [ a r:Fact; r:gives {((2 7 3 5) "=<") list:sort (2 3 5 7)}] - [ a r:Fact; r:gives {((2 7 3 5) ">=") list:sort (7 5 3 2)}] - skolem:lemma2658 - skolem:lemma2659 - [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1736}] + [ a r:Fact; r:gives {(1736 2000) math:sum 3736}] + skolem:lemma3734 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2735]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2357]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1736]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3736]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1736 a r:Inference; r:gives { - 2736 :kaprekar (0 5). + 3737 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2736 math:notEqualTo 0}] - skolem:lemma3154 - [ a r:Fact; r:gives {((2 7 3 6) "=<") list:sort (2 3 6 7)}] - [ a r:Fact; r:gives {((2 7 3 6) ">=") list:sort (7 6 3 2)}] - skolem:lemma2676 - skolem:lemma2677 - [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1737}] + [ a r:Fact; r:gives {(1737 2000) math:sum 3737}] + skolem:lemma3735 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2736]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2367]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1737]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3737]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1737 a r:Inference; r:gives { - 2737 :kaprekar (0 5). + 3738 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2737 math:notEqualTo 0}] - skolem:lemma3155 - [ a r:Fact; r:gives {((2 7 3 7) "=<") list:sort (2 3 7 7)}] - [ a r:Fact; r:gives {((2 7 3 7) ">=") list:sort (7 7 3 2)}] - skolem:lemma2692 - skolem:lemma2693 - [ a r:Fact; r:gives {(7732 2377) math:difference 5355}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5355 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5355 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1738}] + [ a r:Fact; r:gives {(1738 2000) math:sum 3738}] + skolem:lemma3736 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2737]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2377]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7732]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1738]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3738]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1738 a r:Inference; r:gives { - 2738 :kaprekar (0 4). + 3739 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2738 math:notEqualTo 0}] - skolem:lemma3156 - [ a r:Fact; r:gives {((2 7 3 8) "=<") list:sort (2 3 7 8)}] - [ a r:Fact; r:gives {((2 7 3 8) ">=") list:sort (8 7 3 2)}] - skolem:lemma2695 - skolem:lemma2696 - [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1739}] + [ a r:Fact; r:gives {(1739 2000) math:sum 3739}] + skolem:lemma3737 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2738]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2378]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8732]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1739]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3739]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1739 a r:Inference; r:gives { - 2739 :kaprekar (0 3). + 3740 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2739 math:notEqualTo 0}] - skolem:lemma3157 - [ a r:Fact; r:gives {((2 7 3 9) "=<") list:sort (2 3 7 9)}] - [ a r:Fact; r:gives {((2 7 3 9) ">=") list:sort (9 7 3 2)}] - skolem:lemma2698 - skolem:lemma2699 - [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1740}] + [ a r:Fact; r:gives {(1740 2000) math:sum 3740}] + skolem:lemma3738 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2739]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2379]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9732]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1740]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3740]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1740 a r:Inference; r:gives { - 2740 :kaprekar (0 5). + 3741 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2740 math:notEqualTo 0}] - skolem:lemma3158 - [ a r:Fact; r:gives {((2 7 4 0) "=<") list:sort (0 2 4 7)}] - [ a r:Fact; r:gives {((2 7 4 0) ">=") list:sort (7 4 2 0)}] - skolem:lemma2123 - skolem:lemma2124 - [ a r:Fact; r:gives {(7420 247) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1741}] + [ a r:Fact; r:gives {(1741 2000) math:sum 3741}] + skolem:lemma3739 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2740]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 247]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1741]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3741]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1741 a r:Inference; r:gives { - 2741 :kaprekar (0 1). + 3742 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2741 math:notEqualTo 0}] - skolem:lemma3159 - [ a r:Fact; r:gives {((2 7 4 1) "=<") list:sort (1 2 4 7)}] - [ a r:Fact; r:gives {((2 7 4 1) ">=") list:sort (7 4 2 1)}] - skolem:lemma2313 - skolem:lemma2314 - [ a r:Fact; r:gives {(7421 1247) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1742}] + [ a r:Fact; r:gives {(1742 2000) math:sum 3742}] + skolem:lemma3740 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2741]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1247]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1742 a r:Inference; r:gives { - 2742 :kaprekar (0 7). + 3743 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2742 math:notEqualTo 0}] - skolem:lemma3160 - [ a r:Fact; r:gives {((2 7 4 2) "=<") list:sort (2 2 4 7)}] - [ a r:Fact; r:gives {((2 7 4 2) ">=") list:sort (7 4 2 2)}] - skolem:lemma2482 - skolem:lemma2483 - [ a r:Fact; r:gives {(7422 2247) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1743}] + [ a r:Fact; r:gives {(1743 2000) math:sum 3743}] + skolem:lemma3741 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2742]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2247]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1743 a r:Inference; r:gives { - 2743 :kaprekar (0 7). + 3744 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2743 math:notEqualTo 0}] - skolem:lemma3161 - [ a r:Fact; r:gives {((2 7 4 3) "=<") list:sort (2 3 4 7)}] - [ a r:Fact; r:gives {((2 7 4 3) ">=") list:sort (7 4 3 2)}] - skolem:lemma2638 - skolem:lemma2639 - [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1744}] + [ a r:Fact; r:gives {(1744 2000) math:sum 3744}] + skolem:lemma3742 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2743]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2347]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1744]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3744]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1744 a r:Inference; r:gives { - 2744 :kaprekar (0 6). + 3745 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2744 math:notEqualTo 0}] - skolem:lemma3162 - [ a r:Fact; r:gives {((2 7 4 4) "=<") list:sort (2 4 4 7)}] - [ a r:Fact; r:gives {((2 7 4 4) ">=") list:sort (7 4 4 2)}] - skolem:lemma2780 - skolem:lemma2781 - [ a r:Fact; r:gives {(7442 2447) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1745}] + [ a r:Fact; r:gives {(1745 2000) math:sum 3745}] + skolem:lemma3743 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2744]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2447]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1745]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3745]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1745 a r:Inference; r:gives { - 2745 :kaprekar (0 7). + 3746 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2745 math:notEqualTo 0}] - skolem:lemma3163 - [ a r:Fact; r:gives {((2 7 4 5) "=<") list:sort (2 4 5 7)}] - [ a r:Fact; r:gives {((2 7 4 5) ">=") list:sort (7 5 4 2)}] - skolem:lemma2800 - skolem:lemma2801 - [ a r:Fact; r:gives {(7542 2457) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1746}] + [ a r:Fact; r:gives {(1746 2000) math:sum 3746}] + skolem:lemma3744 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2745]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2457]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1746]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3746]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1746 a r:Inference; r:gives { - 2746 :kaprekar (0 7). + 3747 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2746 math:notEqualTo 0}] - skolem:lemma3164 - [ a r:Fact; r:gives {((2 7 4 6) "=<") list:sort (2 4 6 7)}] - [ a r:Fact; r:gives {((2 7 4 6) ">=") list:sort (7 6 4 2)}] - skolem:lemma2818 - skolem:lemma2819 - [ a r:Fact; r:gives {(7642 2467) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1747}] + [ a r:Fact; r:gives {(1747 2000) math:sum 3747}] + skolem:lemma3745 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2746]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2467]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1747]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3747]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1747 a r:Inference; r:gives { - 2747 :kaprekar (0 5). + 3748 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2747 math:notEqualTo 0}] - skolem:lemma3165 - [ a r:Fact; r:gives {((2 7 4 7) "=<") list:sort (2 4 7 7)}] - [ a r:Fact; r:gives {((2 7 4 7) ">=") list:sort (7 7 4 2)}] - skolem:lemma2834 - skolem:lemma2835 - [ a r:Fact; r:gives {(7742 2477) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1748}] + [ a r:Fact; r:gives {(1748 2000) math:sum 3748}] + skolem:lemma3746 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2747]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2477]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7742]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1748]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3748]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1748 a r:Inference; r:gives { - 2748 :kaprekar (0 3). + 3749 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2748 math:notEqualTo 0}] - skolem:lemma3166 - [ a r:Fact; r:gives {((2 7 4 8) "=<") list:sort (2 4 7 8)}] - [ a r:Fact; r:gives {((2 7 4 8) ">=") list:sort (8 7 4 2)}] - skolem:lemma2837 - skolem:lemma2838 - [ a r:Fact; r:gives {(8742 2478) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1749}] + [ a r:Fact; r:gives {(1749 2000) math:sum 3749}] + skolem:lemma3747 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2748]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2478]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8742]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1749]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3749]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1749 a r:Inference; r:gives { - 2749 :kaprekar (0 6). + 3750 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2749 math:notEqualTo 0}] - skolem:lemma3167 - [ a r:Fact; r:gives {((2 7 4 9) "=<") list:sort (2 4 7 9)}] - [ a r:Fact; r:gives {((2 7 4 9) ">=") list:sort (9 7 4 2)}] - skolem:lemma2840 - skolem:lemma2841 - [ a r:Fact; r:gives {(9742 2479) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1750}] + [ a r:Fact; r:gives {(1750 2000) math:sum 3750}] + skolem:lemma3748 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2749]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2479]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9742]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1750]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3750]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1750 a r:Inference; r:gives { - 2750 :kaprekar (0 6). + 3751 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2750 math:notEqualTo 0}] - skolem:lemma3168 - [ a r:Fact; r:gives {((2 7 5 0) "=<") list:sort (0 2 5 7)}] - [ a r:Fact; r:gives {((2 7 5 0) ">=") list:sort (7 5 2 0)}] - skolem:lemma2143 - skolem:lemma2144 - [ a r:Fact; r:gives {(7520 257) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1751}] + [ a r:Fact; r:gives {(1751 2000) math:sum 3751}] + skolem:lemma3749 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2750]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 257]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1751]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3751]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1751 a r:Inference; r:gives { - 2751 :kaprekar (0 3). + 3752 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2751 math:notEqualTo 0}] - skolem:lemma3169 - [ a r:Fact; r:gives {((2 7 5 1) "=<") list:sort (1 2 5 7)}] - [ a r:Fact; r:gives {((2 7 5 1) ">=") list:sort (7 5 2 1)}] - skolem:lemma2333 - skolem:lemma2334 - [ a r:Fact; r:gives {(7521 1257) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1752}] + [ a r:Fact; r:gives {(1752 2000) math:sum 3752}] + skolem:lemma3750 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2751]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1257]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1752 a r:Inference; r:gives { - 2752 :kaprekar (0 5). + 3753 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2752 math:notEqualTo 0}] - skolem:lemma3170 - [ a r:Fact; r:gives {((2 7 5 2) "=<") list:sort (2 2 5 7)}] - [ a r:Fact; r:gives {((2 7 5 2) ">=") list:sort (7 5 2 2)}] - skolem:lemma2502 - skolem:lemma2503 - [ a r:Fact; r:gives {(7522 2257) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1753}] + [ a r:Fact; r:gives {(1753 2000) math:sum 3753}] + skolem:lemma3751 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2752]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2257]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1753 a r:Inference; r:gives { - 2753 :kaprekar (0 7). + 3754 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2753 math:notEqualTo 0}] - skolem:lemma3171 - [ a r:Fact; r:gives {((2 7 5 3) "=<") list:sort (2 3 5 7)}] - [ a r:Fact; r:gives {((2 7 5 3) ">=") list:sort (7 5 3 2)}] - skolem:lemma2658 - skolem:lemma2659 - [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1754}] + [ a r:Fact; r:gives {(1754 2000) math:sum 3754}] + skolem:lemma3752 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2753]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2357]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1754]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3754]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1754 a r:Inference; r:gives { - 2754 :kaprekar (0 7). + 3755 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2754 math:notEqualTo 0}] - skolem:lemma3172 - [ a r:Fact; r:gives {((2 7 5 4) "=<") list:sort (2 4 5 7)}] - [ a r:Fact; r:gives {((2 7 5 4) ">=") list:sort (7 5 4 2)}] - skolem:lemma2800 - skolem:lemma2801 - [ a r:Fact; r:gives {(7542 2457) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1755}] + [ a r:Fact; r:gives {(1755 2000) math:sum 3755}] + skolem:lemma3753 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2754]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2457]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1755]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3755]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1755 a r:Inference; r:gives { - 2755 :kaprekar (0 6). + 3756 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2755 math:notEqualTo 0}] - skolem:lemma3173 - [ a r:Fact; r:gives {((2 7 5 5) "=<") list:sort (2 5 5 7)}] - [ a r:Fact; r:gives {((2 7 5 5) ">=") list:sort (7 5 5 2)}] - skolem:lemma2930 - skolem:lemma2931 - [ a r:Fact; r:gives {(7552 2557) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1756}] + [ a r:Fact; r:gives {(1756 2000) math:sum 3756}] + skolem:lemma3754 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2755]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2557]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7552]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1756]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3756]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1756 a r:Inference; r:gives { - 2756 :kaprekar (0 7). + 3757 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2756 math:notEqualTo 0}] - skolem:lemma3174 - [ a r:Fact; r:gives {((2 7 5 6) "=<") list:sort (2 5 6 7)}] - [ a r:Fact; r:gives {((2 7 5 6) ">=") list:sort (7 6 5 2)}] - skolem:lemma2948 - skolem:lemma2949 - [ a r:Fact; r:gives {(7652 2567) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1757}] + [ a r:Fact; r:gives {(1757 2000) math:sum 3757}] + skolem:lemma3755 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2756]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2567]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1757]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3757]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1757 a r:Inference; r:gives { - 2757 :kaprekar (0 7). + 3758 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2757 math:notEqualTo 0}] - skolem:lemma3175 - [ a r:Fact; r:gives {((2 7 5 7) "=<") list:sort (2 5 7 7)}] - [ a r:Fact; r:gives {((2 7 5 7) ">=") list:sort (7 7 5 2)}] - skolem:lemma2964 - skolem:lemma2965 - [ a r:Fact; r:gives {(7752 2577) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1758}] + [ a r:Fact; r:gives {(1758 2000) math:sum 3758}] + skolem:lemma3756 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2757]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2577]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7752]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1758]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3758]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1758 a r:Inference; r:gives { - 2758 :kaprekar (0 1). + 3759 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2758 math:notEqualTo 0}] - skolem:lemma3176 - [ a r:Fact; r:gives {((2 7 5 8) "=<") list:sort (2 5 7 8)}] - [ a r:Fact; r:gives {((2 7 5 8) ">=") list:sort (8 7 5 2)}] - skolem:lemma2967 - skolem:lemma2968 - [ a r:Fact; r:gives {(8752 2578) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1759}] + [ a r:Fact; r:gives {(1759 2000) math:sum 3759}] + skolem:lemma3757 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2758]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2578]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8752]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1759]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3759]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1759 a r:Inference; r:gives { - 2759 :kaprekar (0 5). + 3760 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2759 math:notEqualTo 0}] - skolem:lemma3177 - [ a r:Fact; r:gives {((2 7 5 9) "=<") list:sort (2 5 7 9)}] - [ a r:Fact; r:gives {((2 7 5 9) ">=") list:sort (9 7 5 2)}] - skolem:lemma2970 - skolem:lemma2971 - [ a r:Fact; r:gives {(9752 2579) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1760}] + [ a r:Fact; r:gives {(1760 2000) math:sum 3760}] + skolem:lemma3758 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2759]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2579]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9752]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1760]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3760]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1760 a r:Inference; r:gives { - 2760 :kaprekar (0 3). + 3761 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2760 math:notEqualTo 0}] - skolem:lemma3178 - [ a r:Fact; r:gives {((2 7 6 0) "=<") list:sort (0 2 6 7)}] - [ a r:Fact; r:gives {((2 7 6 0) ">=") list:sort (7 6 2 0)}] - skolem:lemma2161 - skolem:lemma2162 - [ a r:Fact; r:gives {(7620 267) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1761}] + [ a r:Fact; r:gives {(1761 2000) math:sum 3761}] + skolem:lemma3759 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2760]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7620]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1761]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3761]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1761 a r:Inference; r:gives { - 2761 :kaprekar (0 4). + 3762 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2761 math:notEqualTo 0}] - skolem:lemma3179 - [ a r:Fact; r:gives {((2 7 6 1) "=<") list:sort (1 2 6 7)}] - [ a r:Fact; r:gives {((2 7 6 1) ">=") list:sort (7 6 2 1)}] - skolem:lemma2351 - skolem:lemma2352 - [ a r:Fact; r:gives {(7621 1267) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1762}] + [ a r:Fact; r:gives {(1762 2000) math:sum 3762}] + skolem:lemma3760 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2761]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1762 a r:Inference; r:gives { - 2762 :kaprekar (0 5). + 3763 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2762 math:notEqualTo 0}] - skolem:lemma3180 - [ a r:Fact; r:gives {((2 7 6 2) "=<") list:sort (2 2 6 7)}] - [ a r:Fact; r:gives {((2 7 6 2) ">=") list:sort (7 6 2 2)}] - skolem:lemma2520 - skolem:lemma2521 - [ a r:Fact; r:gives {(7622 2267) math:difference 5355}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5355 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5355 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1763}] + [ a r:Fact; r:gives {(1763 2000) math:sum 3763}] + skolem:lemma3761 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2762]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1763 a r:Inference; r:gives { - 2763 :kaprekar (0 5). + 3764 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2763 math:notEqualTo 0}] - skolem:lemma3181 - [ a r:Fact; r:gives {((2 7 6 3) "=<") list:sort (2 3 6 7)}] - [ a r:Fact; r:gives {((2 7 6 3) ">=") list:sort (7 6 3 2)}] - skolem:lemma2676 - skolem:lemma2677 - [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1764}] + [ a r:Fact; r:gives {(1764 2000) math:sum 3764}] + skolem:lemma3762 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2763]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2367]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1764]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3764]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1764 a r:Inference; r:gives { - 2764 :kaprekar (0 7). + 3765 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2764 math:notEqualTo 0}] - skolem:lemma3182 - [ a r:Fact; r:gives {((2 7 6 4) "=<") list:sort (2 4 6 7)}] - [ a r:Fact; r:gives {((2 7 6 4) ">=") list:sort (7 6 4 2)}] - skolem:lemma2818 - skolem:lemma2819 - [ a r:Fact; r:gives {(7642 2467) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1765}] + [ a r:Fact; r:gives {(1765 2000) math:sum 3765}] + skolem:lemma3763 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2764]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2467]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1765]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3765]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1765 a r:Inference; r:gives { - 2765 :kaprekar (0 7). + 3766 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2765 math:notEqualTo 0}] - skolem:lemma3183 - [ a r:Fact; r:gives {((2 7 6 5) "=<") list:sort (2 5 6 7)}] - [ a r:Fact; r:gives {((2 7 6 5) ">=") list:sort (7 6 5 2)}] - skolem:lemma2948 - skolem:lemma2949 - [ a r:Fact; r:gives {(7652 2567) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1766}] + [ a r:Fact; r:gives {(1766 2000) math:sum 3766}] + skolem:lemma3764 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2765]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2567]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1766]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3766]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1766 a r:Inference; r:gives { - 2766 :kaprekar (0 6). + 3767 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2766 math:notEqualTo 0}] - skolem:lemma3184 - [ a r:Fact; r:gives {((2 7 6 6) "=<") list:sort (2 6 6 7)}] - [ a r:Fact; r:gives {((2 7 6 6) ">=") list:sort (7 6 6 2)}] - skolem:lemma3068 - skolem:lemma3069 - [ a r:Fact; r:gives {(7662 2667) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1767}] + [ a r:Fact; r:gives {(1767 2000) math:sum 3767}] + skolem:lemma3765 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2766]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2667]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7662]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1767]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3767]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1767 a r:Inference; r:gives { - 2767 :kaprekar (0 7). + 3768 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2767 math:notEqualTo 0}] - skolem:lemma3185 - [ a r:Fact; r:gives {((2 7 6 7) "=<") list:sort (2 6 7 7)}] - [ a r:Fact; r:gives {((2 7 6 7) ">=") list:sort (7 7 6 2)}] - skolem:lemma3084 - skolem:lemma3085 - [ a r:Fact; r:gives {(7762 2677) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1768}] + [ a r:Fact; r:gives {(1768 2000) math:sum 3768}] + skolem:lemma3766 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2767]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2677]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7762]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1768]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3768]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1768 a r:Inference; r:gives { - 2768 :kaprekar (0 7). + 3769 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2768 math:notEqualTo 0}] - skolem:lemma3186 - [ a r:Fact; r:gives {((2 7 6 8) "=<") list:sort (2 6 7 8)}] - [ a r:Fact; r:gives {((2 7 6 8) ">=") list:sort (8 7 6 2)}] - skolem:lemma3087 - skolem:lemma3088 - [ a r:Fact; r:gives {(8762 2678) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1769}] + [ a r:Fact; r:gives {(1769 2000) math:sum 3769}] + skolem:lemma3767 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2768]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2678]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8762]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1769]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3769]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1769 a r:Inference; r:gives { - 2769 :kaprekar (0 3). + 3770 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2769 math:notEqualTo 0}] - skolem:lemma3187 - [ a r:Fact; r:gives {((2 7 6 9) "=<") list:sort (2 6 7 9)}] - [ a r:Fact; r:gives {((2 7 6 9) ">=") list:sort (9 7 6 2)}] - skolem:lemma3090 - skolem:lemma3091 - [ a r:Fact; r:gives {(9762 2679) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1770}] + [ a r:Fact; r:gives {(1770 2000) math:sum 3770}] + skolem:lemma3768 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2769]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2679]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9762]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1770]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3770]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1770 a r:Inference; r:gives { - 2770 :kaprekar (0 5). + 3771 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2770 math:notEqualTo 0}] - skolem:lemma3188 - [ a r:Fact; r:gives {((2 7 7 0) "=<") list:sort (0 2 7 7)}] - [ a r:Fact; r:gives {((2 7 7 0) ">=") list:sort (7 7 2 0)}] - skolem:lemma2177 - skolem:lemma2178 - [ a r:Fact; r:gives {(7720 277) math:difference 7443}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7443 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1771}] + [ a r:Fact; r:gives {(1771 2000) math:sum 3771}] + skolem:lemma3769 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2770]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 277]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7720]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1771]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3771]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1771 a r:Inference; r:gives { - 2771 :kaprekar (0 5). + 3772 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2771 math:notEqualTo 0}] - skolem:lemma3189 - [ a r:Fact; r:gives {((2 7 7 1) "=<") list:sort (1 2 7 7)}] - [ a r:Fact; r:gives {((2 7 7 1) ">=") list:sort (7 7 2 1)}] - skolem:lemma2367 - skolem:lemma2368 - [ a r:Fact; r:gives {(7721 1277) math:difference 6444}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6444 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 6444 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1772}] + [ a r:Fact; r:gives {(1772 2000) math:sum 3772}] + skolem:lemma3770 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2771]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1277]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7721]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1772]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3772]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1772 a r:Inference; r:gives { - 2772 :kaprekar (0 5). + 3773 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2772 math:notEqualTo 0}] - skolem:lemma3190 - [ a r:Fact; r:gives {((2 7 7 2) "=<") list:sort (2 2 7 7)}] - [ a r:Fact; r:gives {((2 7 7 2) ">=") list:sort (7 7 2 2)}] - skolem:lemma2536 - skolem:lemma2537 - [ a r:Fact; r:gives {(7722 2277) math:difference 5445}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5445 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5445 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1773}] + [ a r:Fact; r:gives {(1773 2000) math:sum 3773}] + skolem:lemma3771 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2772]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2277]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7722]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5445]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1773]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3773]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1773 a r:Inference; r:gives { - 2773 :kaprekar (0 5). + 3774 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2773 math:notEqualTo 0}] - skolem:lemma3191 - [ a r:Fact; r:gives {((2 7 7 3) "=<") list:sort (2 3 7 7)}] - [ a r:Fact; r:gives {((2 7 7 3) ">=") list:sort (7 7 3 2)}] - skolem:lemma2692 - skolem:lemma2693 - [ a r:Fact; r:gives {(7732 2377) math:difference 5355}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5355 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5355 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1774}] + [ a r:Fact; r:gives {(1774 2000) math:sum 3774}] + skolem:lemma3772 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2773]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2377]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7732]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1774]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3774]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1774 a r:Inference; r:gives { - 2774 :kaprekar (0 5). + 3775 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2774 math:notEqualTo 0}] - skolem:lemma3192 - [ a r:Fact; r:gives {((2 7 7 4) "=<") list:sort (2 4 7 7)}] - [ a r:Fact; r:gives {((2 7 7 4) ">=") list:sort (7 7 4 2)}] - skolem:lemma2834 - skolem:lemma2835 - [ a r:Fact; r:gives {(7742 2477) math:difference 5265}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5265 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 5265 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1775}] + [ a r:Fact; r:gives {(1775 2000) math:sum 3775}] + skolem:lemma3773 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2774]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2477]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7742]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1775]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3775]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1775 a r:Inference; r:gives { - 2775 :kaprekar (0 7). + 3776 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2775 math:notEqualTo 0}] - skolem:lemma3193 - [ a r:Fact; r:gives {((2 7 7 5) "=<") list:sort (2 5 7 7)}] - [ a r:Fact; r:gives {((2 7 7 5) ">=") list:sort (7 7 5 2)}] - skolem:lemma2964 - skolem:lemma2965 - [ a r:Fact; r:gives {(7752 2577) math:difference 5175}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5175 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5175 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1776}] + [ a r:Fact; r:gives {(1776 2000) math:sum 3776}] + skolem:lemma3774 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2775]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2577]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7752]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1776]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3776]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1776 a r:Inference; r:gives { - 2776 :kaprekar (0 7). + 3777 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2776 math:notEqualTo 0}] - skolem:lemma3194 - [ a r:Fact; r:gives {((2 7 7 6) "=<") list:sort (2 6 7 7)}] - [ a r:Fact; r:gives {((2 7 7 6) ">=") list:sort (7 7 6 2)}] - skolem:lemma3084 - skolem:lemma3085 - [ a r:Fact; r:gives {(7762 2677) math:difference 5085}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5085 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 5085 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1777}] + [ a r:Fact; r:gives {(1777 2000) math:sum 3777}] + skolem:lemma3775 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2776]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2677]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7762]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1777]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3777]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1777 a r:Inference; r:gives { - 2777 :kaprekar (0 6). + 3778 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2777 math:notEqualTo 0}] - skolem:lemma3195 - [ a r:Fact; r:gives {((2 7 7 7) "=<") list:sort (2 7 7 7)}] - [ a r:Fact; r:gives {((2 7 7 7) ">=") list:sort (7 7 7 2)}] - skolem:lemma3196 - skolem:lemma3197 - [ a r:Fact; r:gives {(7772 2777) math:difference 4995}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 4995 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 4995 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1778}] + [ a r:Fact; r:gives {(1778 2000) math:sum 3778}] + skolem:lemma3776 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2777]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2777]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7772]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1778]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3778]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1778 a r:Inference; r:gives { - 2778 :kaprekar (0 6). + 3779 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2778 math:notEqualTo 0}] - skolem:lemma3198 - [ a r:Fact; r:gives {((2 7 7 8) "=<") list:sort (2 7 7 8)}] - [ a r:Fact; r:gives {((2 7 7 8) ">=") list:sort (8 7 7 2)}] - skolem:lemma3199 - skolem:lemma3200 - [ a r:Fact; r:gives {(8772 2778) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1779}] + [ a r:Fact; r:gives {(1779 2000) math:sum 3779}] + skolem:lemma3777 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2778]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2778]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8772]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1779]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3779]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1779 a r:Inference; r:gives { - 2779 :kaprekar (0 4). + 3780 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2779 math:notEqualTo 0}] - skolem:lemma3201 - [ a r:Fact; r:gives {((2 7 7 9) "=<") list:sort (2 7 7 9)}] - [ a r:Fact; r:gives {((2 7 7 9) ">=") list:sort (9 7 7 2)}] - skolem:lemma3202 - skolem:lemma3203 - [ a r:Fact; r:gives {(9772 2779) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1780}] + [ a r:Fact; r:gives {(1780 2000) math:sum 3780}] + skolem:lemma3778 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2779]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2779]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9772]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1780]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3780]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1780 a r:Inference; r:gives { - 2780 :kaprekar (0 7). + 3781 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2780 math:notEqualTo 0}] - skolem:lemma3204 - [ a r:Fact; r:gives {((2 7 8 0) "=<") list:sort (0 2 7 8)}] - [ a r:Fact; r:gives {((2 7 8 0) ">=") list:sort (8 7 2 0)}] - skolem:lemma2180 - skolem:lemma2181 - [ a r:Fact; r:gives {(8720 278) math:difference 8442}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8442 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 8442 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1781}] + [ a r:Fact; r:gives {(1781 2000) math:sum 3781}] + skolem:lemma3779 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2780]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 278]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8720]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1781]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3781]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1781 a r:Inference; r:gives { - 2781 :kaprekar (0 5). + 3782 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2781 math:notEqualTo 0}] - skolem:lemma3205 - [ a r:Fact; r:gives {((2 7 8 1) "=<") list:sort (1 2 7 8)}] - [ a r:Fact; r:gives {((2 7 8 1) ">=") list:sort (8 7 2 1)}] - skolem:lemma2370 - skolem:lemma2371 - [ a r:Fact; r:gives {(8721 1278) math:difference 7443}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7443 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1782}] + [ a r:Fact; r:gives {(1782 2000) math:sum 3782}] + skolem:lemma3780 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2781]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1278]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8721]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1782]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3782]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1782 a r:Inference; r:gives { - 2782 :kaprekar (0 5). + 3783 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2782 math:notEqualTo 0}] - skolem:lemma3206 - [ a r:Fact; r:gives {((2 7 8 2) "=<") list:sort (2 2 7 8)}] - [ a r:Fact; r:gives {((2 7 8 2) ">=") list:sort (8 7 2 2)}] - skolem:lemma2539 - skolem:lemma2540 - [ a r:Fact; r:gives {(8722 2278) math:difference 6444}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6444 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 6444 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1783}] + [ a r:Fact; r:gives {(1783 2000) math:sum 3783}] + skolem:lemma3781 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2782]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2278]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8722]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1783]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3783]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1783 a r:Inference; r:gives { - 2783 :kaprekar (0 4). + 3784 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2783 math:notEqualTo 0}] - skolem:lemma3207 - [ a r:Fact; r:gives {((2 7 8 3) "=<") list:sort (2 3 7 8)}] - [ a r:Fact; r:gives {((2 7 8 3) ">=") list:sort (8 7 3 2)}] - skolem:lemma2695 - skolem:lemma2696 - [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1784}] + [ a r:Fact; r:gives {(1784 2000) math:sum 3784}] + skolem:lemma3782 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2783]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2378]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8732]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1784]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3784]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1784 a r:Inference; r:gives { - 2784 :kaprekar (0 3). + 3785 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2784 math:notEqualTo 0}] - skolem:lemma3208 - [ a r:Fact; r:gives {((2 7 8 4) "=<") list:sort (2 4 7 8)}] - [ a r:Fact; r:gives {((2 7 8 4) ">=") list:sort (8 7 4 2)}] - skolem:lemma2837 - skolem:lemma2838 - [ a r:Fact; r:gives {(8742 2478) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1785}] + [ a r:Fact; r:gives {(1785 2000) math:sum 3785}] + skolem:lemma3783 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2784]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2478]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8742]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1785]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3785]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1785 a r:Inference; r:gives { - 2785 :kaprekar (0 1). + 3786 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2785 math:notEqualTo 0}] - skolem:lemma3209 - [ a r:Fact; r:gives {((2 7 8 5) "=<") list:sort (2 5 7 8)}] - [ a r:Fact; r:gives {((2 7 8 5) ">=") list:sort (8 7 5 2)}] - skolem:lemma2967 - skolem:lemma2968 - [ a r:Fact; r:gives {(8752 2578) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1786}] + [ a r:Fact; r:gives {(1786 2000) math:sum 3786}] + skolem:lemma3784 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2785]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2578]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8752]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1786]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3786]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1786 a r:Inference; r:gives { - 2786 :kaprekar (0 7). + 3787 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2786 math:notEqualTo 0}] - skolem:lemma3210 - [ a r:Fact; r:gives {((2 7 8 6) "=<") list:sort (2 6 7 8)}] - [ a r:Fact; r:gives {((2 7 8 6) ">=") list:sort (8 7 6 2)}] - skolem:lemma3087 - skolem:lemma3088 - [ a r:Fact; r:gives {(8762 2678) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1787}] + [ a r:Fact; r:gives {(1787 2000) math:sum 3787}] + skolem:lemma3785 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2786]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2678]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8762]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1787]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3787]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1787 a r:Inference; r:gives { - 2787 :kaprekar (0 6). + 3788 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2787 math:notEqualTo 0}] - skolem:lemma3211 - [ a r:Fact; r:gives {((2 7 8 7) "=<") list:sort (2 7 7 8)}] - [ a r:Fact; r:gives {((2 7 8 7) ">=") list:sort (8 7 7 2)}] - skolem:lemma3199 - skolem:lemma3200 - [ a r:Fact; r:gives {(8772 2778) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1788}] + [ a r:Fact; r:gives {(1788 2000) math:sum 3788}] + skolem:lemma3786 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2787]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2778]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8772]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1788]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3788]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1788 a r:Inference; r:gives { - 2788 :kaprekar (0 7). + 3789 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2788 math:notEqualTo 0}] - skolem:lemma3212 - [ a r:Fact; r:gives {((2 7 8 8) "=<") list:sort (2 7 8 8)}] - [ a r:Fact; r:gives {((2 7 8 8) ">=") list:sort (8 8 7 2)}] - skolem:lemma3213 - skolem:lemma3214 - [ a r:Fact; r:gives {(8872 2788) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1789}] + [ a r:Fact; r:gives {(1789 2000) math:sum 3789}] + skolem:lemma3787 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2788]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2788]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8872]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1789]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3789]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1789 a r:Inference; r:gives { - 2789 :kaprekar (0 3). + 3790 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2789 math:notEqualTo 0}] - skolem:lemma3215 - [ a r:Fact; r:gives {((2 7 8 9) "=<") list:sort (2 7 8 9)}] - [ a r:Fact; r:gives {((2 7 8 9) ">=") list:sort (9 8 7 2)}] - skolem:lemma3216 - skolem:lemma3217 - [ a r:Fact; r:gives {(9872 2789) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1790}] + [ a r:Fact; r:gives {(1790 2000) math:sum 3790}] + skolem:lemma3788 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2789]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2789]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9872]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1790]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3790]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1790 a r:Inference; r:gives { - 2790 :kaprekar (0 7). + 3791 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2790 math:notEqualTo 0}] - skolem:lemma3218 - [ a r:Fact; r:gives {((2 7 9 0) "=<") list:sort (0 2 7 9)}] - [ a r:Fact; r:gives {((2 7 9 0) ">=") list:sort (9 7 2 0)}] - skolem:lemma2183 - skolem:lemma2184 - [ a r:Fact; r:gives {(9720 279) math:difference 9441}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9441 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 9441 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1791}] + [ a r:Fact; r:gives {(1791 2000) math:sum 3791}] + skolem:lemma3789 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2790]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 279]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9720]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9441]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1791]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3791]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1791 a r:Inference; r:gives { - 2791 :kaprekar (0 7). + 3792 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2791 math:notEqualTo 0}] - skolem:lemma3219 - [ a r:Fact; r:gives {((2 7 9 1) "=<") list:sort (1 2 7 9)}] - [ a r:Fact; r:gives {((2 7 9 1) ">=") list:sort (9 7 2 1)}] - skolem:lemma2373 - skolem:lemma2374 - [ a r:Fact; r:gives {(9721 1279) math:difference 8442}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8442 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 8442 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1792}] + [ a r:Fact; r:gives {(1792 2000) math:sum 3792}] + skolem:lemma3790 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2791]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1279]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9721]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1792]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3792]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1792 a r:Inference; r:gives { - 2792 :kaprekar (0 5). + 3793 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2792 math:notEqualTo 0}] - skolem:lemma3220 - [ a r:Fact; r:gives {((2 7 9 2) "=<") list:sort (2 2 7 9)}] - [ a r:Fact; r:gives {((2 7 9 2) ">=") list:sort (9 7 2 2)}] - skolem:lemma2542 - skolem:lemma2543 - [ a r:Fact; r:gives {(9722 2279) math:difference 7443}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7443 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1793}] + [ a r:Fact; r:gives {(1793 2000) math:sum 3793}] + skolem:lemma3791 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2792]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2279]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9722]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1793]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3793]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1793 a r:Inference; r:gives { - 2793 :kaprekar (0 3). + 3794 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2793 math:notEqualTo 0}] - skolem:lemma3221 - [ a r:Fact; r:gives {((2 7 9 3) "=<") list:sort (2 3 7 9)}] - [ a r:Fact; r:gives {((2 7 9 3) ">=") list:sort (9 7 3 2)}] - skolem:lemma2698 - skolem:lemma2699 - [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1794}] + [ a r:Fact; r:gives {(1794 2000) math:sum 3794}] + skolem:lemma3792 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2793]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2379]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9732]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1794]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3794]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1794 a r:Inference; r:gives { - 2794 :kaprekar (0 6). + 3795 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2794 math:notEqualTo 0}] - skolem:lemma3222 - [ a r:Fact; r:gives {((2 7 9 4) "=<") list:sort (2 4 7 9)}] - [ a r:Fact; r:gives {((2 7 9 4) ">=") list:sort (9 7 4 2)}] - skolem:lemma2840 - skolem:lemma2841 - [ a r:Fact; r:gives {(9742 2479) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1795}] + [ a r:Fact; r:gives {(1795 2000) math:sum 3795}] + skolem:lemma3793 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2794]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2479]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9742]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1795]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3795]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1795 a r:Inference; r:gives { - 2795 :kaprekar (0 5). + 3796 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2795 math:notEqualTo 0}] - skolem:lemma3223 - [ a r:Fact; r:gives {((2 7 9 5) "=<") list:sort (2 5 7 9)}] - [ a r:Fact; r:gives {((2 7 9 5) ">=") list:sort (9 7 5 2)}] - skolem:lemma2970 - skolem:lemma2971 - [ a r:Fact; r:gives {(9752 2579) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1796}] + [ a r:Fact; r:gives {(1796 2000) math:sum 3796}] + skolem:lemma3794 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2795]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2579]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9752]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1796]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3796]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1796 a r:Inference; r:gives { - 2796 :kaprekar (0 3). + 3797 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2796 math:notEqualTo 0}] - skolem:lemma3224 - [ a r:Fact; r:gives {((2 7 9 6) "=<") list:sort (2 6 7 9)}] - [ a r:Fact; r:gives {((2 7 9 6) ">=") list:sort (9 7 6 2)}] - skolem:lemma3090 - skolem:lemma3091 - [ a r:Fact; r:gives {(9762 2679) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1797}] + [ a r:Fact; r:gives {(1797 2000) math:sum 3797}] + skolem:lemma3795 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2796]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2679]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9762]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1797]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3797]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1797 a r:Inference; r:gives { - 2797 :kaprekar (0 4). + 3798 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2797 math:notEqualTo 0}] - skolem:lemma3225 - [ a r:Fact; r:gives {((2 7 9 7) "=<") list:sort (2 7 7 9)}] - [ a r:Fact; r:gives {((2 7 9 7) ">=") list:sort (9 7 7 2)}] - skolem:lemma3202 - skolem:lemma3203 - [ a r:Fact; r:gives {(9772 2779) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1798}] + [ a r:Fact; r:gives {(1798 2000) math:sum 3798}] + skolem:lemma3796 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2797]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2779]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9772]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1798]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3798]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1798 a r:Inference; r:gives { - 2798 :kaprekar (0 3). + 3799 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2798 math:notEqualTo 0}] - skolem:lemma3226 - [ a r:Fact; r:gives {((2 7 9 8) "=<") list:sort (2 7 8 9)}] - [ a r:Fact; r:gives {((2 7 9 8) ">=") list:sort (9 8 7 2)}] - skolem:lemma3216 - skolem:lemma3217 - [ a r:Fact; r:gives {(9872 2789) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1799}] + [ a r:Fact; r:gives {(1799 2000) math:sum 3799}] + skolem:lemma3797 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2798]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2789]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9872]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1799]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3799]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1799 a r:Inference; r:gives { - 2799 :kaprekar (0 5). + 3800 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2799 math:notEqualTo 0}] - skolem:lemma3227 - [ a r:Fact; r:gives {((2 7 9 9) "=<") list:sort (2 7 9 9)}] - [ a r:Fact; r:gives {((2 7 9 9) ">=") list:sort (9 9 7 2)}] - skolem:lemma3228 - skolem:lemma3229 - [ a r:Fact; r:gives {(9972 2799) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1800}] + [ a r:Fact; r:gives {(1800 2000) math:sum 3800}] + skolem:lemma3798 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2799]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2799]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9972]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1800 a r:Inference; r:gives { - 2800 :kaprekar (0 6). + 3801 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2800 math:notEqualTo 0}] - skolem:lemma3230 - [ a r:Fact; r:gives {((2 8 0 0) "=<") list:sort (0 0 2 8)}] - [ a r:Fact; r:gives {((2 8 0 0) ">=") list:sort (8 2 0 0)}] - skolem:lemma2026 - skolem:lemma2027 - [ a r:Fact; r:gives {(8200 28) math:difference 8172}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8172 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 8172 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1801}] + [ a r:Fact; r:gives {(1801 2000) math:sum 3801}] + skolem:lemma3799 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2800]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1801]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3801]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1801 a r:Inference; r:gives { - 2801 :kaprekar (0 3). + 3802 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2801 math:notEqualTo 0}] - skolem:lemma3231 - [ a r:Fact; r:gives {((2 8 0 1) "=<") list:sort (0 1 2 8)}] - [ a r:Fact; r:gives {((2 8 0 1) ">=") list:sort (8 2 1 0)}] - skolem:lemma2054 - skolem:lemma2055 - [ a r:Fact; r:gives {(8210 128) math:difference 8082}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8082 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 8082 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1802}] + [ a r:Fact; r:gives {(1802 2000) math:sum 3802}] + skolem:lemma3800 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2801]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 128]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1802]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3802]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1802 a r:Inference; r:gives { - 2802 :kaprekar (0 6). + 3803 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2802 math:notEqualTo 0}] - skolem:lemma3232 - [ a r:Fact; r:gives {((2 8 0 2) "=<") list:sort (0 2 2 8)}] - [ a r:Fact; r:gives {((2 8 0 2) ">=") list:sort (8 2 2 0)}] - skolem:lemma2080 - skolem:lemma2081 - [ a r:Fact; r:gives {(8220 228) math:difference 7992}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7992 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7992 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1803}] + [ a r:Fact; r:gives {(1803 2000) math:sum 3803}] + skolem:lemma3801 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2802]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 228]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1803]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3803]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1803 a r:Inference; r:gives { - 2803 :kaprekar (0 3). + 3804 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2803 math:notEqualTo 0}] - skolem:lemma3233 - [ a r:Fact; r:gives {((2 8 0 3) "=<") list:sort (0 2 3 8)}] - [ a r:Fact; r:gives {((2 8 0 3) ">=") list:sort (8 3 2 0)}] - skolem:lemma2104 - skolem:lemma2105 - [ a r:Fact; r:gives {(8320 238) math:difference 8082}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8082 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 8082 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1804}] + [ a r:Fact; r:gives {(1804 2000) math:sum 3804}] + skolem:lemma3802 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2803]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 238]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1804]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3804]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1804 a r:Inference; r:gives { - 2804 :kaprekar (0 6). + 3805 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2804 math:notEqualTo 0}] - skolem:lemma3234 - [ a r:Fact; r:gives {((2 8 0 4) "=<") list:sort (0 2 4 8)}] - [ a r:Fact; r:gives {((2 8 0 4) ">=") list:sort (8 4 2 0)}] - skolem:lemma2126 - skolem:lemma2127 - [ a r:Fact; r:gives {(8420 248) math:difference 8172}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8172 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 8172 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1805}] + [ a r:Fact; r:gives {(1805 2000) math:sum 3805}] + skolem:lemma3803 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2804]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 248]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1805]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3805]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1805 a r:Inference; r:gives { - 2805 :kaprekar (0 5). + 3806 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2805 math:notEqualTo 0}] - skolem:lemma3235 - [ a r:Fact; r:gives {((2 8 0 5) "=<") list:sort (0 2 5 8)}] - [ a r:Fact; r:gives {((2 8 0 5) ">=") list:sort (8 5 2 0)}] - skolem:lemma2146 - skolem:lemma2147 - [ a r:Fact; r:gives {(8520 258) math:difference 8262}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8262 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 8262 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1806}] + [ a r:Fact; r:gives {(1806 2000) math:sum 3806}] + skolem:lemma3804 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2805]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 258]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1806]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3806]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1806 a r:Inference; r:gives { - 2806 :kaprekar (0 2). + 3807 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2806 math:notEqualTo 0}] - skolem:lemma3236 - [ a r:Fact; r:gives {((2 8 0 6) "=<") list:sort (0 2 6 8)}] - [ a r:Fact; r:gives {((2 8 0 6) ">=") list:sort (8 6 2 0)}] - skolem:lemma2164 - skolem:lemma2165 - [ a r:Fact; r:gives {(8620 268) math:difference 8352}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8352 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 8352 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1807}] + [ a r:Fact; r:gives {(1807 2000) math:sum 3807}] + skolem:lemma3805 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2806]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 268]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8620]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1807]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3807]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1807 a r:Inference; r:gives { - 2807 :kaprekar (0 7). + 3808 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2807 math:notEqualTo 0}] - skolem:lemma3237 - [ a r:Fact; r:gives {((2 8 0 7) "=<") list:sort (0 2 7 8)}] - [ a r:Fact; r:gives {((2 8 0 7) ">=") list:sort (8 7 2 0)}] - skolem:lemma2180 - skolem:lemma2181 - [ a r:Fact; r:gives {(8720 278) math:difference 8442}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8442 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 8442 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1808}] + [ a r:Fact; r:gives {(1808 2000) math:sum 3808}] + skolem:lemma3806 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2807]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 278]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8720]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1808]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3808]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1808 a r:Inference; r:gives { - 2808 :kaprekar (0 2). + 3809 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2808 math:notEqualTo 0}] - skolem:lemma3238 - [ a r:Fact; r:gives {((2 8 0 8) "=<") list:sort (0 2 8 8)}] - [ a r:Fact; r:gives {((2 8 0 8) ">=") list:sort (8 8 2 0)}] - skolem:lemma2194 - skolem:lemma2195 - [ a r:Fact; r:gives {(8820 288) math:difference 8532}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8532 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 8532 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1809}] + [ a r:Fact; r:gives {(1809 2000) math:sum 3809}] + skolem:lemma3807 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2808]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 288]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8820]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1809]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3809]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1809 a r:Inference; r:gives { - 2809 :kaprekar (0 7). + 3810 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2809 math:notEqualTo 0}] - skolem:lemma3239 - [ a r:Fact; r:gives {((2 8 0 9) "=<") list:sort (0 2 8 9)}] - [ a r:Fact; r:gives {((2 8 0 9) ">=") list:sort (9 8 2 0)}] - skolem:lemma2197 - skolem:lemma2198 - [ a r:Fact; r:gives {(9820 289) math:difference 9531}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9531 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 9531 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1810}] + [ a r:Fact; r:gives {(1810 2000) math:sum 3810}] + skolem:lemma3808 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2809]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 289]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9820]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9531]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1810]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3810]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1810 a r:Inference; r:gives { - 2810 :kaprekar (0 3). + 3811 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2810 math:notEqualTo 0}] - skolem:lemma3240 - [ a r:Fact; r:gives {((2 8 1 0) "=<") list:sort (0 1 2 8)}] - [ a r:Fact; r:gives {((2 8 1 0) ">=") list:sort (8 2 1 0)}] - skolem:lemma2054 - skolem:lemma2055 - [ a r:Fact; r:gives {(8210 128) math:difference 8082}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8082 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 8082 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1811}] + [ a r:Fact; r:gives {(1811 2000) math:sum 3811}] + skolem:lemma3809 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2810]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 128]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1811]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3811]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1811 a r:Inference; r:gives { - 2811 :kaprekar (0 3). + 3812 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2811 math:notEqualTo 0}] - skolem:lemma3241 - [ a r:Fact; r:gives {((2 8 1 1) "=<") list:sort (1 1 2 8)}] - [ a r:Fact; r:gives {((2 8 1 1) ">=") list:sort (8 2 1 1)}] - skolem:lemma2244 - skolem:lemma2245 - [ a r:Fact; r:gives {(8211 1128) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1812}] + [ a r:Fact; r:gives {(1812 2000) math:sum 3812}] + skolem:lemma3810 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2811]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1128]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1812]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3812]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1812 a r:Inference; r:gives { - 2812 :kaprekar (0 4). + 3813 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2812 math:notEqualTo 0}] - skolem:lemma3242 - [ a r:Fact; r:gives {((2 8 1 2) "=<") list:sort (1 2 2 8)}] - [ a r:Fact; r:gives {((2 8 1 2) ">=") list:sort (8 2 2 1)}] - skolem:lemma2270 - skolem:lemma2271 - [ a r:Fact; r:gives {(8221 1228) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1813}] + [ a r:Fact; r:gives {(1813 2000) math:sum 3813}] + skolem:lemma3811 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2812]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1228]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1813]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3813]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1813 a r:Inference; r:gives { - 2813 :kaprekar (0 3). + 3814 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2813 math:notEqualTo 0}] - skolem:lemma3243 - [ a r:Fact; r:gives {((2 8 1 3) "=<") list:sort (1 2 3 8)}] - [ a r:Fact; r:gives {((2 8 1 3) ">=") list:sort (8 3 2 1)}] - skolem:lemma2294 - skolem:lemma2295 - [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1814}] + [ a r:Fact; r:gives {(1814 2000) math:sum 3814}] + skolem:lemma3812 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2813]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1238]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1814]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3814]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1814 a r:Inference; r:gives { - 2814 :kaprekar (0 5). + 3815 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2814 math:notEqualTo 0}] - skolem:lemma3244 - [ a r:Fact; r:gives {((2 8 1 4) "=<") list:sort (1 2 4 8)}] - [ a r:Fact; r:gives {((2 8 1 4) ">=") list:sort (8 4 2 1)}] - skolem:lemma2316 - skolem:lemma2317 - [ a r:Fact; r:gives {(8421 1248) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1815}] + [ a r:Fact; r:gives {(1815 2000) math:sum 3815}] + skolem:lemma3813 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2814]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1248]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1815]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3815]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1815 a r:Inference; r:gives { - 2815 :kaprekar (0 6). + 3816 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2815 math:notEqualTo 0}] - skolem:lemma3245 - [ a r:Fact; r:gives {((2 8 1 5) "=<") list:sort (1 2 5 8)}] - [ a r:Fact; r:gives {((2 8 1 5) ">=") list:sort (8 5 2 1)}] - skolem:lemma2336 - skolem:lemma2337 - [ a r:Fact; r:gives {(8521 1258) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1816}] + [ a r:Fact; r:gives {(1816 2000) math:sum 3816}] + skolem:lemma3814 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2815]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1258]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1816]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3816]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1816 a r:Inference; r:gives { - 2816 :kaprekar (0 3). + 3817 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2816 math:notEqualTo 0}] - skolem:lemma3246 - [ a r:Fact; r:gives {((2 8 1 6) "=<") list:sort (1 2 6 8)}] - [ a r:Fact; r:gives {((2 8 1 6) ">=") list:sort (8 6 2 1)}] - skolem:lemma2354 - skolem:lemma2355 - [ a r:Fact; r:gives {(8621 1268) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1817}] + [ a r:Fact; r:gives {(1817 2000) math:sum 3817}] + skolem:lemma3815 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2816]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1268]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1817]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3817]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1817 a r:Inference; r:gives { - 2817 :kaprekar (0 5). + 3818 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2817 math:notEqualTo 0}] - skolem:lemma3247 - [ a r:Fact; r:gives {((2 8 1 7) "=<") list:sort (1 2 7 8)}] - [ a r:Fact; r:gives {((2 8 1 7) ">=") list:sort (8 7 2 1)}] - skolem:lemma2370 - skolem:lemma2371 - [ a r:Fact; r:gives {(8721 1278) math:difference 7443}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7443 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1818}] + [ a r:Fact; r:gives {(1818 2000) math:sum 3818}] + skolem:lemma3816 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2817]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1278]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8721]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1818]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3818]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1818 a r:Inference; r:gives { - 2818 :kaprekar (0 3). + 3819 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2818 math:notEqualTo 0}] - skolem:lemma3248 - [ a r:Fact; r:gives {((2 8 1 8) "=<") list:sort (1 2 8 8)}] - [ a r:Fact; r:gives {((2 8 1 8) ">=") list:sort (8 8 2 1)}] - skolem:lemma2384 - skolem:lemma2385 - [ a r:Fact; r:gives {(8821 1288) math:difference 7533}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7533 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7533 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1819}] + [ a r:Fact; r:gives {(1819 2000) math:sum 3819}] + skolem:lemma3817 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2818]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1288]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8821]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1819]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3819]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1819 a r:Inference; r:gives { - 2819 :kaprekar (0 2). + 3820 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2819 math:notEqualTo 0}] - skolem:lemma3249 - [ a r:Fact; r:gives {((2 8 1 9) "=<") list:sort (1 2 8 9)}] - [ a r:Fact; r:gives {((2 8 1 9) ">=") list:sort (9 8 2 1)}] - skolem:lemma2387 - skolem:lemma2388 - [ a r:Fact; r:gives {(9821 1289) math:difference 8532}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8532 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 8532 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1820}] + [ a r:Fact; r:gives {(1820 2000) math:sum 3820}] + skolem:lemma3818 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2819]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1289]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9821]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1820]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3820]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1820 a r:Inference; r:gives { - 2820 :kaprekar (0 6). + 3821 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2820 math:notEqualTo 0}] - skolem:lemma3250 - [ a r:Fact; r:gives {((2 8 2 0) "=<") list:sort (0 2 2 8)}] - [ a r:Fact; r:gives {((2 8 2 0) ">=") list:sort (8 2 2 0)}] - skolem:lemma2080 - skolem:lemma2081 - [ a r:Fact; r:gives {(8220 228) math:difference 7992}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7992 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7992 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1821}] + [ a r:Fact; r:gives {(1821 2000) math:sum 3821}] + skolem:lemma3819 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2820]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 228]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1821]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3821]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1821 a r:Inference; r:gives { - 2821 :kaprekar (0 4). + 3822 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2821 math:notEqualTo 0}] - skolem:lemma3251 - [ a r:Fact; r:gives {((2 8 2 1) "=<") list:sort (1 2 2 8)}] - [ a r:Fact; r:gives {((2 8 2 1) ">=") list:sort (8 2 2 1)}] - skolem:lemma2270 - skolem:lemma2271 - [ a r:Fact; r:gives {(8221 1228) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1822}] + [ a r:Fact; r:gives {(1822 2000) math:sum 3822}] + skolem:lemma3820 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2821]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1228]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1822]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3822]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1822 a r:Inference; r:gives { - 2822 :kaprekar (0 6). + 3823 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2822 math:notEqualTo 0}] - skolem:lemma3252 - [ a r:Fact; r:gives {((2 8 2 2) "=<") list:sort (2 2 2 8)}] - [ a r:Fact; r:gives {((2 8 2 2) ">=") list:sort (8 2 2 2)}] - skolem:lemma2439 - skolem:lemma2440 - [ a r:Fact; r:gives {(8222 2228) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1823}] + [ a r:Fact; r:gives {(1823 2000) math:sum 3823}] + skolem:lemma3821 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2822]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2228]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1823]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3823]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1823 a r:Inference; r:gives { - 2823 :kaprekar (0 7). + 3824 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2823 math:notEqualTo 0}] - skolem:lemma3253 - [ a r:Fact; r:gives {((2 8 2 3) "=<") list:sort (2 2 3 8)}] - [ a r:Fact; r:gives {((2 8 2 3) ">=") list:sort (8 3 2 2)}] - skolem:lemma2463 - skolem:lemma2464 - [ a r:Fact; r:gives {(8322 2238) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1824}] + [ a r:Fact; r:gives {(1824 2000) math:sum 3824}] + skolem:lemma3822 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2823]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2238]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1824]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3824]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1824 a r:Inference; r:gives { - 2824 :kaprekar (0 1). + 3825 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2824 math:notEqualTo 0}] - skolem:lemma3254 - [ a r:Fact; r:gives {((2 8 2 4) "=<") list:sort (2 2 4 8)}] - [ a r:Fact; r:gives {((2 8 2 4) ">=") list:sort (8 4 2 2)}] - skolem:lemma2485 - skolem:lemma2486 - [ a r:Fact; r:gives {(8422 2248) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1825}] + [ a r:Fact; r:gives {(1825 2000) math:sum 3825}] + skolem:lemma3823 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2824]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2248]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1825]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3825]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1825 a r:Inference; r:gives { - 2825 :kaprekar (0 3). + 3826 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2825 math:notEqualTo 0}] - skolem:lemma3255 - [ a r:Fact; r:gives {((2 8 2 5) "=<") list:sort (2 2 5 8)}] - [ a r:Fact; r:gives {((2 8 2 5) ">=") list:sort (8 5 2 2)}] - skolem:lemma2505 - skolem:lemma2506 - [ a r:Fact; r:gives {(8522 2258) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1826}] + [ a r:Fact; r:gives {(1826 2000) math:sum 3826}] + skolem:lemma3824 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2825]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2258]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1826]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3826]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1826 a r:Inference; r:gives { - 2826 :kaprekar (0 4). + 3827 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2826 math:notEqualTo 0}] - skolem:lemma3256 - [ a r:Fact; r:gives {((2 8 2 6) "=<") list:sort (2 2 6 8)}] - [ a r:Fact; r:gives {((2 8 2 6) ">=") list:sort (8 6 2 2)}] - skolem:lemma2523 - skolem:lemma2524 - [ a r:Fact; r:gives {(8622 2268) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1827}] + [ a r:Fact; r:gives {(1827 2000) math:sum 3827}] + skolem:lemma3825 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2826]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2268]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1827]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3827]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1827 a r:Inference; r:gives { - 2827 :kaprekar (0 5). + 3828 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2827 math:notEqualTo 0}] - skolem:lemma3257 - [ a r:Fact; r:gives {((2 8 2 7) "=<") list:sort (2 2 7 8)}] - [ a r:Fact; r:gives {((2 8 2 7) ">=") list:sort (8 7 2 2)}] - skolem:lemma2539 - skolem:lemma2540 - [ a r:Fact; r:gives {(8722 2278) math:difference 6444}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6444 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 6444 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1828}] + [ a r:Fact; r:gives {(1828 2000) math:sum 3828}] + skolem:lemma3826 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2827]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2278]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8722]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1828]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3828]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1828 a r:Inference; r:gives { - 2828 :kaprekar (0 4). + 3829 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2828 math:notEqualTo 0}] - skolem:lemma3258 - [ a r:Fact; r:gives {((2 8 2 8) "=<") list:sort (2 2 8 8)}] - [ a r:Fact; r:gives {((2 8 2 8) ">=") list:sort (8 8 2 2)}] - skolem:lemma2553 - skolem:lemma2554 - [ a r:Fact; r:gives {(8822 2288) math:difference 6534}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6534 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6534 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1829}] + [ a r:Fact; r:gives {(1829 2000) math:sum 3829}] + skolem:lemma3827 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2828]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2288]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8822]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6534]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1829]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3829]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1829 a r:Inference; r:gives { - 2829 :kaprekar (0 3). + 3830 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2829 math:notEqualTo 0}] - skolem:lemma3259 - [ a r:Fact; r:gives {((2 8 2 9) "=<") list:sort (2 2 8 9)}] - [ a r:Fact; r:gives {((2 8 2 9) ">=") list:sort (9 8 2 2)}] - skolem:lemma2556 - skolem:lemma2557 - [ a r:Fact; r:gives {(9822 2289) math:difference 7533}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7533 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7533 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1830}] + [ a r:Fact; r:gives {(1830 2000) math:sum 3830}] + skolem:lemma3828 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2829]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2289]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9822]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1830]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3830]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1830 a r:Inference; r:gives { - 2830 :kaprekar (0 3). + 3831 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2830 math:notEqualTo 0}] - skolem:lemma3260 - [ a r:Fact; r:gives {((2 8 3 0) "=<") list:sort (0 2 3 8)}] - [ a r:Fact; r:gives {((2 8 3 0) ">=") list:sort (8 3 2 0)}] - skolem:lemma2104 - skolem:lemma2105 - [ a r:Fact; r:gives {(8320 238) math:difference 8082}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8082 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 8082 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1831}] + [ a r:Fact; r:gives {(1831 2000) math:sum 3831}] + skolem:lemma3829 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2830]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 238]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1831]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3831]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1831 a r:Inference; r:gives { - 2831 :kaprekar (0 3). + 3832 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2831 math:notEqualTo 0}] - skolem:lemma3261 - [ a r:Fact; r:gives {((2 8 3 1) "=<") list:sort (1 2 3 8)}] - [ a r:Fact; r:gives {((2 8 3 1) ">=") list:sort (8 3 2 1)}] - skolem:lemma2294 - skolem:lemma2295 - [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1832}] + [ a r:Fact; r:gives {(1832 2000) math:sum 3832}] + skolem:lemma3830 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2831]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1238]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1832 a r:Inference; r:gives { - 2832 :kaprekar (0 7). + 3833 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2832 math:notEqualTo 0}] - skolem:lemma3262 - [ a r:Fact; r:gives {((2 8 3 2) "=<") list:sort (2 2 3 8)}] - [ a r:Fact; r:gives {((2 8 3 2) ">=") list:sort (8 3 2 2)}] - skolem:lemma2463 - skolem:lemma2464 - [ a r:Fact; r:gives {(8322 2238) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1833}] + [ a r:Fact; r:gives {(1833 2000) math:sum 3833}] + skolem:lemma3831 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2832]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2238]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1833]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3833]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1833 a r:Inference; r:gives { - 2833 :kaprekar (0 6). + 3834 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2833 math:notEqualTo 0}] - skolem:lemma3263 - [ a r:Fact; r:gives {((2 8 3 3) "=<") list:sort (2 3 3 8)}] - [ a r:Fact; r:gives {((2 8 3 3) ">=") list:sort (8 3 3 2)}] - skolem:lemma2619 - skolem:lemma2620 - [ a r:Fact; r:gives {(8332 2338) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1834}] + [ a r:Fact; r:gives {(1834 2000) math:sum 3834}] + skolem:lemma3832 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2833]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2338]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1834]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3834]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1834 a r:Inference; r:gives { - 2834 :kaprekar (0 7). + 3835 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2834 math:notEqualTo 0}] - skolem:lemma3264 - [ a r:Fact; r:gives {((2 8 3 4) "=<") list:sort (2 3 4 8)}] - [ a r:Fact; r:gives {((2 8 3 4) ">=") list:sort (8 4 3 2)}] - skolem:lemma2641 - skolem:lemma2642 - [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1835}] + [ a r:Fact; r:gives {(1835 2000) math:sum 3835}] + skolem:lemma3833 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2834]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2348]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1835]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3835]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1835 a r:Inference; r:gives { - 2835 :kaprekar (0 1). + 3836 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2835 math:notEqualTo 0}] - skolem:lemma3265 - [ a r:Fact; r:gives {((2 8 3 5) "=<") list:sort (2 3 5 8)}] - [ a r:Fact; r:gives {((2 8 3 5) ">=") list:sort (8 5 3 2)}] - skolem:lemma2661 - skolem:lemma2662 - [ a r:Fact; r:gives {(8532 2358) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1836}] + [ a r:Fact; r:gives {(1836 2000) math:sum 3836}] + skolem:lemma3834 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2835]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2358]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1836]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3836]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1836 a r:Inference; r:gives { - 2836 :kaprekar (0 3). + 3837 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2836 math:notEqualTo 0}] - skolem:lemma3266 - [ a r:Fact; r:gives {((2 8 3 6) "=<") list:sort (2 3 6 8)}] - [ a r:Fact; r:gives {((2 8 3 6) ">=") list:sort (8 6 3 2)}] - skolem:lemma2679 - skolem:lemma2680 - [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1837}] + [ a r:Fact; r:gives {(1837 2000) math:sum 3837}] + skolem:lemma3835 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2836]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2368]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1837]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3837]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1837 a r:Inference; r:gives { - 2837 :kaprekar (0 4). + 3838 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2837 math:notEqualTo 0}] - skolem:lemma3267 - [ a r:Fact; r:gives {((2 8 3 7) "=<") list:sort (2 3 7 8)}] - [ a r:Fact; r:gives {((2 8 3 7) ">=") list:sort (8 7 3 2)}] - skolem:lemma2695 - skolem:lemma2696 - [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1838}] + [ a r:Fact; r:gives {(1838 2000) math:sum 3838}] + skolem:lemma3836 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2837]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2378]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8732]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1838]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3838]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1838 a r:Inference; r:gives { - 2838 :kaprekar (0 5). + 3839 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2838 math:notEqualTo 0}] - skolem:lemma3268 - [ a r:Fact; r:gives {((2 8 3 8) "=<") list:sort (2 3 8 8)}] - [ a r:Fact; r:gives {((2 8 3 8) ">=") list:sort (8 8 3 2)}] - skolem:lemma2709 - skolem:lemma2710 - [ a r:Fact; r:gives {(8832 2388) math:difference 6444}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6444 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 6444 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1839}] + [ a r:Fact; r:gives {(1839 2000) math:sum 3839}] + skolem:lemma3837 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2838]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2388]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8832]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1839]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3839]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1839 a r:Inference; r:gives { - 2839 :kaprekar (0 5). + 3840 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2839 math:notEqualTo 0}] - skolem:lemma3269 - [ a r:Fact; r:gives {((2 8 3 9) "=<") list:sort (2 3 8 9)}] - [ a r:Fact; r:gives {((2 8 3 9) ">=") list:sort (9 8 3 2)}] - skolem:lemma2712 - skolem:lemma2713 - [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7443 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1840}] + [ a r:Fact; r:gives {(1840 2000) math:sum 3840}] + skolem:lemma3838 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2839]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2389]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9832]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1840]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3840]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1840 a r:Inference; r:gives { - 2840 :kaprekar (0 6). + 3841 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2840 math:notEqualTo 0}] - skolem:lemma3270 - [ a r:Fact; r:gives {((2 8 4 0) "=<") list:sort (0 2 4 8)}] - [ a r:Fact; r:gives {((2 8 4 0) ">=") list:sort (8 4 2 0)}] - skolem:lemma2126 - skolem:lemma2127 - [ a r:Fact; r:gives {(8420 248) math:difference 8172}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8172 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 8172 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1841}] + [ a r:Fact; r:gives {(1841 2000) math:sum 3841}] + skolem:lemma3839 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2840]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 248]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1841]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3841]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1841 a r:Inference; r:gives { - 2841 :kaprekar (0 5). + 3842 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2841 math:notEqualTo 0}] - skolem:lemma3271 - [ a r:Fact; r:gives {((2 8 4 1) "=<") list:sort (1 2 4 8)}] - [ a r:Fact; r:gives {((2 8 4 1) ">=") list:sort (8 4 2 1)}] - skolem:lemma2316 - skolem:lemma2317 - [ a r:Fact; r:gives {(8421 1248) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1842}] + [ a r:Fact; r:gives {(1842 2000) math:sum 3842}] + skolem:lemma3840 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2841]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1248]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1842]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3842]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1842 a r:Inference; r:gives { - 2842 :kaprekar (0 1). + 3843 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2842 math:notEqualTo 0}] - skolem:lemma3272 - [ a r:Fact; r:gives {((2 8 4 2) "=<") list:sort (2 2 4 8)}] - [ a r:Fact; r:gives {((2 8 4 2) ">=") list:sort (8 4 2 2)}] - skolem:lemma2485 - skolem:lemma2486 - [ a r:Fact; r:gives {(8422 2248) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1843}] + [ a r:Fact; r:gives {(1843 2000) math:sum 3843}] + skolem:lemma3841 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2842]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2248]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1843]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3843]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1843 a r:Inference; r:gives { - 2843 :kaprekar (0 7). + 3844 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2843 math:notEqualTo 0}] - skolem:lemma3273 - [ a r:Fact; r:gives {((2 8 4 3) "=<") list:sort (2 3 4 8)}] - [ a r:Fact; r:gives {((2 8 4 3) ">=") list:sort (8 4 3 2)}] - skolem:lemma2641 - skolem:lemma2642 - [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1844}] + [ a r:Fact; r:gives {(1844 2000) math:sum 3844}] + skolem:lemma3842 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2843]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2348]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1844]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3844]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1844 a r:Inference; r:gives { - 2844 :kaprekar (0 6). + 3845 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2844 math:notEqualTo 0}] - skolem:lemma3274 - [ a r:Fact; r:gives {((2 8 4 4) "=<") list:sort (2 4 4 8)}] - [ a r:Fact; r:gives {((2 8 4 4) ">=") list:sort (8 4 4 2)}] - skolem:lemma2783 - skolem:lemma2784 - [ a r:Fact; r:gives {(8442 2448) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1845}] + [ a r:Fact; r:gives {(1845 2000) math:sum 3845}] + skolem:lemma3843 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2844]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2448]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1845]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3845]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1845 a r:Inference; r:gives { - 2845 :kaprekar (0 7). + 3846 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2845 math:notEqualTo 0}] - skolem:lemma3275 - [ a r:Fact; r:gives {((2 8 4 5) "=<") list:sort (2 4 5 8)}] - [ a r:Fact; r:gives {((2 8 4 5) ">=") list:sort (8 5 4 2)}] - skolem:lemma2803 - skolem:lemma2804 - [ a r:Fact; r:gives {(8542 2458) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1846}] + [ a r:Fact; r:gives {(1846 2000) math:sum 3846}] + skolem:lemma3844 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2845]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2458]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1846]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3846]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1846 a r:Inference; r:gives { - 2846 :kaprekar (0 1). + 3847 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2846 math:notEqualTo 0}] - skolem:lemma3276 - [ a r:Fact; r:gives {((2 8 4 6) "=<") list:sort (2 4 6 8)}] - [ a r:Fact; r:gives {((2 8 4 6) ">=") list:sort (8 6 4 2)}] - skolem:lemma2821 - skolem:lemma2822 - [ a r:Fact; r:gives {(8642 2468) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1847}] + [ a r:Fact; r:gives {(1847 2000) math:sum 3847}] + skolem:lemma3845 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2846]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2468]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1847]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3847]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1847 a r:Inference; r:gives { - 2847 :kaprekar (0 3). + 3848 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2847 math:notEqualTo 0}] - skolem:lemma3277 - [ a r:Fact; r:gives {((2 8 4 7) "=<") list:sort (2 4 7 8)}] - [ a r:Fact; r:gives {((2 8 4 7) ">=") list:sort (8 7 4 2)}] - skolem:lemma2837 - skolem:lemma2838 - [ a r:Fact; r:gives {(8742 2478) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1848}] + [ a r:Fact; r:gives {(1848 2000) math:sum 3848}] + skolem:lemma3846 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2847]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2478]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8742]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1848]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3848]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1848 a r:Inference; r:gives { - 2848 :kaprekar (0 4). + 3849 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2848 math:notEqualTo 0}] - skolem:lemma3278 - [ a r:Fact; r:gives {((2 8 4 8) "=<") list:sort (2 4 8 8)}] - [ a r:Fact; r:gives {((2 8 4 8) ">=") list:sort (8 8 4 2)}] - skolem:lemma2851 - skolem:lemma2852 - [ a r:Fact; r:gives {(8842 2488) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1849}] + [ a r:Fact; r:gives {(1849 2000) math:sum 3849}] + skolem:lemma3847 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2848]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2488]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8842]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1849]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3849]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1849 a r:Inference; r:gives { - 2849 :kaprekar (0 3). + 3850 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2849 math:notEqualTo 0}] - skolem:lemma3279 - [ a r:Fact; r:gives {((2 8 4 9) "=<") list:sort (2 4 8 9)}] - [ a r:Fact; r:gives {((2 8 4 9) ">=") list:sort (9 8 4 2)}] - skolem:lemma2854 - skolem:lemma2855 - [ a r:Fact; r:gives {(9842 2489) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1850}] + [ a r:Fact; r:gives {(1850 2000) math:sum 3850}] + skolem:lemma3848 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2849]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2489]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9842]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1850]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3850]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1850 a r:Inference; r:gives { - 2850 :kaprekar (0 5). + 3851 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2850 math:notEqualTo 0}] - skolem:lemma3280 - [ a r:Fact; r:gives {((2 8 5 0) "=<") list:sort (0 2 5 8)}] - [ a r:Fact; r:gives {((2 8 5 0) ">=") list:sort (8 5 2 0)}] - skolem:lemma2146 - skolem:lemma2147 - [ a r:Fact; r:gives {(8520 258) math:difference 8262}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8262 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 8262 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1851}] + [ a r:Fact; r:gives {(1851 2000) math:sum 3851}] + skolem:lemma3849 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2850]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 258]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1851]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3851]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1851 a r:Inference; r:gives { - 2851 :kaprekar (0 6). + 3852 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2851 math:notEqualTo 0}] - skolem:lemma3281 - [ a r:Fact; r:gives {((2 8 5 1) "=<") list:sort (1 2 5 8)}] - [ a r:Fact; r:gives {((2 8 5 1) ">=") list:sort (8 5 2 1)}] - skolem:lemma2336 - skolem:lemma2337 - [ a r:Fact; r:gives {(8521 1258) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1852}] + [ a r:Fact; r:gives {(1852 2000) math:sum 3852}] + skolem:lemma3850 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2851]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1258]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1852]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3852]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1852 a r:Inference; r:gives { - 2852 :kaprekar (0 3). + 3853 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2852 math:notEqualTo 0}] - skolem:lemma3282 - [ a r:Fact; r:gives {((2 8 5 2) "=<") list:sort (2 2 5 8)}] - [ a r:Fact; r:gives {((2 8 5 2) ">=") list:sort (8 5 2 2)}] - skolem:lemma2505 - skolem:lemma2506 - [ a r:Fact; r:gives {(8522 2258) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1853}] + [ a r:Fact; r:gives {(1853 2000) math:sum 3853}] + skolem:lemma3851 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2852]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2258]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1853]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3853]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1853 a r:Inference; r:gives { - 2853 :kaprekar (0 1). + 3854 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2853 math:notEqualTo 0}] - skolem:lemma3283 - [ a r:Fact; r:gives {((2 8 5 3) "=<") list:sort (2 3 5 8)}] - [ a r:Fact; r:gives {((2 8 5 3) ">=") list:sort (8 5 3 2)}] - skolem:lemma2661 - skolem:lemma2662 - [ a r:Fact; r:gives {(8532 2358) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1854}] + [ a r:Fact; r:gives {(1854 2000) math:sum 3854}] + skolem:lemma3852 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2853]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2358]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1854]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3854]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1854 a r:Inference; r:gives { - 2854 :kaprekar (0 7). + 3855 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2854 math:notEqualTo 0}] - skolem:lemma3284 - [ a r:Fact; r:gives {((2 8 5 4) "=<") list:sort (2 4 5 8)}] - [ a r:Fact; r:gives {((2 8 5 4) ">=") list:sort (8 5 4 2)}] - skolem:lemma2803 - skolem:lemma2804 - [ a r:Fact; r:gives {(8542 2458) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1855}] + [ a r:Fact; r:gives {(1855 2000) math:sum 3855}] + skolem:lemma3853 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2854]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2458]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1855]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3855]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1855 a r:Inference; r:gives { - 2855 :kaprekar (0 6). + 3856 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2855 math:notEqualTo 0}] - skolem:lemma3285 - [ a r:Fact; r:gives {((2 8 5 5) "=<") list:sort (2 5 5 8)}] - [ a r:Fact; r:gives {((2 8 5 5) ">=") list:sort (8 5 5 2)}] - skolem:lemma2933 - skolem:lemma2934 - [ a r:Fact; r:gives {(8552 2558) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1856}] + [ a r:Fact; r:gives {(1856 2000) math:sum 3856}] + skolem:lemma3854 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2855]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2558]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8552]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1856]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3856]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1856 a r:Inference; r:gives { - 2856 :kaprekar (0 7). + 3857 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2856 math:notEqualTo 0}] - skolem:lemma3286 - [ a r:Fact; r:gives {((2 8 5 6) "=<") list:sort (2 5 6 8)}] - [ a r:Fact; r:gives {((2 8 5 6) ">=") list:sort (8 6 5 2)}] - skolem:lemma2951 - skolem:lemma2952 - [ a r:Fact; r:gives {(8652 2568) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1857}] + [ a r:Fact; r:gives {(1857 2000) math:sum 3857}] + skolem:lemma3855 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2856]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2568]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1857]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3857]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1857 a r:Inference; r:gives { - 2857 :kaprekar (0 1). + 3858 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2857 math:notEqualTo 0}] - skolem:lemma3287 - [ a r:Fact; r:gives {((2 8 5 7) "=<") list:sort (2 5 7 8)}] - [ a r:Fact; r:gives {((2 8 5 7) ">=") list:sort (8 7 5 2)}] - skolem:lemma2967 - skolem:lemma2968 - [ a r:Fact; r:gives {(8752 2578) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1858}] + [ a r:Fact; r:gives {(1858 2000) math:sum 3858}] + skolem:lemma3856 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2857]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2578]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8752]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1858]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3858]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1858 a r:Inference; r:gives { - 2858 :kaprekar (0 3). + 3859 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2858 math:notEqualTo 0}] - skolem:lemma3288 - [ a r:Fact; r:gives {((2 8 5 8) "=<") list:sort (2 5 8 8)}] - [ a r:Fact; r:gives {((2 8 5 8) ">=") list:sort (8 8 5 2)}] - skolem:lemma2981 - skolem:lemma2982 - [ a r:Fact; r:gives {(8852 2588) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1859}] + [ a r:Fact; r:gives {(1859 2000) math:sum 3859}] + skolem:lemma3857 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2858]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2588]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8852]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1859]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3859]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1859 a r:Inference; r:gives { - 2859 :kaprekar (0 6). + 3860 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2859 math:notEqualTo 0}] - skolem:lemma3289 - [ a r:Fact; r:gives {((2 8 5 9) "=<") list:sort (2 5 8 9)}] - [ a r:Fact; r:gives {((2 8 5 9) ">=") list:sort (9 8 5 2)}] - skolem:lemma2984 - skolem:lemma2985 - [ a r:Fact; r:gives {(9852 2589) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1860}] + [ a r:Fact; r:gives {(1860 2000) math:sum 3860}] + skolem:lemma3858 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2859]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2589]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9852]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1860]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3860]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1860 a r:Inference; r:gives { - 2860 :kaprekar (0 2). + 3861 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2860 math:notEqualTo 0}] - skolem:lemma3290 - [ a r:Fact; r:gives {((2 8 6 0) "=<") list:sort (0 2 6 8)}] - [ a r:Fact; r:gives {((2 8 6 0) ">=") list:sort (8 6 2 0)}] - skolem:lemma2164 - skolem:lemma2165 - [ a r:Fact; r:gives {(8620 268) math:difference 8352}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8352 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 8352 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1861}] + [ a r:Fact; r:gives {(1861 2000) math:sum 3861}] + skolem:lemma3859 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2860]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 268]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8620]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1861]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3861]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1861 a r:Inference; r:gives { - 2861 :kaprekar (0 3). + 3862 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2861 math:notEqualTo 0}] - skolem:lemma3291 - [ a r:Fact; r:gives {((2 8 6 1) "=<") list:sort (1 2 6 8)}] - [ a r:Fact; r:gives {((2 8 6 1) ">=") list:sort (8 6 2 1)}] - skolem:lemma2354 - skolem:lemma2355 - [ a r:Fact; r:gives {(8621 1268) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1862}] + [ a r:Fact; r:gives {(1862 2000) math:sum 3862}] + skolem:lemma3860 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2861]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1268]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1862]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3862]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1862 a r:Inference; r:gives { - 2862 :kaprekar (0 4). + 3863 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2862 math:notEqualTo 0}] - skolem:lemma3292 - [ a r:Fact; r:gives {((2 8 6 2) "=<") list:sort (2 2 6 8)}] - [ a r:Fact; r:gives {((2 8 6 2) ">=") list:sort (8 6 2 2)}] - skolem:lemma2523 - skolem:lemma2524 - [ a r:Fact; r:gives {(8622 2268) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1863}] + [ a r:Fact; r:gives {(1863 2000) math:sum 3863}] + skolem:lemma3861 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2862]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2268]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1863]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3863]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1863 a r:Inference; r:gives { - 2863 :kaprekar (0 3). + 3864 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2863 math:notEqualTo 0}] - skolem:lemma3293 - [ a r:Fact; r:gives {((2 8 6 3) "=<") list:sort (2 3 6 8)}] - [ a r:Fact; r:gives {((2 8 6 3) ">=") list:sort (8 6 3 2)}] - skolem:lemma2679 - skolem:lemma2680 - [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1864}] + [ a r:Fact; r:gives {(1864 2000) math:sum 3864}] + skolem:lemma3862 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2863]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2368]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1864]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3864]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1864 a r:Inference; r:gives { - 2864 :kaprekar (0 1). + 3865 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2864 math:notEqualTo 0}] - skolem:lemma3294 - [ a r:Fact; r:gives {((2 8 6 4) "=<") list:sort (2 4 6 8)}] - [ a r:Fact; r:gives {((2 8 6 4) ">=") list:sort (8 6 4 2)}] - skolem:lemma2821 - skolem:lemma2822 - [ a r:Fact; r:gives {(8642 2468) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1865}] + [ a r:Fact; r:gives {(1865 2000) math:sum 3865}] + skolem:lemma3863 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2864]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2468]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1865]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3865]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1865 a r:Inference; r:gives { - 2865 :kaprekar (0 7). + 3866 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2865 math:notEqualTo 0}] - skolem:lemma3295 - [ a r:Fact; r:gives {((2 8 6 5) "=<") list:sort (2 5 6 8)}] - [ a r:Fact; r:gives {((2 8 6 5) ">=") list:sort (8 6 5 2)}] - skolem:lemma2951 - skolem:lemma2952 - [ a r:Fact; r:gives {(8652 2568) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1866}] + [ a r:Fact; r:gives {(1866 2000) math:sum 3866}] + skolem:lemma3864 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2865]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2568]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1866]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3866]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1866 a r:Inference; r:gives { - 2866 :kaprekar (0 6). + 3867 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2866 math:notEqualTo 0}] - skolem:lemma3296 - [ a r:Fact; r:gives {((2 8 6 6) "=<") list:sort (2 6 6 8)}] - [ a r:Fact; r:gives {((2 8 6 6) ">=") list:sort (8 6 6 2)}] - skolem:lemma3071 - skolem:lemma3072 - [ a r:Fact; r:gives {(8662 2668) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1867}] + [ a r:Fact; r:gives {(1867 2000) math:sum 3867}] + skolem:lemma3865 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2866]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2668]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8662]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1867]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3867]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1867 a r:Inference; r:gives { - 2867 :kaprekar (0 7). + 3868 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2867 math:notEqualTo 0}] - skolem:lemma3297 - [ a r:Fact; r:gives {((2 8 6 7) "=<") list:sort (2 6 7 8)}] - [ a r:Fact; r:gives {((2 8 6 7) ">=") list:sort (8 7 6 2)}] - skolem:lemma3087 - skolem:lemma3088 - [ a r:Fact; r:gives {(8762 2678) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1868}] + [ a r:Fact; r:gives {(1868 2000) math:sum 3868}] + skolem:lemma3866 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2867]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2678]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8762]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1868]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3868]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1868 a r:Inference; r:gives { - 2868 :kaprekar (0 1). + 3869 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2868 math:notEqualTo 0}] - skolem:lemma3298 - [ a r:Fact; r:gives {((2 8 6 8) "=<") list:sort (2 6 8 8)}] - [ a r:Fact; r:gives {((2 8 6 8) ">=") list:sort (8 8 6 2)}] - skolem:lemma3101 - skolem:lemma3102 - [ a r:Fact; r:gives {(8862 2688) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1869}] + [ a r:Fact; r:gives {(1869 2000) math:sum 3869}] + skolem:lemma3867 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2868]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2688]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8862]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1869]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3869]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1869 a r:Inference; r:gives { - 2869 :kaprekar (0 5). + 3870 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2869 math:notEqualTo 0}] - skolem:lemma3299 - [ a r:Fact; r:gives {((2 8 6 9) "=<") list:sort (2 6 8 9)}] - [ a r:Fact; r:gives {((2 8 6 9) ">=") list:sort (9 8 6 2)}] - skolem:lemma3104 - skolem:lemma3105 - [ a r:Fact; r:gives {(9862 2689) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1870}] + [ a r:Fact; r:gives {(1870 2000) math:sum 3870}] + skolem:lemma3868 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2869]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2689]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9862]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1870]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3870]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1870 a r:Inference; r:gives { - 2870 :kaprekar (0 7). + 3871 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2870 math:notEqualTo 0}] - skolem:lemma3300 - [ a r:Fact; r:gives {((2 8 7 0) "=<") list:sort (0 2 7 8)}] - [ a r:Fact; r:gives {((2 8 7 0) ">=") list:sort (8 7 2 0)}] - skolem:lemma2180 - skolem:lemma2181 - [ a r:Fact; r:gives {(8720 278) math:difference 8442}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8442 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 8442 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1871}] + [ a r:Fact; r:gives {(1871 2000) math:sum 3871}] + skolem:lemma3869 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2870]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 278]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8720]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1871]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3871]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1871 a r:Inference; r:gives { - 2871 :kaprekar (0 5). + 3872 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2871 math:notEqualTo 0}] - skolem:lemma3301 - [ a r:Fact; r:gives {((2 8 7 1) "=<") list:sort (1 2 7 8)}] - [ a r:Fact; r:gives {((2 8 7 1) ">=") list:sort (8 7 2 1)}] - skolem:lemma2370 - skolem:lemma2371 - [ a r:Fact; r:gives {(8721 1278) math:difference 7443}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7443 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1872}] + [ a r:Fact; r:gives {(1872 2000) math:sum 3872}] + skolem:lemma3870 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2871]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1278]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8721]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1872]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3872]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1872 a r:Inference; r:gives { - 2872 :kaprekar (0 5). + 3873 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2872 math:notEqualTo 0}] - skolem:lemma3302 - [ a r:Fact; r:gives {((2 8 7 2) "=<") list:sort (2 2 7 8)}] - [ a r:Fact; r:gives {((2 8 7 2) ">=") list:sort (8 7 2 2)}] - skolem:lemma2539 - skolem:lemma2540 - [ a r:Fact; r:gives {(8722 2278) math:difference 6444}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6444 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 6444 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1873}] + [ a r:Fact; r:gives {(1873 2000) math:sum 3873}] + skolem:lemma3871 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2872]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2278]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8722]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1873]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3873]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1873 a r:Inference; r:gives { - 2873 :kaprekar (0 4). + 3874 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2873 math:notEqualTo 0}] - skolem:lemma3303 - [ a r:Fact; r:gives {((2 8 7 3) "=<") list:sort (2 3 7 8)}] - [ a r:Fact; r:gives {((2 8 7 3) ">=") list:sort (8 7 3 2)}] - skolem:lemma2695 - skolem:lemma2696 - [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1874}] + [ a r:Fact; r:gives {(1874 2000) math:sum 3874}] + skolem:lemma3872 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2873]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2378]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8732]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1874]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3874]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1874 a r:Inference; r:gives { - 2874 :kaprekar (0 3). + 3875 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2874 math:notEqualTo 0}] - skolem:lemma3304 - [ a r:Fact; r:gives {((2 8 7 4) "=<") list:sort (2 4 7 8)}] - [ a r:Fact; r:gives {((2 8 7 4) ">=") list:sort (8 7 4 2)}] - skolem:lemma2837 - skolem:lemma2838 - [ a r:Fact; r:gives {(8742 2478) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1875}] + [ a r:Fact; r:gives {(1875 2000) math:sum 3875}] + skolem:lemma3873 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2874]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2478]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8742]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1875]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3875]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1875 a r:Inference; r:gives { - 2875 :kaprekar (0 1). + 3876 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2875 math:notEqualTo 0}] - skolem:lemma3305 - [ a r:Fact; r:gives {((2 8 7 5) "=<") list:sort (2 5 7 8)}] - [ a r:Fact; r:gives {((2 8 7 5) ">=") list:sort (8 7 5 2)}] - skolem:lemma2967 - skolem:lemma2968 - [ a r:Fact; r:gives {(8752 2578) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1876}] + [ a r:Fact; r:gives {(1876 2000) math:sum 3876}] + skolem:lemma3874 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2875]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2578]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8752]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1876]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3876]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1876 a r:Inference; r:gives { - 2876 :kaprekar (0 7). + 3877 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2876 math:notEqualTo 0}] - skolem:lemma3306 - [ a r:Fact; r:gives {((2 8 7 6) "=<") list:sort (2 6 7 8)}] - [ a r:Fact; r:gives {((2 8 7 6) ">=") list:sort (8 7 6 2)}] - skolem:lemma3087 - skolem:lemma3088 - [ a r:Fact; r:gives {(8762 2678) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1877}] + [ a r:Fact; r:gives {(1877 2000) math:sum 3877}] + skolem:lemma3875 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2876]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2678]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8762]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1877]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3877]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1877 a r:Inference; r:gives { - 2877 :kaprekar (0 6). + 3878 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2877 math:notEqualTo 0}] - skolem:lemma3307 - [ a r:Fact; r:gives {((2 8 7 7) "=<") list:sort (2 7 7 8)}] - [ a r:Fact; r:gives {((2 8 7 7) ">=") list:sort (8 7 7 2)}] - skolem:lemma3199 - skolem:lemma3200 - [ a r:Fact; r:gives {(8772 2778) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1878}] + [ a r:Fact; r:gives {(1878 2000) math:sum 3878}] + skolem:lemma3876 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2877]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2778]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8772]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1878]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3878]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1878 a r:Inference; r:gives { - 2878 :kaprekar (0 7). + 3879 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2878 math:notEqualTo 0}] - skolem:lemma3308 - [ a r:Fact; r:gives {((2 8 7 8) "=<") list:sort (2 7 8 8)}] - [ a r:Fact; r:gives {((2 8 7 8) ">=") list:sort (8 8 7 2)}] - skolem:lemma3213 - skolem:lemma3214 - [ a r:Fact; r:gives {(8872 2788) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1879}] + [ a r:Fact; r:gives {(1879 2000) math:sum 3879}] + skolem:lemma3877 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2878]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2788]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8872]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1879]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3879]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1879 a r:Inference; r:gives { - 2879 :kaprekar (0 3). + 3880 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2879 math:notEqualTo 0}] - skolem:lemma3309 - [ a r:Fact; r:gives {((2 8 7 9) "=<") list:sort (2 7 8 9)}] - [ a r:Fact; r:gives {((2 8 7 9) ">=") list:sort (9 8 7 2)}] - skolem:lemma3216 - skolem:lemma3217 - [ a r:Fact; r:gives {(9872 2789) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1880}] + [ a r:Fact; r:gives {(1880 2000) math:sum 3880}] + skolem:lemma3878 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2879]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2789]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9872]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1880]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3880]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1880 a r:Inference; r:gives { - 2880 :kaprekar (0 2). + 3881 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2880 math:notEqualTo 0}] - skolem:lemma3310 - [ a r:Fact; r:gives {((2 8 8 0) "=<") list:sort (0 2 8 8)}] - [ a r:Fact; r:gives {((2 8 8 0) ">=") list:sort (8 8 2 0)}] - skolem:lemma2194 - skolem:lemma2195 - [ a r:Fact; r:gives {(8820 288) math:difference 8532}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8532 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 8532 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1881}] + [ a r:Fact; r:gives {(1881 2000) math:sum 3881}] + skolem:lemma3879 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2880]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 288]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8820]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1881]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3881]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1881 a r:Inference; r:gives { - 2881 :kaprekar (0 3). + 3882 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2881 math:notEqualTo 0}] - skolem:lemma3311 - [ a r:Fact; r:gives {((2 8 8 1) "=<") list:sort (1 2 8 8)}] - [ a r:Fact; r:gives {((2 8 8 1) ">=") list:sort (8 8 2 1)}] - skolem:lemma2384 - skolem:lemma2385 - [ a r:Fact; r:gives {(8821 1288) math:difference 7533}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7533 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7533 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1882}] + [ a r:Fact; r:gives {(1882 2000) math:sum 3882}] + skolem:lemma3880 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2881]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1288]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8821]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1882]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3882]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1882 a r:Inference; r:gives { - 2882 :kaprekar (0 4). + 3883 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2882 math:notEqualTo 0}] - skolem:lemma3312 - [ a r:Fact; r:gives {((2 8 8 2) "=<") list:sort (2 2 8 8)}] - [ a r:Fact; r:gives {((2 8 8 2) ">=") list:sort (8 8 2 2)}] - skolem:lemma2553 - skolem:lemma2554 - [ a r:Fact; r:gives {(8822 2288) math:difference 6534}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6534 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6534 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1883}] + [ a r:Fact; r:gives {(1883 2000) math:sum 3883}] + skolem:lemma3881 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2882]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2288]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8822]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6534]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1883]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3883]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1883 a r:Inference; r:gives { - 2883 :kaprekar (0 5). + 3884 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2883 math:notEqualTo 0}] - skolem:lemma3313 - [ a r:Fact; r:gives {((2 8 8 3) "=<") list:sort (2 3 8 8)}] - [ a r:Fact; r:gives {((2 8 8 3) ">=") list:sort (8 8 3 2)}] - skolem:lemma2709 - skolem:lemma2710 - [ a r:Fact; r:gives {(8832 2388) math:difference 6444}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6444 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 6444 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1884}] + [ a r:Fact; r:gives {(1884 2000) math:sum 3884}] + skolem:lemma3882 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2883]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2388]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8832]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1884]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3884]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1884 a r:Inference; r:gives { - 2884 :kaprekar (0 4). + 3885 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2884 math:notEqualTo 0}] - skolem:lemma3314 - [ a r:Fact; r:gives {((2 8 8 4) "=<") list:sort (2 4 8 8)}] - [ a r:Fact; r:gives {((2 8 8 4) ">=") list:sort (8 8 4 2)}] - skolem:lemma2851 - skolem:lemma2852 - [ a r:Fact; r:gives {(8842 2488) math:difference 6354}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6354 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6354 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1885}] + [ a r:Fact; r:gives {(1885 2000) math:sum 3885}] + skolem:lemma3883 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2884]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2488]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8842]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1885]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3885]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1885 a r:Inference; r:gives { - 2885 :kaprekar (0 3). + 3886 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2885 math:notEqualTo 0}] - skolem:lemma3315 - [ a r:Fact; r:gives {((2 8 8 5) "=<") list:sort (2 5 8 8)}] - [ a r:Fact; r:gives {((2 8 8 5) ">=") list:sort (8 8 5 2)}] - skolem:lemma2981 - skolem:lemma2982 - [ a r:Fact; r:gives {(8852 2588) math:difference 6264}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6264 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 6264 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1886}] + [ a r:Fact; r:gives {(1886 2000) math:sum 3886}] + skolem:lemma3884 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2885]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2588]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8852]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1886]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3886]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1886 a r:Inference; r:gives { - 2886 :kaprekar (0 1). + 3887 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2886 math:notEqualTo 0}] - skolem:lemma3316 - [ a r:Fact; r:gives {((2 8 8 6) "=<") list:sort (2 6 8 8)}] - [ a r:Fact; r:gives {((2 8 8 6) ">=") list:sort (8 8 6 2)}] - skolem:lemma3101 - skolem:lemma3102 - [ a r:Fact; r:gives {(8862 2688) math:difference 6174}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6174 math:equalTo 6174. - } { - 1 log:equalTo 1. - } { - 6174 :kaprekar (1 1). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1887}] + [ a r:Fact; r:gives {(1887 2000) math:sum 3887}] + skolem:lemma3885 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2886]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2688]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8862]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1887]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3887]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1887 a r:Inference; r:gives { - 2887 :kaprekar (0 7). + 3888 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2887 math:notEqualTo 0}] - skolem:lemma3317 - [ a r:Fact; r:gives {((2 8 8 7) "=<") list:sort (2 7 8 8)}] - [ a r:Fact; r:gives {((2 8 8 7) ">=") list:sort (8 8 7 2)}] - skolem:lemma3213 - skolem:lemma3214 - [ a r:Fact; r:gives {(8872 2788) math:difference 6084}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6084 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 6084 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1888}] + [ a r:Fact; r:gives {(1888 2000) math:sum 3888}] + skolem:lemma3886 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2887]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2788]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8872]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1888]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3888]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1888 a r:Inference; r:gives { - 2888 :kaprekar (0 6). + 3889 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2888 math:notEqualTo 0}] - skolem:lemma3318 - [ a r:Fact; r:gives {((2 8 8 8) "=<") list:sort (2 8 8 8)}] - [ a r:Fact; r:gives {((2 8 8 8) ">=") list:sort (8 8 8 2)}] - skolem:lemma3319 - skolem:lemma3320 - [ a r:Fact; r:gives {(8882 2888) math:difference 5994}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 5994 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 5994 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1889}] + [ a r:Fact; r:gives {(1889 2000) math:sum 3889}] + skolem:lemma3887 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2888]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 8 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2888]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8882]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1889]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3889]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1889 a r:Inference; r:gives { - 2889 :kaprekar (0 4). + 3890 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2889 math:notEqualTo 0}] - skolem:lemma3321 - [ a r:Fact; r:gives {((2 8 8 9) "=<") list:sort (2 8 8 9)}] - [ a r:Fact; r:gives {((2 8 8 9) ">=") list:sort (9 8 8 2)}] - skolem:lemma3322 - skolem:lemma3323 - [ a r:Fact; r:gives {(9882 2889) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1890}] + [ a r:Fact; r:gives {(1890 2000) math:sum 3890}] + skolem:lemma3888 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2889]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 8 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2889]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9882]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1890]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3890]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1890 a r:Inference; r:gives { - 2890 :kaprekar (0 7). + 3891 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2890 math:notEqualTo 0}] - skolem:lemma3324 - [ a r:Fact; r:gives {((2 8 9 0) "=<") list:sort (0 2 8 9)}] - [ a r:Fact; r:gives {((2 8 9 0) ">=") list:sort (9 8 2 0)}] - skolem:lemma2197 - skolem:lemma2198 - [ a r:Fact; r:gives {(9820 289) math:difference 9531}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9531 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 9531 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1891}] + [ a r:Fact; r:gives {(1891 2000) math:sum 3891}] + skolem:lemma3889 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2890]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 289]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9820]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9531]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1891]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3891]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1891 a r:Inference; r:gives { - 2891 :kaprekar (0 2). + 3892 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2891 math:notEqualTo 0}] - skolem:lemma3325 - [ a r:Fact; r:gives {((2 8 9 1) "=<") list:sort (1 2 8 9)}] - [ a r:Fact; r:gives {((2 8 9 1) ">=") list:sort (9 8 2 1)}] - skolem:lemma2387 - skolem:lemma2388 - [ a r:Fact; r:gives {(9821 1289) math:difference 8532}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8532 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 8532 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1892}] + [ a r:Fact; r:gives {(1892 2000) math:sum 3892}] + skolem:lemma3890 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2891]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1289]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9821]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1892]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3892]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1892 a r:Inference; r:gives { - 2892 :kaprekar (0 3). + 3893 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2892 math:notEqualTo 0}] - skolem:lemma3326 - [ a r:Fact; r:gives {((2 8 9 2) "=<") list:sort (2 2 8 9)}] - [ a r:Fact; r:gives {((2 8 9 2) ">=") list:sort (9 8 2 2)}] - skolem:lemma2556 - skolem:lemma2557 - [ a r:Fact; r:gives {(9822 2289) math:difference 7533}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7533 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7533 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1893}] + [ a r:Fact; r:gives {(1893 2000) math:sum 3893}] + skolem:lemma3891 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2892]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2289]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9822]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1893]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3893]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1893 a r:Inference; r:gives { - 2893 :kaprekar (0 5). + 3894 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2893 math:notEqualTo 0}] - skolem:lemma3327 - [ a r:Fact; r:gives {((2 8 9 3) "=<") list:sort (2 3 8 9)}] - [ a r:Fact; r:gives {((2 8 9 3) ">=") list:sort (9 8 3 2)}] - skolem:lemma2712 - skolem:lemma2713 - [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7443 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1894}] + [ a r:Fact; r:gives {(1894 2000) math:sum 3894}] + skolem:lemma3892 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2893]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2389]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9832]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1894]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3894]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1894 a r:Inference; r:gives { - 2894 :kaprekar (0 3). + 3895 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2894 math:notEqualTo 0}] - skolem:lemma3328 - [ a r:Fact; r:gives {((2 8 9 4) "=<") list:sort (2 4 8 9)}] - [ a r:Fact; r:gives {((2 8 9 4) ">=") list:sort (9 8 4 2)}] - skolem:lemma2854 - skolem:lemma2855 - [ a r:Fact; r:gives {(9842 2489) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1895}] + [ a r:Fact; r:gives {(1895 2000) math:sum 3895}] + skolem:lemma3893 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2894]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2489]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9842]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1895]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3895]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1895 a r:Inference; r:gives { - 2895 :kaprekar (0 6). + 3896 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2895 math:notEqualTo 0}] - skolem:lemma3329 - [ a r:Fact; r:gives {((2 8 9 5) "=<") list:sort (2 5 8 9)}] - [ a r:Fact; r:gives {((2 8 9 5) ">=") list:sort (9 8 5 2)}] - skolem:lemma2984 - skolem:lemma2985 - [ a r:Fact; r:gives {(9852 2589) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1896}] + [ a r:Fact; r:gives {(1896 2000) math:sum 3896}] + skolem:lemma3894 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2895]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2589]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9852]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1896]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3896]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1896 a r:Inference; r:gives { - 2896 :kaprekar (0 5). + 3897 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2896 math:notEqualTo 0}] - skolem:lemma3330 - [ a r:Fact; r:gives {((2 8 9 6) "=<") list:sort (2 6 8 9)}] - [ a r:Fact; r:gives {((2 8 9 6) ">=") list:sort (9 8 6 2)}] - skolem:lemma3104 - skolem:lemma3105 - [ a r:Fact; r:gives {(9862 2689) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1897}] + [ a r:Fact; r:gives {(1897 2000) math:sum 3897}] + skolem:lemma3895 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2896]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2689]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9862]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1897]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3897]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1897 a r:Inference; r:gives { - 2897 :kaprekar (0 3). + 3898 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2897 math:notEqualTo 0}] - skolem:lemma3331 - [ a r:Fact; r:gives {((2 8 9 7) "=<") list:sort (2 7 8 9)}] - [ a r:Fact; r:gives {((2 8 9 7) ">=") list:sort (9 8 7 2)}] - skolem:lemma3216 - skolem:lemma3217 - [ a r:Fact; r:gives {(9872 2789) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1898}] + [ a r:Fact; r:gives {(1898 2000) math:sum 3898}] + skolem:lemma3896 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2897]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2789]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9872]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1898]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3898]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1898 a r:Inference; r:gives { - 2898 :kaprekar (0 4). + 3899 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2898 math:notEqualTo 0}] - skolem:lemma3332 - [ a r:Fact; r:gives {((2 8 9 8) "=<") list:sort (2 8 8 9)}] - [ a r:Fact; r:gives {((2 8 9 8) ">=") list:sort (9 8 8 2)}] - skolem:lemma3322 - skolem:lemma3323 - [ a r:Fact; r:gives {(9882 2889) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1899}] + [ a r:Fact; r:gives {(1899 2000) math:sum 3899}] + skolem:lemma3897 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2898]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 8 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2889]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9882]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1899]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3899]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1899 a r:Inference; r:gives { - 2899 :kaprekar (0 3). + 3900 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2899 math:notEqualTo 0}] - skolem:lemma3333 - [ a r:Fact; r:gives {((2 8 9 9) "=<") list:sort (2 8 9 9)}] - [ a r:Fact; r:gives {((2 8 9 9) ">=") list:sort (9 9 8 2)}] - skolem:lemma3334 - skolem:lemma3335 - [ a r:Fact; r:gives {(9982 2899) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1900}] + [ a r:Fact; r:gives {(1900 2000) math:sum 3900}] + skolem:lemma3898 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2899]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2899]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9982]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1900]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3900]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1900 a r:Inference; r:gives { - 2900 :kaprekar (0 3). + 3901 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2900 math:notEqualTo 0}] - skolem:lemma3336 - [ a r:Fact; r:gives {((2 9 0 0) "=<") list:sort (0 0 2 9)}] - [ a r:Fact; r:gives {((2 9 0 0) ">=") list:sort (9 2 0 0)}] - skolem:lemma2029 - skolem:lemma2030 - [ a r:Fact; r:gives {(9200 29) math:difference 9171}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9171 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 9171 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1901}] + [ a r:Fact; r:gives {(1901 2000) math:sum 3901}] + skolem:lemma3899 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2900]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 0 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1901]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3901]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1901 a r:Inference; r:gives { - 2901 :kaprekar (0 4). + 3902 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2901 math:notEqualTo 0}] - skolem:lemma3337 - [ a r:Fact; r:gives {((2 9 0 1) "=<") list:sort (0 1 2 9)}] - [ a r:Fact; r:gives {((2 9 0 1) ">=") list:sort (9 2 1 0)}] - skolem:lemma2057 - skolem:lemma2058 - [ a r:Fact; r:gives {(9210 129) math:difference 9081}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9081 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 9081 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1902}] + [ a r:Fact; r:gives {(1902 2000) math:sum 3902}] + skolem:lemma3900 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2901]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 0 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 129]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1902]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3902]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1902 a r:Inference; r:gives { - 2902 :kaprekar (0 4). + 3903 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2902 math:notEqualTo 0}] - skolem:lemma3338 - [ a r:Fact; r:gives {((2 9 0 2) "=<") list:sort (0 2 2 9)}] - [ a r:Fact; r:gives {((2 9 0 2) ">=") list:sort (9 2 2 0)}] - skolem:lemma2083 - skolem:lemma2084 - [ a r:Fact; r:gives {(9220 229) math:difference 8991}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8991 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 8991 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1903}] + [ a r:Fact; r:gives {(1903 2000) math:sum 3903}] + skolem:lemma3901 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2902]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 0 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 229]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8991]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1903]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3903]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1903 a r:Inference; r:gives { - 2903 :kaprekar (0 4). + 3904 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2903 math:notEqualTo 0}] - skolem:lemma3339 - [ a r:Fact; r:gives {((2 9 0 3) "=<") list:sort (0 2 3 9)}] - [ a r:Fact; r:gives {((2 9 0 3) ">=") list:sort (9 3 2 0)}] - skolem:lemma2107 - skolem:lemma2108 - [ a r:Fact; r:gives {(9320 239) math:difference 9081}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9081 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 9081 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1904}] + [ a r:Fact; r:gives {(1904 2000) math:sum 3904}] + skolem:lemma3902 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2903]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 0 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 239]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1904]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3904]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1904 a r:Inference; r:gives { - 2904 :kaprekar (0 3). + 3905 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2904 math:notEqualTo 0}] - skolem:lemma3340 - [ a r:Fact; r:gives {((2 9 0 4) "=<") list:sort (0 2 4 9)}] - [ a r:Fact; r:gives {((2 9 0 4) ">=") list:sort (9 4 2 0)}] - skolem:lemma2129 - skolem:lemma2130 - [ a r:Fact; r:gives {(9420 249) math:difference 9171}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9171 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 9171 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1905}] + [ a r:Fact; r:gives {(1905 2000) math:sum 3905}] + skolem:lemma3903 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2904]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 0 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 249]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1905]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3905]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1905 a r:Inference; r:gives { - 2905 :kaprekar (0 3). + 3906 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2905 math:notEqualTo 0}] - skolem:lemma3341 - [ a r:Fact; r:gives {((2 9 0 5) "=<") list:sort (0 2 5 9)}] - [ a r:Fact; r:gives {((2 9 0 5) ">=") list:sort (9 5 2 0)}] - skolem:lemma2149 - skolem:lemma2150 - [ a r:Fact; r:gives {(9520 259) math:difference 9261}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9261 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 9261 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1906}] + [ a r:Fact; r:gives {(1906 2000) math:sum 3906}] + skolem:lemma3904 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2905]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 0 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 259]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9261]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1906]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3906]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1906 a r:Inference; r:gives { - 2906 :kaprekar (0 7). + 3907 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2906 math:notEqualTo 0}] - skolem:lemma3342 - [ a r:Fact; r:gives {((2 9 0 6) "=<") list:sort (0 2 6 9)}] - [ a r:Fact; r:gives {((2 9 0 6) ">=") list:sort (9 6 2 0)}] - skolem:lemma2167 - skolem:lemma2168 - [ a r:Fact; r:gives {(9620 269) math:difference 9351}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9351 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 9351 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1907}] + [ a r:Fact; r:gives {(1907 2000) math:sum 3907}] + skolem:lemma3905 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2906]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 0 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 269]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9620]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9351]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1907]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3907]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1907 a r:Inference; r:gives { - 2907 :kaprekar (0 7). + 3908 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2907 math:notEqualTo 0}] - skolem:lemma3343 - [ a r:Fact; r:gives {((2 9 0 7) "=<") list:sort (0 2 7 9)}] - [ a r:Fact; r:gives {((2 9 0 7) ">=") list:sort (9 7 2 0)}] - skolem:lemma2183 - skolem:lemma2184 - [ a r:Fact; r:gives {(9720 279) math:difference 9441}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9441 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 9441 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1908}] + [ a r:Fact; r:gives {(1908 2000) math:sum 3908}] + skolem:lemma3906 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2907]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 0 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 279]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9720]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9441]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1908]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3908]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1908 a r:Inference; r:gives { - 2908 :kaprekar (0 7). + 3909 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2908 math:notEqualTo 0}] - skolem:lemma3344 - [ a r:Fact; r:gives {((2 9 0 8) "=<") list:sort (0 2 8 9)}] - [ a r:Fact; r:gives {((2 9 0 8) ">=") list:sort (9 8 2 0)}] - skolem:lemma2197 - skolem:lemma2198 - [ a r:Fact; r:gives {(9820 289) math:difference 9531}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9531 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 9531 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1909}] + [ a r:Fact; r:gives {(1909 2000) math:sum 3909}] + skolem:lemma3907 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2908]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 0 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 289]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9820]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9531]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1909]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3909]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1909 a r:Inference; r:gives { - 2909 :kaprekar (0 3). + 3910 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2909 math:notEqualTo 0}] - skolem:lemma3345 - [ a r:Fact; r:gives {((2 9 0 9) "=<") list:sort (0 2 9 9)}] - [ a r:Fact; r:gives {((2 9 0 9) ">=") list:sort (9 9 2 0)}] - skolem:lemma2209 - skolem:lemma2210 - [ a r:Fact; r:gives {(9920 299) math:difference 9621}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9621 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 9621 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1910}] + [ a r:Fact; r:gives {(1910 2000) math:sum 3910}] + skolem:lemma3908 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2909]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 0 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 299]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9920]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1910]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3910]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1910 a r:Inference; r:gives { - 2910 :kaprekar (0 4). + 3911 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2910 math:notEqualTo 0}] - skolem:lemma3346 - [ a r:Fact; r:gives {((2 9 1 0) "=<") list:sort (0 1 2 9)}] - [ a r:Fact; r:gives {((2 9 1 0) ">=") list:sort (9 2 1 0)}] - skolem:lemma2057 - skolem:lemma2058 - [ a r:Fact; r:gives {(9210 129) math:difference 9081}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9081 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 9081 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1911}] + [ a r:Fact; r:gives {(1911 2000) math:sum 3911}] + skolem:lemma3909 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2910]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 1 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 129]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1911]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3911]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1911 a r:Inference; r:gives { - 2911 :kaprekar (0 3). + 3912 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2911 math:notEqualTo 0}] - skolem:lemma3347 - [ a r:Fact; r:gives {((2 9 1 1) "=<") list:sort (1 1 2 9)}] - [ a r:Fact; r:gives {((2 9 1 1) ">=") list:sort (9 2 1 1)}] - skolem:lemma2247 - skolem:lemma2248 - [ a r:Fact; r:gives {(9211 1129) math:difference 8082}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8082 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 8082 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1912}] + [ a r:Fact; r:gives {(1912 2000) math:sum 3912}] + skolem:lemma3910 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2911]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 1 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1129]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1912]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3912]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1912 a r:Inference; r:gives { - 2912 :kaprekar (0 6). + 3913 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2912 math:notEqualTo 0}] - skolem:lemma3348 - [ a r:Fact; r:gives {((2 9 1 2) "=<") list:sort (1 2 2 9)}] - [ a r:Fact; r:gives {((2 9 1 2) ">=") list:sort (9 2 2 1)}] - skolem:lemma2273 - skolem:lemma2274 - [ a r:Fact; r:gives {(9221 1229) math:difference 7992}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7992 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7992 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1913}] + [ a r:Fact; r:gives {(1913 2000) math:sum 3913}] + skolem:lemma3911 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2912]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 1 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1229]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1913]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3913]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1913 a r:Inference; r:gives { - 2913 :kaprekar (0 3). + 3914 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2913 math:notEqualTo 0}] - skolem:lemma3349 - [ a r:Fact; r:gives {((2 9 1 3) "=<") list:sort (1 2 3 9)}] - [ a r:Fact; r:gives {((2 9 1 3) ">=") list:sort (9 3 2 1)}] - skolem:lemma2297 - skolem:lemma2298 - [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8082 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 8082 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1914}] + [ a r:Fact; r:gives {(1914 2000) math:sum 3914}] + skolem:lemma3912 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2913]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 1 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1239]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1914]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3914]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1914 a r:Inference; r:gives { - 2914 :kaprekar (0 6). + 3915 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2914 math:notEqualTo 0}] - skolem:lemma3350 - [ a r:Fact; r:gives {((2 9 1 4) "=<") list:sort (1 2 4 9)}] - [ a r:Fact; r:gives {((2 9 1 4) ">=") list:sort (9 4 2 1)}] - skolem:lemma2319 - skolem:lemma2320 - [ a r:Fact; r:gives {(9421 1249) math:difference 8172}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8172 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 8172 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1915}] + [ a r:Fact; r:gives {(1915 2000) math:sum 3915}] + skolem:lemma3913 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2914]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 1 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1249]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1915]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3915]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1915 a r:Inference; r:gives { - 2915 :kaprekar (0 5). + 3916 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2915 math:notEqualTo 0}] - skolem:lemma3351 - [ a r:Fact; r:gives {((2 9 1 5) "=<") list:sort (1 2 5 9)}] - [ a r:Fact; r:gives {((2 9 1 5) ">=") list:sort (9 5 2 1)}] - skolem:lemma2339 - skolem:lemma2340 - [ a r:Fact; r:gives {(9521 1259) math:difference 8262}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8262 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 8262 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1916}] + [ a r:Fact; r:gives {(1916 2000) math:sum 3916}] + skolem:lemma3914 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2915]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 1 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1259]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1916]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3916]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1916 a r:Inference; r:gives { - 2916 :kaprekar (0 2). + 3917 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2916 math:notEqualTo 0}] - skolem:lemma3352 - [ a r:Fact; r:gives {((2 9 1 6) "=<") list:sort (1 2 6 9)}] - [ a r:Fact; r:gives {((2 9 1 6) ">=") list:sort (9 6 2 1)}] - skolem:lemma2357 - skolem:lemma2358 - [ a r:Fact; r:gives {(9621 1269) math:difference 8352}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8352 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 8352 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1917}] + [ a r:Fact; r:gives {(1917 2000) math:sum 3917}] + skolem:lemma3915 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2916]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 1 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1269]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1917]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3917]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1917 a r:Inference; r:gives { - 2917 :kaprekar (0 7). + 3918 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2917 math:notEqualTo 0}] - skolem:lemma3353 - [ a r:Fact; r:gives {((2 9 1 7) "=<") list:sort (1 2 7 9)}] - [ a r:Fact; r:gives {((2 9 1 7) ">=") list:sort (9 7 2 1)}] - skolem:lemma2373 - skolem:lemma2374 - [ a r:Fact; r:gives {(9721 1279) math:difference 8442}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8442 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 8442 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1918}] + [ a r:Fact; r:gives {(1918 2000) math:sum 3918}] + skolem:lemma3916 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2917]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 1 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1279]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9721]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1918]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3918]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1918 a r:Inference; r:gives { - 2918 :kaprekar (0 2). + 3919 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2918 math:notEqualTo 0}] - skolem:lemma3354 - [ a r:Fact; r:gives {((2 9 1 8) "=<") list:sort (1 2 8 9)}] - [ a r:Fact; r:gives {((2 9 1 8) ">=") list:sort (9 8 2 1)}] - skolem:lemma2387 - skolem:lemma2388 - [ a r:Fact; r:gives {(9821 1289) math:difference 8532}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8532 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 8532 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1919}] + [ a r:Fact; r:gives {(1919 2000) math:sum 3919}] + skolem:lemma3917 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2918]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 1 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1289]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9821]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1919]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3919]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1919 a r:Inference; r:gives { - 2919 :kaprekar (0 5). + 3920 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2919 math:notEqualTo 0}] - skolem:lemma3355 - [ a r:Fact; r:gives {((2 9 1 9) "=<") list:sort (1 2 9 9)}] - [ a r:Fact; r:gives {((2 9 1 9) ">=") list:sort (9 9 2 1)}] - skolem:lemma2399 - skolem:lemma2400 - [ a r:Fact; r:gives {(9921 1299) math:difference 8622}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8622 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 8622 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1920}] + [ a r:Fact; r:gives {(1920 2000) math:sum 3920}] + skolem:lemma3918 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2919]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 1 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1299]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9921]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1920]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3920]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1920 a r:Inference; r:gives { - 2920 :kaprekar (0 4). + 3921 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2920 math:notEqualTo 0}] - skolem:lemma3356 - [ a r:Fact; r:gives {((2 9 2 0) "=<") list:sort (0 2 2 9)}] - [ a r:Fact; r:gives {((2 9 2 0) ">=") list:sort (9 2 2 0)}] - skolem:lemma2083 - skolem:lemma2084 - [ a r:Fact; r:gives {(9220 229) math:difference 8991}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8991 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 8991 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1921}] + [ a r:Fact; r:gives {(1921 2000) math:sum 3921}] + skolem:lemma3919 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2920]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 229]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8991]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1921]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3921]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1921 a r:Inference; r:gives { - 2921 :kaprekar (0 6). + 3922 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2921 math:notEqualTo 0}] - skolem:lemma3357 - [ a r:Fact; r:gives {((2 9 2 1) "=<") list:sort (1 2 2 9)}] - [ a r:Fact; r:gives {((2 9 2 1) ">=") list:sort (9 2 2 1)}] - skolem:lemma2273 - skolem:lemma2274 - [ a r:Fact; r:gives {(9221 1229) math:difference 7992}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7992 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7992 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1922}] + [ a r:Fact; r:gives {(1922 2000) math:sum 3922}] + skolem:lemma3920 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2921]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1229]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1922]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3922]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1922 a r:Inference; r:gives { - 2922 :kaprekar (0 4). + 3923 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2922 math:notEqualTo 0}] - skolem:lemma3358 - [ a r:Fact; r:gives {((2 9 2 2) "=<") list:sort (2 2 2 9)}] - [ a r:Fact; r:gives {((2 9 2 2) ">=") list:sort (9 2 2 2)}] - skolem:lemma2442 - skolem:lemma2443 - [ a r:Fact; r:gives {(9222 2229) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1923}] + [ a r:Fact; r:gives {(1923 2000) math:sum 3923}] + skolem:lemma3921 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2922]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2229]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1923]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3923]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1923 a r:Inference; r:gives { - 2923 :kaprekar (0 3). + 3924 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2923 math:notEqualTo 0}] - skolem:lemma3359 - [ a r:Fact; r:gives {((2 9 2 3) "=<") list:sort (2 2 3 9)}] - [ a r:Fact; r:gives {((2 9 2 3) ">=") list:sort (9 3 2 2)}] - skolem:lemma2466 - skolem:lemma2467 - [ a r:Fact; r:gives {(9322 2239) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1924}] + [ a r:Fact; r:gives {(1924 2000) math:sum 3924}] + skolem:lemma3922 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2923]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 2 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2239]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1924]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3924]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1924 a r:Inference; r:gives { - 2924 :kaprekar (0 5). + 3925 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2924 math:notEqualTo 0}] - skolem:lemma3360 - [ a r:Fact; r:gives {((2 9 2 4) "=<") list:sort (2 2 4 9)}] - [ a r:Fact; r:gives {((2 9 2 4) ">=") list:sort (9 4 2 2)}] - skolem:lemma2488 - skolem:lemma2489 - [ a r:Fact; r:gives {(9422 2249) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1925}] + [ a r:Fact; r:gives {(1925 2000) math:sum 3925}] + skolem:lemma3923 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2924]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 2 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2249]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1925]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3925]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1925 a r:Inference; r:gives { - 2925 :kaprekar (0 6). + 3926 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2925 math:notEqualTo 0}] - skolem:lemma3361 - [ a r:Fact; r:gives {((2 9 2 5) "=<") list:sort (2 2 5 9)}] - [ a r:Fact; r:gives {((2 9 2 5) ">=") list:sort (9 5 2 2)}] - skolem:lemma2508 - skolem:lemma2509 - [ a r:Fact; r:gives {(9522 2259) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1926}] + [ a r:Fact; r:gives {(1926 2000) math:sum 3926}] + skolem:lemma3924 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2925]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 2 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2259]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1926]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3926]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1926 a r:Inference; r:gives { - 2926 :kaprekar (0 3). + 3927 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2926 math:notEqualTo 0}] - skolem:lemma3362 - [ a r:Fact; r:gives {((2 9 2 6) "=<") list:sort (2 2 6 9)}] - [ a r:Fact; r:gives {((2 9 2 6) ">=") list:sort (9 6 2 2)}] - skolem:lemma2526 - skolem:lemma2527 - [ a r:Fact; r:gives {(9622 2269) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1927}] + [ a r:Fact; r:gives {(1927 2000) math:sum 3927}] + skolem:lemma3925 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2926]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 2 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2269]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1927]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3927]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1927 a r:Inference; r:gives { - 2927 :kaprekar (0 5). + 3928 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2927 math:notEqualTo 0}] - skolem:lemma3363 - [ a r:Fact; r:gives {((2 9 2 7) "=<") list:sort (2 2 7 9)}] - [ a r:Fact; r:gives {((2 9 2 7) ">=") list:sort (9 7 2 2)}] - skolem:lemma2542 - skolem:lemma2543 - [ a r:Fact; r:gives {(9722 2279) math:difference 7443}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7443 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1928}] + [ a r:Fact; r:gives {(1928 2000) math:sum 3928}] + skolem:lemma3926 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2927]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 2 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2279]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9722]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1928]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3928]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1928 a r:Inference; r:gives { - 2928 :kaprekar (0 3). + 3929 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2928 math:notEqualTo 0}] - skolem:lemma3364 - [ a r:Fact; r:gives {((2 9 2 8) "=<") list:sort (2 2 8 9)}] - [ a r:Fact; r:gives {((2 9 2 8) ">=") list:sort (9 8 2 2)}] - skolem:lemma2556 - skolem:lemma2557 - [ a r:Fact; r:gives {(9822 2289) math:difference 7533}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7533 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7533 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1929}] + [ a r:Fact; r:gives {(1929 2000) math:sum 3929}] + skolem:lemma3927 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2928]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 2 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2289]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9822]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1929]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3929]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1929 a r:Inference; r:gives { - 2929 :kaprekar (0 6). + 3930 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2929 math:notEqualTo 0}] - skolem:lemma3365 - [ a r:Fact; r:gives {((2 9 2 9) "=<") list:sort (2 2 9 9)}] - [ a r:Fact; r:gives {((2 9 2 9) ">=") list:sort (9 9 2 2)}] - skolem:lemma2568 - skolem:lemma2569 - [ a r:Fact; r:gives {(9922 2299) math:difference 7623}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7623 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7623 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1930}] + [ a r:Fact; r:gives {(1930 2000) math:sum 3930}] + skolem:lemma3928 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2929]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 2 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2299]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9922]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7623]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1930]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3930]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1930 a r:Inference; r:gives { - 2930 :kaprekar (0 4). + 3931 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2930 math:notEqualTo 0}] - skolem:lemma3366 - [ a r:Fact; r:gives {((2 9 3 0) "=<") list:sort (0 2 3 9)}] - [ a r:Fact; r:gives {((2 9 3 0) ">=") list:sort (9 3 2 0)}] - skolem:lemma2107 - skolem:lemma2108 - [ a r:Fact; r:gives {(9320 239) math:difference 9081}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9081 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 9081 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1931}] + [ a r:Fact; r:gives {(1931 2000) math:sum 3931}] + skolem:lemma3929 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2930]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 3 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 239]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9320]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1931]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3931]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1931 a r:Inference; r:gives { - 2931 :kaprekar (0 3). + 3932 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2931 math:notEqualTo 0}] - skolem:lemma3367 - [ a r:Fact; r:gives {((2 9 3 1) "=<") list:sort (1 2 3 9)}] - [ a r:Fact; r:gives {((2 9 3 1) ">=") list:sort (9 3 2 1)}] - skolem:lemma2297 - skolem:lemma2298 - [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8082 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 8082 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1932}] + [ a r:Fact; r:gives {(1932 2000) math:sum 3932}] + skolem:lemma3930 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2931]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 3 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1239]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9321]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1932]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3932]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1932 a r:Inference; r:gives { - 2932 :kaprekar (0 3). + 3933 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2932 math:notEqualTo 0}] - skolem:lemma3368 - [ a r:Fact; r:gives {((2 9 3 2) "=<") list:sort (2 2 3 9)}] - [ a r:Fact; r:gives {((2 9 3 2) ">=") list:sort (9 3 2 2)}] - skolem:lemma2466 - skolem:lemma2467 - [ a r:Fact; r:gives {(9322 2239) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1933}] + [ a r:Fact; r:gives {(1933 2000) math:sum 3933}] + skolem:lemma3931 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2932]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2239]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1933]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3933]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1933 a r:Inference; r:gives { - 2933 :kaprekar (0 4). + 3934 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2933 math:notEqualTo 0}] - skolem:lemma3369 - [ a r:Fact; r:gives {((2 9 3 3) "=<") list:sort (2 3 3 9)}] - [ a r:Fact; r:gives {((2 9 3 3) ">=") list:sort (9 3 3 2)}] - skolem:lemma2622 - skolem:lemma2623 - [ a r:Fact; r:gives {(9332 2339) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1934}] + [ a r:Fact; r:gives {(1934 2000) math:sum 3934}] + skolem:lemma3932 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2933]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 3 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2339]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1934]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3934]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1934 a r:Inference; r:gives { - 2934 :kaprekar (0 3). + 3935 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2934 math:notEqualTo 0}] - skolem:lemma3370 - [ a r:Fact; r:gives {((2 9 3 4) "=<") list:sort (2 3 4 9)}] - [ a r:Fact; r:gives {((2 9 3 4) ">=") list:sort (9 4 3 2)}] - skolem:lemma2644 - skolem:lemma2645 - [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1935}] + [ a r:Fact; r:gives {(1935 2000) math:sum 3935}] + skolem:lemma3933 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2934]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 3 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2349]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1935]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3935]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1935 a r:Inference; r:gives { - 2935 :kaprekar (0 5). + 3936 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2935 math:notEqualTo 0}] - skolem:lemma3371 - [ a r:Fact; r:gives {((2 9 3 5) "=<") list:sort (2 3 5 9)}] - [ a r:Fact; r:gives {((2 9 3 5) ">=") list:sort (9 5 3 2)}] - skolem:lemma2664 - skolem:lemma2665 - [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1936}] + [ a r:Fact; r:gives {(1936 2000) math:sum 3936}] + skolem:lemma3934 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2935]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 3 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2359]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1936]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3936]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1936 a r:Inference; r:gives { - 2936 :kaprekar (0 6). + 3937 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2936 math:notEqualTo 0}] - skolem:lemma3372 - [ a r:Fact; r:gives {((2 9 3 6) "=<") list:sort (2 3 6 9)}] - [ a r:Fact; r:gives {((2 9 3 6) ">=") list:sort (9 6 3 2)}] - skolem:lemma2682 - skolem:lemma2683 - [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1937}] + [ a r:Fact; r:gives {(1937 2000) math:sum 3937}] + skolem:lemma3935 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2936]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 3 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2369]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1937]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3937]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1937 a r:Inference; r:gives { - 2937 :kaprekar (0 3). + 3938 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2937 math:notEqualTo 0}] - skolem:lemma3373 - [ a r:Fact; r:gives {((2 9 3 7) "=<") list:sort (2 3 7 9)}] - [ a r:Fact; r:gives {((2 9 3 7) ">=") list:sort (9 7 3 2)}] - skolem:lemma2698 - skolem:lemma2699 - [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1938}] + [ a r:Fact; r:gives {(1938 2000) math:sum 3938}] + skolem:lemma3936 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2937]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 3 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2379]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9732]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1938]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3938]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1938 a r:Inference; r:gives { - 2938 :kaprekar (0 5). + 3939 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2938 math:notEqualTo 0}] - skolem:lemma3374 - [ a r:Fact; r:gives {((2 9 3 8) "=<") list:sort (2 3 8 9)}] - [ a r:Fact; r:gives {((2 9 3 8) ">=") list:sort (9 8 3 2)}] - skolem:lemma2712 - skolem:lemma2713 - [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7443 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1939}] + [ a r:Fact; r:gives {(1939 2000) math:sum 3939}] + skolem:lemma3937 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2938]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 3 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2389]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9832]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1939]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3939]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1939 a r:Inference; r:gives { - 2939 :kaprekar (0 3). + 3940 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2939 math:notEqualTo 0}] - skolem:lemma3375 - [ a r:Fact; r:gives {((2 9 3 9) "=<") list:sort (2 3 9 9)}] - [ a r:Fact; r:gives {((2 9 3 9) ">=") list:sort (9 9 3 2)}] - skolem:lemma2724 - skolem:lemma2725 - [ a r:Fact; r:gives {(9932 2399) math:difference 7533}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7533 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7533 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1940}] + [ a r:Fact; r:gives {(1940 2000) math:sum 3940}] + skolem:lemma3938 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2939]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 3 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2399]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9932]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1940]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3940]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1940 a r:Inference; r:gives { - 2940 :kaprekar (0 3). + 3941 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2940 math:notEqualTo 0}] - skolem:lemma3376 - [ a r:Fact; r:gives {((2 9 4 0) "=<") list:sort (0 2 4 9)}] - [ a r:Fact; r:gives {((2 9 4 0) ">=") list:sort (9 4 2 0)}] - skolem:lemma2129 - skolem:lemma2130 - [ a r:Fact; r:gives {(9420 249) math:difference 9171}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9171 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 9171 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1941}] + [ a r:Fact; r:gives {(1941 2000) math:sum 3941}] + skolem:lemma3939 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2940]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 4 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 249]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9420]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1941]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3941]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1941 a r:Inference; r:gives { - 2941 :kaprekar (0 6). + 3942 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2941 math:notEqualTo 0}] - skolem:lemma3377 - [ a r:Fact; r:gives {((2 9 4 1) "=<") list:sort (1 2 4 9)}] - [ a r:Fact; r:gives {((2 9 4 1) ">=") list:sort (9 4 2 1)}] - skolem:lemma2319 - skolem:lemma2320 - [ a r:Fact; r:gives {(9421 1249) math:difference 8172}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8172 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 8172 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1942}] + [ a r:Fact; r:gives {(1942 2000) math:sum 3942}] + skolem:lemma3940 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2941]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 4 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1249]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9421]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1942]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3942]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1942 a r:Inference; r:gives { - 2942 :kaprekar (0 5). + 3943 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2942 math:notEqualTo 0}] - skolem:lemma3378 - [ a r:Fact; r:gives {((2 9 4 2) "=<") list:sort (2 2 4 9)}] - [ a r:Fact; r:gives {((2 9 4 2) ">=") list:sort (9 4 2 2)}] - skolem:lemma2488 - skolem:lemma2489 - [ a r:Fact; r:gives {(9422 2249) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1943}] + [ a r:Fact; r:gives {(1943 2000) math:sum 3943}] + skolem:lemma3941 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2942]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2249]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1943]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3943]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1943 a r:Inference; r:gives { - 2943 :kaprekar (0 3). + 3944 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2943 math:notEqualTo 0}] - skolem:lemma3379 - [ a r:Fact; r:gives {((2 9 4 3) "=<") list:sort (2 3 4 9)}] - [ a r:Fact; r:gives {((2 9 4 3) ">=") list:sort (9 4 3 2)}] - skolem:lemma2644 - skolem:lemma2645 - [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1944}] + [ a r:Fact; r:gives {(1944 2000) math:sum 3944}] + skolem:lemma3942 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2943]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 4 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2349]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1944]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3944]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1944 a r:Inference; r:gives { - 2944 :kaprekar (0 4). + 3945 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2944 math:notEqualTo 0}] - skolem:lemma3380 - [ a r:Fact; r:gives {((2 9 4 4) "=<") list:sort (2 4 4 9)}] - [ a r:Fact; r:gives {((2 9 4 4) ">=") list:sort (9 4 4 2)}] - skolem:lemma2786 - skolem:lemma2787 - [ a r:Fact; r:gives {(9442 2449) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1945}] + [ a r:Fact; r:gives {(1945 2000) math:sum 3945}] + skolem:lemma3943 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2944]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 4 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2449]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1945]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3945]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1945 a r:Inference; r:gives { - 2945 :kaprekar (0 3). + 3946 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2945 math:notEqualTo 0}] - skolem:lemma3381 - [ a r:Fact; r:gives {((2 9 4 5) "=<") list:sort (2 4 5 9)}] - [ a r:Fact; r:gives {((2 9 4 5) ">=") list:sort (9 5 4 2)}] - skolem:lemma2806 - skolem:lemma2807 - [ a r:Fact; r:gives {(9542 2459) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1946}] + [ a r:Fact; r:gives {(1946 2000) math:sum 3946}] + skolem:lemma3944 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2945]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 4 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2459]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1946]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3946]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1946 a r:Inference; r:gives { - 2946 :kaprekar (0 5). + 3947 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2946 math:notEqualTo 0}] - skolem:lemma3382 - [ a r:Fact; r:gives {((2 9 4 6) "=<") list:sort (2 4 6 9)}] - [ a r:Fact; r:gives {((2 9 4 6) ">=") list:sort (9 6 4 2)}] - skolem:lemma2824 - skolem:lemma2825 - [ a r:Fact; r:gives {(9642 2469) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1947}] + [ a r:Fact; r:gives {(1947 2000) math:sum 3947}] + skolem:lemma3945 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2946]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 4 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2469]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1947]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3947]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1947 a r:Inference; r:gives { - 2947 :kaprekar (0 6). + 3948 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2947 math:notEqualTo 0}] - skolem:lemma3383 - [ a r:Fact; r:gives {((2 9 4 7) "=<") list:sort (2 4 7 9)}] - [ a r:Fact; r:gives {((2 9 4 7) ">=") list:sort (9 7 4 2)}] - skolem:lemma2840 - skolem:lemma2841 - [ a r:Fact; r:gives {(9742 2479) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1948}] + [ a r:Fact; r:gives {(1948 2000) math:sum 3948}] + skolem:lemma3946 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2947]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 4 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2479]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9742]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1948]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3948]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1948 a r:Inference; r:gives { - 2948 :kaprekar (0 3). + 3949 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2948 math:notEqualTo 0}] - skolem:lemma3384 - [ a r:Fact; r:gives {((2 9 4 8) "=<") list:sort (2 4 8 9)}] - [ a r:Fact; r:gives {((2 9 4 8) ">=") list:sort (9 8 4 2)}] - skolem:lemma2854 - skolem:lemma2855 - [ a r:Fact; r:gives {(9842 2489) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1949}] + [ a r:Fact; r:gives {(1949 2000) math:sum 3949}] + skolem:lemma3947 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2948]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 4 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2489]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9842]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1949]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3949]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1949 a r:Inference; r:gives { - 2949 :kaprekar (0 5). + 3950 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2949 math:notEqualTo 0}] - skolem:lemma3385 - [ a r:Fact; r:gives {((2 9 4 9) "=<") list:sort (2 4 9 9)}] - [ a r:Fact; r:gives {((2 9 4 9) ">=") list:sort (9 9 4 2)}] - skolem:lemma2866 - skolem:lemma2867 - [ a r:Fact; r:gives {(9942 2499) math:difference 7443}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7443 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1950}] + [ a r:Fact; r:gives {(1950 2000) math:sum 3950}] + skolem:lemma3948 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2949]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 4 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2499]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9942]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1950]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3950]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1950 a r:Inference; r:gives { - 2950 :kaprekar (0 3). + 3951 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2950 math:notEqualTo 0}] - skolem:lemma3386 - [ a r:Fact; r:gives {((2 9 5 0) "=<") list:sort (0 2 5 9)}] - [ a r:Fact; r:gives {((2 9 5 0) ">=") list:sort (9 5 2 0)}] - skolem:lemma2149 - skolem:lemma2150 - [ a r:Fact; r:gives {(9520 259) math:difference 9261}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9261 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 9261 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1951}] + [ a r:Fact; r:gives {(1951 2000) math:sum 3951}] + skolem:lemma3949 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2950]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 5 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 259]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9520]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9261]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1951]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3951]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1951 a r:Inference; r:gives { - 2951 :kaprekar (0 5). + 3952 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2951 math:notEqualTo 0}] - skolem:lemma3387 - [ a r:Fact; r:gives {((2 9 5 1) "=<") list:sort (1 2 5 9)}] - [ a r:Fact; r:gives {((2 9 5 1) ">=") list:sort (9 5 2 1)}] - skolem:lemma2339 - skolem:lemma2340 - [ a r:Fact; r:gives {(9521 1259) math:difference 8262}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8262 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 8262 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1952}] + [ a r:Fact; r:gives {(1952 2000) math:sum 3952}] + skolem:lemma3950 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2951]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 5 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1259]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9521]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1952]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3952]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1952 a r:Inference; r:gives { - 2952 :kaprekar (0 6). + 3953 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2952 math:notEqualTo 0}] - skolem:lemma3388 - [ a r:Fact; r:gives {((2 9 5 2) "=<") list:sort (2 2 5 9)}] - [ a r:Fact; r:gives {((2 9 5 2) ">=") list:sort (9 5 2 2)}] - skolem:lemma2508 - skolem:lemma2509 - [ a r:Fact; r:gives {(9522 2259) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1953}] + [ a r:Fact; r:gives {(1953 2000) math:sum 3953}] + skolem:lemma3951 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2952]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2259]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1953]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3953]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1953 a r:Inference; r:gives { - 2953 :kaprekar (0 5). + 3954 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2953 math:notEqualTo 0}] - skolem:lemma3389 - [ a r:Fact; r:gives {((2 9 5 3) "=<") list:sort (2 3 5 9)}] - [ a r:Fact; r:gives {((2 9 5 3) ">=") list:sort (9 5 3 2)}] - skolem:lemma2664 - skolem:lemma2665 - [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1954}] + [ a r:Fact; r:gives {(1954 2000) math:sum 3954}] + skolem:lemma3952 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2953]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 5 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2359]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1954]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3954]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1954 a r:Inference; r:gives { - 2954 :kaprekar (0 3). + 3955 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2954 math:notEqualTo 0}] - skolem:lemma3390 - [ a r:Fact; r:gives {((2 9 5 4) "=<") list:sort (2 4 5 9)}] - [ a r:Fact; r:gives {((2 9 5 4) ">=") list:sort (9 5 4 2)}] - skolem:lemma2806 - skolem:lemma2807 - [ a r:Fact; r:gives {(9542 2459) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1955}] + [ a r:Fact; r:gives {(1955 2000) math:sum 3955}] + skolem:lemma3953 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2954]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 5 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2459]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1955]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3955]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1955 a r:Inference; r:gives { - 2955 :kaprekar (0 4). + 3956 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2955 math:notEqualTo 0}] - skolem:lemma3391 - [ a r:Fact; r:gives {((2 9 5 5) "=<") list:sort (2 5 5 9)}] - [ a r:Fact; r:gives {((2 9 5 5) ">=") list:sort (9 5 5 2)}] - skolem:lemma2936 - skolem:lemma2937 - [ a r:Fact; r:gives {(9552 2559) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1956}] + [ a r:Fact; r:gives {(1956 2000) math:sum 3956}] + skolem:lemma3954 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2955]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 5 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2559]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9552]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1956]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3956]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1956 a r:Inference; r:gives { - 2956 :kaprekar (0 3). + 3957 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2956 math:notEqualTo 0}] - skolem:lemma3392 - [ a r:Fact; r:gives {((2 9 5 6) "=<") list:sort (2 5 6 9)}] - [ a r:Fact; r:gives {((2 9 5 6) ">=") list:sort (9 6 5 2)}] - skolem:lemma2954 - skolem:lemma2955 - [ a r:Fact; r:gives {(9652 2569) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1957}] + [ a r:Fact; r:gives {(1957 2000) math:sum 3957}] + skolem:lemma3955 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2956]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 5 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2569]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1957]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3957]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1957 a r:Inference; r:gives { - 2957 :kaprekar (0 5). + 3958 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2957 math:notEqualTo 0}] - skolem:lemma3393 - [ a r:Fact; r:gives {((2 9 5 7) "=<") list:sort (2 5 7 9)}] - [ a r:Fact; r:gives {((2 9 5 7) ">=") list:sort (9 7 5 2)}] - skolem:lemma2970 - skolem:lemma2971 - [ a r:Fact; r:gives {(9752 2579) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1958}] + [ a r:Fact; r:gives {(1958 2000) math:sum 3958}] + skolem:lemma3956 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2957]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 5 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2579]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9752]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1958]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3958]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1958 a r:Inference; r:gives { - 2958 :kaprekar (0 6). + 3959 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2958 math:notEqualTo 0}] - skolem:lemma3394 - [ a r:Fact; r:gives {((2 9 5 8) "=<") list:sort (2 5 8 9)}] - [ a r:Fact; r:gives {((2 9 5 8) ">=") list:sort (9 8 5 2)}] - skolem:lemma2984 - skolem:lemma2985 - [ a r:Fact; r:gives {(9852 2589) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1959}] + [ a r:Fact; r:gives {(1959 2000) math:sum 3959}] + skolem:lemma3957 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2958]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 5 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2589]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9852]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1959]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3959]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1959 a r:Inference; r:gives { - 2959 :kaprekar (0 3). + 3960 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2959 math:notEqualTo 0}] - skolem:lemma3395 - [ a r:Fact; r:gives {((2 9 5 9) "=<") list:sort (2 5 9 9)}] - [ a r:Fact; r:gives {((2 9 5 9) ">=") list:sort (9 9 5 2)}] - skolem:lemma2996 - skolem:lemma2997 - [ a r:Fact; r:gives {(9952 2599) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1960}] + [ a r:Fact; r:gives {(1960 2000) math:sum 3960}] + skolem:lemma3958 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2959]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 5 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2599]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9952]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1960]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3960]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1960 a r:Inference; r:gives { - 2960 :kaprekar (0 7). + 3961 :recursionCount 5 . }; r:evidence ( - [ a r:Fact; r:gives {2960 math:notEqualTo 0}] - skolem:lemma3396 - [ a r:Fact; r:gives {((2 9 6 0) "=<") list:sort (0 2 6 9)}] - [ a r:Fact; r:gives {((2 9 6 0) ">=") list:sort (9 6 2 0)}] - skolem:lemma2167 - skolem:lemma2168 - [ a r:Fact; r:gives {(9620 269) math:difference 9351}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9351 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 9351 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1961}] + [ a r:Fact; r:gives {(1961 2000) math:sum 3961}] + skolem:lemma3959 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2960]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 6 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 269]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9620]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9351]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1961]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3961]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. skolem:lemma1961 a r:Inference; r:gives { - 2961 :kaprekar (0 2). + 3962 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2961 math:notEqualTo 0}] - skolem:lemma3397 - [ a r:Fact; r:gives {((2 9 6 1) "=<") list:sort (1 2 6 9)}] - [ a r:Fact; r:gives {((2 9 6 1) ">=") list:sort (9 6 2 1)}] - skolem:lemma2357 - skolem:lemma2358 - [ a r:Fact; r:gives {(9621 1269) math:difference 8352}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8352 math:equalTo 6174. - } { - 2 log:equalTo 1. - } { - 8352 :kaprekar (1 2). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1962}] + [ a r:Fact; r:gives {(1962 2000) math:sum 3962}] + skolem:lemma3960 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2961]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 6 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1269]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9621]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1962]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3962]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1962 a r:Inference; r:gives { - 2962 :kaprekar (0 3). + 3963 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2962 math:notEqualTo 0}] - skolem:lemma3398 - [ a r:Fact; r:gives {((2 9 6 2) "=<") list:sort (2 2 6 9)}] - [ a r:Fact; r:gives {((2 9 6 2) ">=") list:sort (9 6 2 2)}] - skolem:lemma2526 - skolem:lemma2527 - [ a r:Fact; r:gives {(9622 2269) math:difference 7353}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7353 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1963}] + [ a r:Fact; r:gives {(1963 2000) math:sum 3963}] + skolem:lemma3961 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2962]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2269]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1963]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3963]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1963 a r:Inference; r:gives { - 2963 :kaprekar (0 6). + 3964 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2963 math:notEqualTo 0}] - skolem:lemma3399 - [ a r:Fact; r:gives {((2 9 6 3) "=<") list:sort (2 3 6 9)}] - [ a r:Fact; r:gives {((2 9 6 3) ">=") list:sort (9 6 3 2)}] - skolem:lemma2682 - skolem:lemma2683 - [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1964}] + [ a r:Fact; r:gives {(1964 2000) math:sum 3964}] + skolem:lemma3962 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2963]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 6 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2369]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1964]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3964]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1964 a r:Inference; r:gives { - 2964 :kaprekar (0 5). + 3965 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2964 math:notEqualTo 0}] - skolem:lemma3400 - [ a r:Fact; r:gives {((2 9 6 4) "=<") list:sort (2 4 6 9)}] - [ a r:Fact; r:gives {((2 9 6 4) ">=") list:sort (9 6 4 2)}] - skolem:lemma2824 - skolem:lemma2825 - [ a r:Fact; r:gives {(9642 2469) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1965}] + [ a r:Fact; r:gives {(1965 2000) math:sum 3965}] + skolem:lemma3963 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2964]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 6 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2469]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1965]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3965]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1965 a r:Inference; r:gives { - 2965 :kaprekar (0 3). + 3966 :recursionCount 6 . }; r:evidence ( - [ a r:Fact; r:gives {2965 math:notEqualTo 0}] - skolem:lemma3401 - [ a r:Fact; r:gives {((2 9 6 5) "=<") list:sort (2 5 6 9)}] - [ a r:Fact; r:gives {((2 9 6 5) ">=") list:sort (9 6 5 2)}] - skolem:lemma2954 - skolem:lemma2955 - [ a r:Fact; r:gives {(9652 2569) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1966}] + [ a r:Fact; r:gives {(1966 2000) math:sum 3966}] + skolem:lemma3964 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2965]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 6 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2569]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1966]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3966]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. skolem:lemma1966 a r:Inference; r:gives { - 2966 :kaprekar (0 4). + 3967 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2966 math:notEqualTo 0}] - skolem:lemma3402 - [ a r:Fact; r:gives {((2 9 6 6) "=<") list:sort (2 6 6 9)}] - [ a r:Fact; r:gives {((2 9 6 6) ">=") list:sort (9 6 6 2)}] - skolem:lemma3074 - skolem:lemma3075 - [ a r:Fact; r:gives {(9662 2669) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1967}] + [ a r:Fact; r:gives {(1967 2000) math:sum 3967}] + skolem:lemma3965 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2966]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 6 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2669]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9662]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1967]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3967]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1967 a r:Inference; r:gives { - 2967 :kaprekar (0 3). + 3968 :recursionCount 1 . }; r:evidence ( - [ a r:Fact; r:gives {2967 math:notEqualTo 0}] - skolem:lemma3403 - [ a r:Fact; r:gives {((2 9 6 7) "=<") list:sort (2 6 7 9)}] - [ a r:Fact; r:gives {((2 9 6 7) ">=") list:sort (9 7 6 2)}] - skolem:lemma3090 - skolem:lemma3091 - [ a r:Fact; r:gives {(9762 2679) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1968}] + [ a r:Fact; r:gives {(1968 2000) math:sum 3968}] + skolem:lemma3966 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2967]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 6 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2679]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9762]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1968]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3968]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. skolem:lemma1968 a r:Inference; r:gives { - 2968 :kaprekar (0 5). + 3969 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2968 math:notEqualTo 0}] - skolem:lemma3404 - [ a r:Fact; r:gives {((2 9 6 8) "=<") list:sort (2 6 8 9)}] - [ a r:Fact; r:gives {((2 9 6 8) ">=") list:sort (9 8 6 2)}] - skolem:lemma3104 - skolem:lemma3105 - [ a r:Fact; r:gives {(9862 2689) math:difference 7173}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7173 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1969}] + [ a r:Fact; r:gives {(1969 2000) math:sum 3969}] + skolem:lemma3967 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2968]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 6 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2689]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9862]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1969]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3969]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1969 a r:Inference; r:gives { - 2969 :kaprekar (0 6). + 3970 :recursionCount 7 . }; r:evidence ( - [ a r:Fact; r:gives {2969 math:notEqualTo 0}] - skolem:lemma3405 - [ a r:Fact; r:gives {((2 9 6 9) "=<") list:sort (2 6 9 9)}] - [ a r:Fact; r:gives {((2 9 6 9) ">=") list:sort (9 9 6 2)}] - skolem:lemma3116 - skolem:lemma3117 - [ a r:Fact; r:gives {(9962 2699) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. - } { - 6 log:equalTo 1. - } { - 7263 :kaprekar (1 6). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1970}] + [ a r:Fact; r:gives {(1970 2000) math:sum 3970}] + skolem:lemma3968 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2969]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 6 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2699]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9962]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1970]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3970]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. skolem:lemma1970 a r:Inference; r:gives { - 2970 :kaprekar (0 7). + 3971 :recursionCount 2 . }; r:evidence ( - [ a r:Fact; r:gives {2970 math:notEqualTo 0}] - skolem:lemma3406 - [ a r:Fact; r:gives {((2 9 7 0) "=<") list:sort (0 2 7 9)}] - [ a r:Fact; r:gives {((2 9 7 0) ">=") list:sort (9 7 2 0)}] - skolem:lemma2183 - skolem:lemma2184 - [ a r:Fact; r:gives {(9720 279) math:difference 9441}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 9441 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 9441 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1971}] + [ a r:Fact; r:gives {(1971 2000) math:sum 3971}] + skolem:lemma3969 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2970]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 7 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 279]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9720]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9441]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1971]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3971]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. skolem:lemma1971 a r:Inference; r:gives { - 2971 :kaprekar (0 7). + 3972 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2971 math:notEqualTo 0}] - skolem:lemma3407 - [ a r:Fact; r:gives {((2 9 7 1) "=<") list:sort (1 2 7 9)}] - [ a r:Fact; r:gives {((2 9 7 1) ">=") list:sort (9 7 2 1)}] - skolem:lemma2373 - skolem:lemma2374 - [ a r:Fact; r:gives {(9721 1279) math:difference 8442}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 8442 math:equalTo 6174. - } { - 7 log:equalTo 1. - } { - 8442 :kaprekar (1 7). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1972}] + [ a r:Fact; r:gives {(1972 2000) math:sum 3972}] + skolem:lemma3970 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2971]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 7 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1279]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9721]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1972]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3972]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. skolem:lemma1972 a r:Inference; r:gives { - 2972 :kaprekar (0 5). + 3973 :recursionCount 4 . }; r:evidence ( - [ a r:Fact; r:gives {2972 math:notEqualTo 0}] - skolem:lemma3408 - [ a r:Fact; r:gives {((2 9 7 2) "=<") list:sort (2 2 7 9)}] - [ a r:Fact; r:gives {((2 9 7 2) ">=") list:sort (9 7 2 2)}] - skolem:lemma2542 - skolem:lemma2543 - [ a r:Fact; r:gives {(9722 2279) math:difference 7443}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. - } { - 5 log:equalTo 1. - } { - 7443 :kaprekar (1 5). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {2000 log:repeat 1973}] + [ a r:Fact; r:gives {(1973 2000) math:sum 3973}] + skolem:lemma3971 ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2972]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2279]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9722]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1973]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3973]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. skolem:lemma1973 a r:Inference; r:gives { - 2973 :kaprekar (0 3). + 3974 :recursionCount 3 . }; r:evidence ( - [ a r:Fact; r:gives {2973 math:notEqualTo 0}] - skolem:lemma3409 - [ a r:Fact; r:gives {((2 9 7 3) "=<") list:sort (2 3 7 9)}] - [ a r:Fact; r:gives {((2 9 7 3) ">=") list:sort (9 7 3 2)}] - skolem:lemma2698 - skolem:lemma2699 - [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] + [ a r:Fact; r:gives {2000 log:repeat 1974}] + [ a r:Fact; r:gives {(1974 2000) math:sum 3974}] + skolem:lemma3972 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1974]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3974]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. + +skolem:lemma1974 a r:Inference; + r:gives { + 3975 :recursionCount 1 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1975}] + [ a r:Fact; r:gives {(1975 2000) math:sum 3975}] + skolem:lemma3973 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1975]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3975]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. + +skolem:lemma1975 a r:Inference; + r:gives { + 3976 :recursionCount 7 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1976}] + [ a r:Fact; r:gives {(1976 2000) math:sum 3976}] + skolem:lemma3974 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1976]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3976]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. + +skolem:lemma1976 a r:Inference; + r:gives { + 3977 :recursionCount 6 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1977}] + [ a r:Fact; r:gives {(1977 2000) math:sum 3977}] + skolem:lemma3975 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1977]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3977]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. + +skolem:lemma1977 a r:Inference; + r:gives { + 3978 :recursionCount 7 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1978}] + [ a r:Fact; r:gives {(1978 2000) math:sum 3978}] + skolem:lemma3976 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1978]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3978]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. + +skolem:lemma1978 a r:Inference; + r:gives { + 3979 :recursionCount 1 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1979}] + [ a r:Fact; r:gives {(1979 2000) math:sum 3979}] + skolem:lemma3977 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1979]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3979]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. + +skolem:lemma1979 a r:Inference; + r:gives { + 3980 :recursionCount 7 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1980}] + [ a r:Fact; r:gives {(1980 2000) math:sum 3980}] + skolem:lemma3978 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1980]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3980]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. + +skolem:lemma1980 a r:Inference; + r:gives { + 3981 :recursionCount 7 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1981}] + [ a r:Fact; r:gives {(1981 2000) math:sum 3981}] + skolem:lemma3979 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1981]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3981]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. + +skolem:lemma1981 a r:Inference; + r:gives { + 3982 :recursionCount 5 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1982}] + [ a r:Fact; r:gives {(1982 2000) math:sum 3982}] + skolem:lemma3980 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1982]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3982]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. + +skolem:lemma1982 a r:Inference; + r:gives { + 3983 :recursionCount 5 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1983}] + [ a r:Fact; r:gives {(1983 2000) math:sum 3983}] + skolem:lemma3981 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1983]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3983]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. + +skolem:lemma1983 a r:Inference; + r:gives { + 3984 :recursionCount 4 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1984}] + [ a r:Fact; r:gives {(1984 2000) math:sum 3984}] + skolem:lemma3982 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1984]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3984]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. + +skolem:lemma1984 a r:Inference; + r:gives { + 3985 :recursionCount 3 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1985}] + [ a r:Fact; r:gives {(1985 2000) math:sum 3985}] + skolem:lemma3983 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1985]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3985]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. + +skolem:lemma1985 a r:Inference; + r:gives { + 3986 :recursionCount 1 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1986}] + [ a r:Fact; r:gives {(1986 2000) math:sum 3986}] + skolem:lemma3984 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1986]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3986]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. + +skolem:lemma1986 a r:Inference; + r:gives { + 3987 :recursionCount 7 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1987}] + [ a r:Fact; r:gives {(1987 2000) math:sum 3987}] + skolem:lemma3985 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1987]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3987]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. + +skolem:lemma1987 a r:Inference; + r:gives { + 3988 :recursionCount 6 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1988}] + [ a r:Fact; r:gives {(1988 2000) math:sum 3988}] + skolem:lemma3986 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1988]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3988]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. + +skolem:lemma1988 a r:Inference; + r:gives { + 3989 :recursionCount 7 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1989}] + [ a r:Fact; r:gives {(1989 2000) math:sum 3989}] + skolem:lemma3987 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1989]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3989]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. + +skolem:lemma1989 a r:Inference; + r:gives { + 3990 :recursionCount 7 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1990}] + [ a r:Fact; r:gives {(1990 2000) math:sum 3990}] + skolem:lemma3988 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1990]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3990]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. + +skolem:lemma1990 a r:Inference; + r:gives { + 3991 :recursionCount 2 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1991}] + [ a r:Fact; r:gives {(1991 2000) math:sum 3991}] + skolem:lemma3989 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1991]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3991]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:rule skolem:lemma2000. + +skolem:lemma1991 a r:Inference; + r:gives { + 3992 :recursionCount 3 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1992}] + [ a r:Fact; r:gives {(1992 2000) math:sum 3992}] + skolem:lemma3990 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. + +skolem:lemma1992 a r:Inference; + r:gives { + 3993 :recursionCount 4 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1993}] + [ a r:Fact; r:gives {(1993 2000) math:sum 3993}] + skolem:lemma3991 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. + +skolem:lemma1993 a r:Inference; + r:gives { + 3994 :recursionCount 5 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1994}] + [ a r:Fact; r:gives {(1994 2000) math:sum 3994}] + skolem:lemma3992 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:rule skolem:lemma2000. + +skolem:lemma1994 a r:Inference; + r:gives { + 3995 :recursionCount 4 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1995}] + [ a r:Fact; r:gives {(1995 2000) math:sum 3995}] + skolem:lemma3993 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:rule skolem:lemma2000. + +skolem:lemma1995 a r:Inference; + r:gives { + 3996 :recursionCount 3 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1996}] + [ a r:Fact; r:gives {(1996 2000) math:sum 3996}] + skolem:lemma3994 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:rule skolem:lemma2000. + +skolem:lemma1996 a r:Inference; + r:gives { + 3997 :recursionCount 1 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1997}] + [ a r:Fact; r:gives {(1997 2000) math:sum 3997}] + skolem:lemma3995 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:rule skolem:lemma2000. + +skolem:lemma1997 a r:Inference; + r:gives { + 3998 :recursionCount 7 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1998}] + [ a r:Fact; r:gives {(1998 2000) math:sum 3998}] + skolem:lemma3996 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:rule skolem:lemma2000. + +skolem:lemma1998 a r:Inference; + r:gives { + 3999 :recursionCount 6 . + }; + r:evidence ( + [ a r:Fact; r:gives {2000 log:repeat 1999}] + [ a r:Fact; r:gives {(1999 2000) math:sum 3999}] + skolem:lemma3997 + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:rule skolem:lemma2000. + +skolem:lemma1999 a r:Inference; + r:gives { + 2000 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2000 math:notEqualTo 0}] + skolem:lemma3998 + [ a r:Fact; r:gives {((2 0 0 0) "=<") list:sort (0 0 0 2)}] + [ a r:Fact; r:gives {((2 0 0 0) ">=") list:sort (2 0 0 0)}] + skolem:lemma3999 + skolem:lemma4000 + [ a r:Fact; r:gives {(2000 2) math:difference 1998}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 0 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 0 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2000 a r:Extraction; + r:gives { + @forAll var:x_0, var:x_1, var:x_2. { + 2000 log:repeat var:x_0. + (var:x_0 2000) math:sum var:x_1. + var:x_1 :kaprekar (0 var:x_2). + } => { + var:x_1 :recursionCount var:x_2. + }. + }; + r:because [ a r:Parsing; r:source ]. + +skolem:lemma2001 a r:Inference; + r:gives { + 2001 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2001 math:notEqualTo 0}] + skolem:lemma4002 + [ a r:Fact; r:gives {((2 0 0 1) "=<") list:sort (0 0 1 2)}] + [ a r:Fact; r:gives {((2 0 0 1) ">=") list:sort (2 1 0 0)}] + skolem:lemma4003 + skolem:lemma4004 + [ a r:Fact; r:gives {(2100 12) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. } { 3 log:equalTo 1. } { - 7353 :kaprekar (1 3). + 2088 :kaprekar (1 3). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2973]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 7 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2379]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9732]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2001]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 0 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:rule skolem:lemma4001. -skolem:lemma1974 a r:Inference; +skolem:lemma2002 a r:Inference; r:gives { - 2974 :kaprekar (0 6). + 2002 :kaprekar (0 6). }; r:evidence ( - [ a r:Fact; r:gives {2974 math:notEqualTo 0}] - skolem:lemma3410 - [ a r:Fact; r:gives {((2 9 7 4) "=<") list:sort (2 4 7 9)}] - [ a r:Fact; r:gives {((2 9 7 4) ">=") list:sort (9 7 4 2)}] - skolem:lemma2840 - skolem:lemma2841 - [ a r:Fact; r:gives {(9742 2479) math:difference 7263}] + [ a r:Fact; r:gives {2002 math:notEqualTo 0}] + skolem:lemma4005 + [ a r:Fact; r:gives {((2 0 0 2) "=<") list:sort (0 0 2 2)}] + [ a r:Fact; r:gives {((2 0 0 2) ">=") list:sort (2 2 0 0)}] + skolem:lemma4006 + skolem:lemma4007 + [ a r:Fact; r:gives {(2200 22) math:difference 2178}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. + 2178 math:equalTo 6174. } { 6 log:equalTo 1. } { - 7263 :kaprekar (1 6). + 2178 :kaprekar (1 6). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2974]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 7 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2479]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9742]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2002]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 0 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2178]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:rule skolem:lemma4001. -skolem:lemma1975 a r:Inference; +skolem:lemma2003 a r:Inference; r:gives { - 2975 :kaprekar (0 5). + 2003 :kaprekar (0 5). }; r:evidence ( - [ a r:Fact; r:gives {2975 math:notEqualTo 0}] - skolem:lemma3411 - [ a r:Fact; r:gives {((2 9 7 5) "=<") list:sort (2 5 7 9)}] - [ a r:Fact; r:gives {((2 9 7 5) ">=") list:sort (9 7 5 2)}] - skolem:lemma2970 - skolem:lemma2971 - [ a r:Fact; r:gives {(9752 2579) math:difference 7173}] + [ a r:Fact; r:gives {2003 math:notEqualTo 0}] + skolem:lemma4008 + [ a r:Fact; r:gives {((2 0 0 3) "=<") list:sort (0 0 2 3)}] + [ a r:Fact; r:gives {((2 0 0 3) ">=") list:sort (3 2 0 0)}] + skolem:lemma4009 + skolem:lemma4010 + [ a r:Fact; r:gives {(3200 23) math:difference 3177}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. + 3177 math:equalTo 6174. } { 5 log:equalTo 1. } { - 7173 :kaprekar (1 5). + 3177 :kaprekar (1 5). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2975]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 7 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2579]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9752]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2003]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 0 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:rule skolem:lemma4001. -skolem:lemma1976 a r:Inference; +skolem:lemma2004 a r:Inference; r:gives { - 2976 :kaprekar (0 3). + 2004 :kaprekar (0 2). }; r:evidence ( - [ a r:Fact; r:gives {2976 math:notEqualTo 0}] - skolem:lemma3412 - [ a r:Fact; r:gives {((2 9 7 6) "=<") list:sort (2 6 7 9)}] - [ a r:Fact; r:gives {((2 9 7 6) ">=") list:sort (9 7 6 2)}] - skolem:lemma3090 - skolem:lemma3091 - [ a r:Fact; r:gives {(9762 2679) math:difference 7083}] + [ a r:Fact; r:gives {2004 math:notEqualTo 0}] + skolem:lemma4011 + [ a r:Fact; r:gives {((2 0 0 4) "=<") list:sort (0 0 2 4)}] + [ a r:Fact; r:gives {((2 0 0 4) ">=") list:sort (4 2 0 0)}] + skolem:lemma4012 + skolem:lemma4013 + [ a r:Fact; r:gives {(4200 24) math:difference 4176}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. + 4176 math:equalTo 6174. } { - 3 log:equalTo 1. + 2 log:equalTo 1. } { - 7083 :kaprekar (1 3). + 4176 :kaprekar (1 2). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2976]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 7 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2679]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9762]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2004]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 0 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. -skolem:lemma1977 a r:Inference; +skolem:lemma2005 a r:Inference; r:gives { - 2977 :kaprekar (0 4). + 2005 :kaprekar (0 7). }; r:evidence ( - [ a r:Fact; r:gives {2977 math:notEqualTo 0}] - skolem:lemma3413 - [ a r:Fact; r:gives {((2 9 7 7) "=<") list:sort (2 7 7 9)}] - [ a r:Fact; r:gives {((2 9 7 7) ">=") list:sort (9 7 7 2)}] - skolem:lemma3202 - skolem:lemma3203 - [ a r:Fact; r:gives {(9772 2779) math:difference 6993}] + [ a r:Fact; r:gives {2005 math:notEqualTo 0}] + skolem:lemma4014 + [ a r:Fact; r:gives {((2 0 0 5) "=<") list:sort (0 0 2 5)}] + [ a r:Fact; r:gives {((2 0 0 5) ">=") list:sort (5 2 0 0)}] + skolem:lemma4015 + skolem:lemma4016 + [ a r:Fact; r:gives {(5200 25) math:difference 5175}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. + 5175 math:equalTo 6174. } { - 4 log:equalTo 1. + 7 log:equalTo 1. } { - 6993 :kaprekar (1 4). + 5175 :kaprekar (1 7). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2977]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 7 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2779]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9772]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2005]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 0 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. -skolem:lemma1978 a r:Inference; +skolem:lemma2006 a r:Inference; r:gives { - 2978 :kaprekar (0 3). + 2006 :kaprekar (0 1). }; r:evidence ( - [ a r:Fact; r:gives {2978 math:notEqualTo 0}] - skolem:lemma3414 - [ a r:Fact; r:gives {((2 9 7 8) "=<") list:sort (2 7 8 9)}] - [ a r:Fact; r:gives {((2 9 7 8) ">=") list:sort (9 8 7 2)}] - skolem:lemma3216 - skolem:lemma3217 - [ a r:Fact; r:gives {(9872 2789) math:difference 7083}] + [ a r:Fact; r:gives {2006 math:notEqualTo 0}] + skolem:lemma4017 + [ a r:Fact; r:gives {((2 0 0 6) "=<") list:sort (0 0 2 6)}] + [ a r:Fact; r:gives {((2 0 0 6) ">=") list:sort (6 2 0 0)}] + skolem:lemma4018 + skolem:lemma4019 + [ a r:Fact; r:gives {(6200 26) math:difference 6174}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. + 6174 math:equalTo 6174. } { - 3 log:equalTo 1. + 1 log:equalTo 1. } { - 7083 :kaprekar (1 3). + 6174 :kaprekar (1 1). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2978]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 7 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2789]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9872]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2006]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 0 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. -skolem:lemma1979 a r:Inference; +skolem:lemma2007 a r:Inference; r:gives { - 2979 :kaprekar (0 5). + 2007 :kaprekar (0 5). }; r:evidence ( - [ a r:Fact; r:gives {2979 math:notEqualTo 0}] - skolem:lemma3415 - [ a r:Fact; r:gives {((2 9 7 9) "=<") list:sort (2 7 9 9)}] - [ a r:Fact; r:gives {((2 9 7 9) ">=") list:sort (9 9 7 2)}] - skolem:lemma3228 - skolem:lemma3229 - [ a r:Fact; r:gives {(9972 2799) math:difference 7173}] + [ a r:Fact; r:gives {2007 math:notEqualTo 0}] + skolem:lemma4020 + [ a r:Fact; r:gives {((2 0 0 7) "=<") list:sort (0 0 2 7)}] + [ a r:Fact; r:gives {((2 0 0 7) ">=") list:sort (7 2 0 0)}] + skolem:lemma4021 + skolem:lemma4022 + [ a r:Fact; r:gives {(7200 27) math:difference 7173}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ 7173 math:equalTo 6174. @@ -49280,337 +32250,337 @@ skolem:lemma1979 a r:Inference; 7173 :kaprekar (1 5). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2979]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 7 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2799]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9972]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2007]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 0 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7200]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:rule skolem:lemma4001. -skolem:lemma1980 a r:Inference; +skolem:lemma2008 a r:Inference; r:gives { - 2980 :kaprekar (0 7). + 2008 :kaprekar (0 6). }; r:evidence ( - [ a r:Fact; r:gives {2980 math:notEqualTo 0}] - skolem:lemma3416 - [ a r:Fact; r:gives {((2 9 8 0) "=<") list:sort (0 2 8 9)}] - [ a r:Fact; r:gives {((2 9 8 0) ">=") list:sort (9 8 2 0)}] - skolem:lemma2197 - skolem:lemma2198 - [ a r:Fact; r:gives {(9820 289) math:difference 9531}] + [ a r:Fact; r:gives {2008 math:notEqualTo 0}] + skolem:lemma4023 + [ a r:Fact; r:gives {((2 0 0 8) "=<") list:sort (0 0 2 8)}] + [ a r:Fact; r:gives {((2 0 0 8) ">=") list:sort (8 2 0 0)}] + skolem:lemma4024 + skolem:lemma4025 + [ a r:Fact; r:gives {(8200 28) math:difference 8172}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ - 9531 math:equalTo 6174. + 8172 math:equalTo 6174. } { - 7 log:equalTo 1. + 6 log:equalTo 1. } { - 9531 :kaprekar (1 7). + 8172 :kaprekar (1 6). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2980]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 8 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 289]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9820]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2008]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 0 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. -skolem:lemma1981 a r:Inference; +skolem:lemma2009 a r:Inference; r:gives { - 2981 :kaprekar (0 2). + 2009 :kaprekar (0 3). }; r:evidence ( - [ a r:Fact; r:gives {2981 math:notEqualTo 0}] - skolem:lemma3417 - [ a r:Fact; r:gives {((2 9 8 1) "=<") list:sort (1 2 8 9)}] - [ a r:Fact; r:gives {((2 9 8 1) ">=") list:sort (9 8 2 1)}] - skolem:lemma2387 - skolem:lemma2388 - [ a r:Fact; r:gives {(9821 1289) math:difference 8532}] + [ a r:Fact; r:gives {2009 math:notEqualTo 0}] + skolem:lemma4026 + [ a r:Fact; r:gives {((2 0 0 9) "=<") list:sort (0 0 2 9)}] + [ a r:Fact; r:gives {((2 0 0 9) ">=") list:sort (9 2 0 0)}] + skolem:lemma4027 + skolem:lemma4028 + [ a r:Fact; r:gives {(9200 29) math:difference 9171}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ - 8532 math:equalTo 6174. + 9171 math:equalTo 6174. } { - 2 log:equalTo 1. + 3 log:equalTo 1. } { - 8532 :kaprekar (1 2). + 9171 :kaprekar (1 3). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2981]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 8 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1289]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9821]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2009]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 0 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. -skolem:lemma1982 a r:Inference; +skolem:lemma2010 a r:Inference; r:gives { - 2982 :kaprekar (0 3). + 2010 :kaprekar (0 3). }; r:evidence ( - [ a r:Fact; r:gives {2982 math:notEqualTo 0}] - skolem:lemma3418 - [ a r:Fact; r:gives {((2 9 8 2) "=<") list:sort (2 2 8 9)}] - [ a r:Fact; r:gives {((2 9 8 2) ">=") list:sort (9 8 2 2)}] - skolem:lemma2556 - skolem:lemma2557 - [ a r:Fact; r:gives {(9822 2289) math:difference 7533}] + [ a r:Fact; r:gives {2010 math:notEqualTo 0}] + skolem:lemma4029 + [ a r:Fact; r:gives {((2 0 1 0) "=<") list:sort (0 0 1 2)}] + [ a r:Fact; r:gives {((2 0 1 0) ">=") list:sort (2 1 0 0)}] + skolem:lemma4003 + skolem:lemma4004 + [ a r:Fact; r:gives {(2100 12) math:difference 2088}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ - 7533 math:equalTo 6174. + 2088 math:equalTo 6174. } { 3 log:equalTo 1. } { - 7533 :kaprekar (1 3). + 2088 :kaprekar (1 3). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2982]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2289]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9822]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2010]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:rule skolem:lemma4001. -skolem:lemma1983 a r:Inference; +skolem:lemma2011 a r:Inference; r:gives { - 2983 :kaprekar (0 5). + 2011 :kaprekar (0 4). }; r:evidence ( - [ a r:Fact; r:gives {2983 math:notEqualTo 0}] - skolem:lemma3419 - [ a r:Fact; r:gives {((2 9 8 3) "=<") list:sort (2 3 8 9)}] - [ a r:Fact; r:gives {((2 9 8 3) ">=") list:sort (9 8 3 2)}] - skolem:lemma2712 - skolem:lemma2713 - [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] + [ a r:Fact; r:gives {2011 math:notEqualTo 0}] + skolem:lemma4030 + [ a r:Fact; r:gives {((2 0 1 1) "=<") list:sort (0 1 1 2)}] + [ a r:Fact; r:gives {((2 0 1 1) ">=") list:sort (2 1 1 0)}] + skolem:lemma4031 + skolem:lemma4032 + [ a r:Fact; r:gives {(2110 112) math:difference 1998}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. + 1998 math:equalTo 6174. } { - 5 log:equalTo 1. + 4 log:equalTo 1. } { - 7443 :kaprekar (1 5). + 1998 :kaprekar (1 4). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2983]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 8 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2389]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9832]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2011]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 112]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2110]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. -skolem:lemma1984 a r:Inference; +skolem:lemma2012 a r:Inference; r:gives { - 2984 :kaprekar (0 3). + 2012 :kaprekar (0 3). }; r:evidence ( - [ a r:Fact; r:gives {2984 math:notEqualTo 0}] - skolem:lemma3420 - [ a r:Fact; r:gives {((2 9 8 4) "=<") list:sort (2 4 8 9)}] - [ a r:Fact; r:gives {((2 9 8 4) ">=") list:sort (9 8 4 2)}] - skolem:lemma2854 - skolem:lemma2855 - [ a r:Fact; r:gives {(9842 2489) math:difference 7353}] + [ a r:Fact; r:gives {2012 math:notEqualTo 0}] + skolem:lemma4033 + [ a r:Fact; r:gives {((2 0 1 2) "=<") list:sort (0 1 2 2)}] + [ a r:Fact; r:gives {((2 0 1 2) ">=") list:sort (2 2 1 0)}] + skolem:lemma4034 + skolem:lemma4035 + [ a r:Fact; r:gives {(2210 122) math:difference 2088}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. + 2088 math:equalTo 6174. } { 3 log:equalTo 1. } { - 7353 :kaprekar (1 3). + 2088 :kaprekar (1 3). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2984]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 8 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2489]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9842]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2012]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 122]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:rule skolem:lemma4001. -skolem:lemma1985 a r:Inference; +skolem:lemma2013 a r:Inference; r:gives { - 2985 :kaprekar (0 6). + 2013 :kaprekar (0 3). }; r:evidence ( - [ a r:Fact; r:gives {2985 math:notEqualTo 0}] - skolem:lemma3421 - [ a r:Fact; r:gives {((2 9 8 5) "=<") list:sort (2 5 8 9)}] - [ a r:Fact; r:gives {((2 9 8 5) ">=") list:sort (9 8 5 2)}] - skolem:lemma2984 - skolem:lemma2985 - [ a r:Fact; r:gives {(9852 2589) math:difference 7263}] + [ a r:Fact; r:gives {2013 math:notEqualTo 0}] + skolem:lemma4036 + [ a r:Fact; r:gives {((2 0 1 3) "=<") list:sort (0 1 2 3)}] + [ a r:Fact; r:gives {((2 0 1 3) ">=") list:sort (3 2 1 0)}] + skolem:lemma4037 + skolem:lemma4038 + [ a r:Fact; r:gives {(3210 123) math:difference 3087}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. + 3087 math:equalTo 6174. } { - 6 log:equalTo 1. + 3 log:equalTo 1. } { - 7263 :kaprekar (1 6). + 3087 :kaprekar (1 3). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2985]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 8 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2589]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9852]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2013]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. -skolem:lemma1986 a r:Inference; +skolem:lemma2014 a r:Inference; r:gives { - 2986 :kaprekar (0 5). + 2014 :kaprekar (0 7). }; r:evidence ( - [ a r:Fact; r:gives {2986 math:notEqualTo 0}] - skolem:lemma3422 - [ a r:Fact; r:gives {((2 9 8 6) "=<") list:sort (2 6 8 9)}] - [ a r:Fact; r:gives {((2 9 8 6) ">=") list:sort (9 8 6 2)}] - skolem:lemma3104 - skolem:lemma3105 - [ a r:Fact; r:gives {(9862 2689) math:difference 7173}] + [ a r:Fact; r:gives {2014 math:notEqualTo 0}] + skolem:lemma4039 + [ a r:Fact; r:gives {((2 0 1 4) "=<") list:sort (0 1 2 4)}] + [ a r:Fact; r:gives {((2 0 1 4) ">=") list:sort (4 2 1 0)}] + skolem:lemma4040 + skolem:lemma4041 + [ a r:Fact; r:gives {(4210 124) math:difference 4086}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. + 4086 math:equalTo 6174. } { - 5 log:equalTo 1. + 7 log:equalTo 1. } { - 7173 :kaprekar (1 5). + 4086 :kaprekar (1 7). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2986]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 8 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2689]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9862]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2014]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 1 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. -skolem:lemma1987 a r:Inference; +skolem:lemma2015 a r:Inference; r:gives { - 2987 :kaprekar (0 3). + 2015 :kaprekar (0 7). }; r:evidence ( - [ a r:Fact; r:gives {2987 math:notEqualTo 0}] - skolem:lemma3423 - [ a r:Fact; r:gives {((2 9 8 7) "=<") list:sort (2 7 8 9)}] - [ a r:Fact; r:gives {((2 9 8 7) ">=") list:sort (9 8 7 2)}] - skolem:lemma3216 - skolem:lemma3217 - [ a r:Fact; r:gives {(9872 2789) math:difference 7083}] + [ a r:Fact; r:gives {2015 math:notEqualTo 0}] + skolem:lemma4042 + [ a r:Fact; r:gives {((2 0 1 5) "=<") list:sort (0 1 2 5)}] + [ a r:Fact; r:gives {((2 0 1 5) ">=") list:sort (5 2 1 0)}] + skolem:lemma4043 + skolem:lemma4044 + [ a r:Fact; r:gives {(5210 125) math:difference 5085}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. + 5085 math:equalTo 6174. } { - 3 log:equalTo 1. + 7 log:equalTo 1. } { - 7083 :kaprekar (1 3). + 5085 :kaprekar (1 7). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2987]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 8 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2789]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9872]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2015]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 1 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. -skolem:lemma1988 a r:Inference; +skolem:lemma2016 a r:Inference; r:gives { - 2988 :kaprekar (0 4). + 2016 :kaprekar (0 7). }; r:evidence ( - [ a r:Fact; r:gives {2988 math:notEqualTo 0}] - skolem:lemma3424 - [ a r:Fact; r:gives {((2 9 8 8) "=<") list:sort (2 8 8 9)}] - [ a r:Fact; r:gives {((2 9 8 8) ">=") list:sort (9 8 8 2)}] - skolem:lemma3322 - skolem:lemma3323 - [ a r:Fact; r:gives {(9882 2889) math:difference 6993}] + [ a r:Fact; r:gives {2016 math:notEqualTo 0}] + skolem:lemma4045 + [ a r:Fact; r:gives {((2 0 1 6) "=<") list:sort (0 1 2 6)}] + [ a r:Fact; r:gives {((2 0 1 6) ">=") list:sort (6 2 1 0)}] + skolem:lemma4046 + skolem:lemma4047 + [ a r:Fact; r:gives {(6210 126) math:difference 6084}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. + 6084 math:equalTo 6174. } { - 4 log:equalTo 1. + 7 log:equalTo 1. } { - 6993 :kaprekar (1 4). + 6084 :kaprekar (1 7). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2988]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 8 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 8 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2889]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9882]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2016]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 1 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. -skolem:lemma1989 a r:Inference; +skolem:lemma2017 a r:Inference; r:gives { - 2989 :kaprekar (0 3). + 2017 :kaprekar (0 3). }; r:evidence ( - [ a r:Fact; r:gives {2989 math:notEqualTo 0}] - skolem:lemma3425 - [ a r:Fact; r:gives {((2 9 8 9) "=<") list:sort (2 8 9 9)}] - [ a r:Fact; r:gives {((2 9 8 9) ">=") list:sort (9 9 8 2)}] - skolem:lemma3334 - skolem:lemma3335 - [ a r:Fact; r:gives {(9982 2899) math:difference 7083}] + [ a r:Fact; r:gives {2017 math:notEqualTo 0}] + skolem:lemma4048 + [ a r:Fact; r:gives {((2 0 1 7) "=<") list:sort (0 1 2 7)}] + [ a r:Fact; r:gives {((2 0 1 7) ">=") list:sort (7 2 1 0)}] + skolem:lemma4049 + skolem:lemma4050 + [ a r:Fact; r:gives {(7210 127) math:difference 7083}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ 7083 math:equalTo 6174. @@ -49620,389 +32590,97132 @@ skolem:lemma1989 a r:Inference; 7083 :kaprekar (1 3). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2989]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 8 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2899]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9982]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2017]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 1 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7210]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:rule skolem:lemma4001. -skolem:lemma1990 a r:Inference; +skolem:lemma2018 a r:Inference; r:gives { - 2990 :kaprekar (0 3). + 2018 :kaprekar (0 3). }; r:evidence ( - [ a r:Fact; r:gives {2990 math:notEqualTo 0}] - skolem:lemma3426 - [ a r:Fact; r:gives {((2 9 9 0) "=<") list:sort (0 2 9 9)}] - [ a r:Fact; r:gives {((2 9 9 0) ">=") list:sort (9 9 2 0)}] - skolem:lemma2209 - skolem:lemma2210 - [ a r:Fact; r:gives {(9920 299) math:difference 9621}] + [ a r:Fact; r:gives {2018 math:notEqualTo 0}] + skolem:lemma4051 + [ a r:Fact; r:gives {((2 0 1 8) "=<") list:sort (0 1 2 8)}] + [ a r:Fact; r:gives {((2 0 1 8) ">=") list:sort (8 2 1 0)}] + skolem:lemma4052 + skolem:lemma4053 + [ a r:Fact; r:gives {(8210 128) math:difference 8082}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ - 9621 math:equalTo 6174. + 8082 math:equalTo 6174. } { 3 log:equalTo 1. } { - 9621 :kaprekar (1 3). + 8082 :kaprekar (1 3). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2990]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 9 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 2 0)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 299]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9920]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2018]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 1 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:rule skolem:lemma4001. -skolem:lemma1991 a r:Inference; +skolem:lemma2019 a r:Inference; r:gives { - 2991 :kaprekar (0 5). + 2019 :kaprekar (0 4). }; r:evidence ( - [ a r:Fact; r:gives {2991 math:notEqualTo 0}] - skolem:lemma3427 - [ a r:Fact; r:gives {((2 9 9 1) "=<") list:sort (1 2 9 9)}] - [ a r:Fact; r:gives {((2 9 9 1) ">=") list:sort (9 9 2 1)}] - skolem:lemma2399 - skolem:lemma2400 - [ a r:Fact; r:gives {(9921 1299) math:difference 8622}] + [ a r:Fact; r:gives {2019 math:notEqualTo 0}] + skolem:lemma4054 + [ a r:Fact; r:gives {((2 0 1 9) "=<") list:sort (0 1 2 9)}] + [ a r:Fact; r:gives {((2 0 1 9) ">=") list:sort (9 2 1 0)}] + skolem:lemma4055 + skolem:lemma4056 + [ a r:Fact; r:gives {(9210 129) math:difference 9081}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ - 8622 math:equalTo 6174. + 9081 math:equalTo 6174. } { - 5 log:equalTo 1. + 4 log:equalTo 1. } { - 8622 :kaprekar (1 5). + 9081 :kaprekar (1 4). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2991]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 9 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 2 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1299]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9921]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2019]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 1 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. -skolem:lemma1992 a r:Inference; +skolem:lemma2020 a r:Inference; r:gives { - 2992 :kaprekar (0 6). + 2020 :kaprekar (0 6). }; r:evidence ( - [ a r:Fact; r:gives {2992 math:notEqualTo 0}] - skolem:lemma3428 - [ a r:Fact; r:gives {((2 9 9 2) "=<") list:sort (2 2 9 9)}] - [ a r:Fact; r:gives {((2 9 9 2) ">=") list:sort (9 9 2 2)}] - skolem:lemma2568 - skolem:lemma2569 - [ a r:Fact; r:gives {(9922 2299) math:difference 7623}] + [ a r:Fact; r:gives {2020 math:notEqualTo 0}] + skolem:lemma4057 + [ a r:Fact; r:gives {((2 0 2 0) "=<") list:sort (0 0 2 2)}] + [ a r:Fact; r:gives {((2 0 2 0) ">=") list:sort (2 2 0 0)}] + skolem:lemma4006 + skolem:lemma4007 + [ a r:Fact; r:gives {(2200 22) math:difference 2178}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ - 7623 math:equalTo 6174. + 2178 math:equalTo 6174. } { 6 log:equalTo 1. } { - 7623 :kaprekar (1 6). + 2178 :kaprekar (1 6). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 2 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2299]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9922]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7623]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2020]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2178]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:rule skolem:lemma4001. -skolem:lemma1993 a r:Inference; +skolem:lemma2021 a r:Inference; r:gives { - 2993 :kaprekar (0 3). + 2021 :kaprekar (0 3). }; r:evidence ( - [ a r:Fact; r:gives {2993 math:notEqualTo 0}] - skolem:lemma3429 - [ a r:Fact; r:gives {((2 9 9 3) "=<") list:sort (2 3 9 9)}] - [ a r:Fact; r:gives {((2 9 9 3) ">=") list:sort (9 9 3 2)}] - skolem:lemma2724 - skolem:lemma2725 - [ a r:Fact; r:gives {(9932 2399) math:difference 7533}] + [ a r:Fact; r:gives {2021 math:notEqualTo 0}] + skolem:lemma4058 + [ a r:Fact; r:gives {((2 0 2 1) "=<") list:sort (0 1 2 2)}] + [ a r:Fact; r:gives {((2 0 2 1) ">=") list:sort (2 2 1 0)}] + skolem:lemma4034 + skolem:lemma4035 + [ a r:Fact; r:gives {(2210 122) math:difference 2088}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ - 7533 math:equalTo 6174. + 2088 math:equalTo 6174. } { 3 log:equalTo 1. } { - 7533 :kaprekar (1 3). + 2088 :kaprekar (1 3). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 9 3)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 3 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2399]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9932]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2021]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 122]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:rule skolem:lemma4001. -skolem:lemma1994 a r:Inference; +skolem:lemma2022 a r:Inference; r:gives { - 2994 :kaprekar (0 5). + 2022 :kaprekar (0 4). }; r:evidence ( - [ a r:Fact; r:gives {2994 math:notEqualTo 0}] - skolem:lemma3430 - [ a r:Fact; r:gives {((2 9 9 4) "=<") list:sort (2 4 9 9)}] - [ a r:Fact; r:gives {((2 9 9 4) ">=") list:sort (9 9 4 2)}] - skolem:lemma2866 - skolem:lemma2867 - [ a r:Fact; r:gives {(9942 2499) math:difference 7443}] + [ a r:Fact; r:gives {2022 math:notEqualTo 0}] + skolem:lemma4059 + [ a r:Fact; r:gives {((2 0 2 2) "=<") list:sort (0 2 2 2)}] + [ a r:Fact; r:gives {((2 0 2 2) ">=") list:sort (2 2 2 0)}] + skolem:lemma4060 + skolem:lemma4061 + [ a r:Fact; r:gives {(2220 222) math:difference 1998}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ - 7443 math:equalTo 6174. + 1998 math:equalTo 6174. } { - 5 log:equalTo 1. + 4 log:equalTo 1. } { - 7443 :kaprekar (1 5). + 1998 :kaprekar (1 4). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2994]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 9 4)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 4 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2499]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9942]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2022]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. -skolem:lemma1995 a r:Inference; +skolem:lemma2023 a r:Inference; r:gives { - 2995 :kaprekar (0 3). + 2023 :kaprekar (0 6). }; r:evidence ( - [ a r:Fact; r:gives {2995 math:notEqualTo 0}] - skolem:lemma3431 - [ a r:Fact; r:gives {((2 9 9 5) "=<") list:sort (2 5 9 9)}] - [ a r:Fact; r:gives {((2 9 9 5) ">=") list:sort (9 9 5 2)}] - skolem:lemma2996 - skolem:lemma2997 - [ a r:Fact; r:gives {(9952 2599) math:difference 7353}] + [ a r:Fact; r:gives {2023 math:notEqualTo 0}] + skolem:lemma4062 + [ a r:Fact; r:gives {((2 0 2 3) "=<") list:sort (0 2 2 3)}] + [ a r:Fact; r:gives {((2 0 2 3) ">=") list:sort (3 2 2 0)}] + skolem:lemma4063 + skolem:lemma4064 + [ a r:Fact; r:gives {(3220 223) math:difference 2997}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ - 7353 math:equalTo 6174. + 2997 math:equalTo 6174. } { - 3 log:equalTo 1. + 6 log:equalTo 1. } { - 7353 :kaprekar (1 3). + 2997 :kaprekar (1 6). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2995]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 9 5)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 5 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2599]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9952]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2023]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. -skolem:lemma1996 a r:Inference; +skolem:lemma2024 a r:Inference; r:gives { - 2996 :kaprekar (0 6). + 2024 :kaprekar (0 4). }; r:evidence ( - [ a r:Fact; r:gives {2996 math:notEqualTo 0}] - skolem:lemma3432 - [ a r:Fact; r:gives {((2 9 9 6) "=<") list:sort (2 6 9 9)}] - [ a r:Fact; r:gives {((2 9 9 6) ">=") list:sort (9 9 6 2)}] - skolem:lemma3116 - skolem:lemma3117 - [ a r:Fact; r:gives {(9962 2699) math:difference 7263}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7263 math:equalTo 6174. + [ a r:Fact; r:gives {2024 math:notEqualTo 0}] + skolem:lemma4065 + [ a r:Fact; r:gives {((2 0 2 4) "=<") list:sort (0 2 2 4)}] + [ a r:Fact; r:gives {((2 0 2 4) ">=") list:sort (4 2 2 0)}] + skolem:lemma4066 + skolem:lemma4067 + [ a r:Fact; r:gives {(4220 224) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2024]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2025 a r:Inference; + r:gives { + 2025 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2025 math:notEqualTo 0}] + skolem:lemma4068 + [ a r:Fact; r:gives {((2 0 2 5) "=<") list:sort (0 2 2 5)}] + [ a r:Fact; r:gives {((2 0 2 5) ">=") list:sort (5 2 2 0)}] + skolem:lemma4069 + skolem:lemma4070 + [ a r:Fact; r:gives {(5220 225) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. } { 6 log:equalTo 1. } { - 7263 :kaprekar (1 6). + 4995 :kaprekar (1 6). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2996]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 9 6)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 6 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2699]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9962]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2025]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; - r:rule skolem:lemma2003. + r:rule skolem:lemma4001. -skolem:lemma1997 a r:Inference; +skolem:lemma2026 a r:Inference; r:gives { - 2997 :kaprekar (0 5). + 2026 :kaprekar (0 6). }; r:evidence ( - [ a r:Fact; r:gives {2997 math:notEqualTo 0}] - skolem:lemma3433 - [ a r:Fact; r:gives {((2 9 9 7) "=<") list:sort (2 7 9 9)}] - [ a r:Fact; r:gives {((2 9 9 7) ">=") list:sort (9 9 7 2)}] - skolem:lemma3228 - skolem:lemma3229 - [ a r:Fact; r:gives {(9972 2799) math:difference 7173}] + [ a r:Fact; r:gives {2026 math:notEqualTo 0}] + skolem:lemma4071 + [ a r:Fact; r:gives {((2 0 2 6) "=<") list:sort (0 2 2 6)}] + [ a r:Fact; r:gives {((2 0 2 6) ">=") list:sort (6 2 2 0)}] + skolem:lemma4072 + skolem:lemma4073 + [ a r:Fact; r:gives {(6220 226) math:difference 5994}] [ a r:Fact; r:gives {(0 1) math:sum 1}] [ a r:Fact; r:gives {({ - 7173 math:equalTo 6174. + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2026]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2027 a r:Inference; + r:gives { + 2027 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2027 math:notEqualTo 0}] + skolem:lemma4074 + [ a r:Fact; r:gives {((2 0 2 7) "=<") list:sort (0 2 2 7)}] + [ a r:Fact; r:gives {((2 0 2 7) ">=") list:sort (7 2 2 0)}] + skolem:lemma4075 + skolem:lemma4076 + [ a r:Fact; r:gives {(7220 227) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2027]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2028 a r:Inference; + r:gives { + 2028 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2028 math:notEqualTo 0}] + skolem:lemma4077 + [ a r:Fact; r:gives {((2 0 2 8) "=<") list:sort (0 2 2 8)}] + [ a r:Fact; r:gives {((2 0 2 8) ">=") list:sort (8 2 2 0)}] + skolem:lemma4078 + skolem:lemma4079 + [ a r:Fact; r:gives {(8220 228) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2028]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2029 a r:Inference; + r:gives { + 2029 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2029 math:notEqualTo 0}] + skolem:lemma4080 + [ a r:Fact; r:gives {((2 0 2 9) "=<") list:sort (0 2 2 9)}] + [ a r:Fact; r:gives {((2 0 2 9) ">=") list:sort (9 2 2 0)}] + skolem:lemma4081 + skolem:lemma4082 + [ a r:Fact; r:gives {(9220 229) math:difference 8991}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8991 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 8991 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2029]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8991]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2030 a r:Inference; + r:gives { + 2030 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2030 math:notEqualTo 0}] + skolem:lemma4083 + [ a r:Fact; r:gives {((2 0 3 0) "=<") list:sort (0 0 2 3)}] + [ a r:Fact; r:gives {((2 0 3 0) ">=") list:sort (3 2 0 0)}] + skolem:lemma4009 + skolem:lemma4010 + [ a r:Fact; r:gives {(3200 23) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. } { 5 log:equalTo 1. } { - 7173 :kaprekar (1 5). + 3177 :kaprekar (1 5). }) log:ifThenElseIn (() 1)}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2997]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 9 7)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 7 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2799]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9972]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2030]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; - r:rule skolem:lemma2003. + r:rule skolem:lemma4001. -skolem:lemma1998 a r:Inference; +skolem:lemma2031 a r:Inference; r:gives { - 2998 :kaprekar (0 3). + 2031 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2031 math:notEqualTo 0}] + skolem:lemma4084 + [ a r:Fact; r:gives {((2 0 3 1) "=<") list:sort (0 1 2 3)}] + [ a r:Fact; r:gives {((2 0 3 1) ">=") list:sort (3 2 1 0)}] + skolem:lemma4037 + skolem:lemma4038 + [ a r:Fact; r:gives {(3210 123) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2031]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2032 a r:Inference; + r:gives { + 2032 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2032 math:notEqualTo 0}] + skolem:lemma4085 + [ a r:Fact; r:gives {((2 0 3 2) "=<") list:sort (0 2 2 3)}] + [ a r:Fact; r:gives {((2 0 3 2) ">=") list:sort (3 2 2 0)}] + skolem:lemma4063 + skolem:lemma4064 + [ a r:Fact; r:gives {(3220 223) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2032]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2033 a r:Inference; + r:gives { + 2033 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2033 math:notEqualTo 0}] + skolem:lemma4086 + [ a r:Fact; r:gives {((2 0 3 3) "=<") list:sort (0 2 3 3)}] + [ a r:Fact; r:gives {((2 0 3 3) ">=") list:sort (3 3 2 0)}] + skolem:lemma4087 + skolem:lemma4088 + [ a r:Fact; r:gives {(3320 233) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2033]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2034 a r:Inference; + r:gives { + 2034 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2034 math:notEqualTo 0}] + skolem:lemma4089 + [ a r:Fact; r:gives {((2 0 3 4) "=<") list:sort (0 2 3 4)}] + [ a r:Fact; r:gives {((2 0 3 4) ">=") list:sort (4 3 2 0)}] + skolem:lemma4090 + skolem:lemma4091 + [ a r:Fact; r:gives {(4320 234) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2034]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2035 a r:Inference; + r:gives { + 2035 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2035 math:notEqualTo 0}] + skolem:lemma4092 + [ a r:Fact; r:gives {((2 0 3 5) "=<") list:sort (0 2 3 5)}] + [ a r:Fact; r:gives {((2 0 3 5) ">=") list:sort (5 3 2 0)}] + skolem:lemma4093 + skolem:lemma4094 + [ a r:Fact; r:gives {(5320 235) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2035]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2036 a r:Inference; + r:gives { + 2036 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2036 math:notEqualTo 0}] + skolem:lemma4095 + [ a r:Fact; r:gives {((2 0 3 6) "=<") list:sort (0 2 3 6)}] + [ a r:Fact; r:gives {((2 0 3 6) ">=") list:sort (6 3 2 0)}] + skolem:lemma4096 + skolem:lemma4097 + [ a r:Fact; r:gives {(6320 236) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2036]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2037 a r:Inference; + r:gives { + 2037 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2037 math:notEqualTo 0}] + skolem:lemma4098 + [ a r:Fact; r:gives {((2 0 3 7) "=<") list:sort (0 2 3 7)}] + [ a r:Fact; r:gives {((2 0 3 7) ">=") list:sort (7 3 2 0)}] + skolem:lemma4099 + skolem:lemma4100 + [ a r:Fact; r:gives {(7320 237) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2037]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2038 a r:Inference; + r:gives { + 2038 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2038 math:notEqualTo 0}] + skolem:lemma4101 + [ a r:Fact; r:gives {((2 0 3 8) "=<") list:sort (0 2 3 8)}] + [ a r:Fact; r:gives {((2 0 3 8) ">=") list:sort (8 3 2 0)}] + skolem:lemma4102 + skolem:lemma4103 + [ a r:Fact; r:gives {(8320 238) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2038]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2039 a r:Inference; + r:gives { + 2039 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2039 math:notEqualTo 0}] + skolem:lemma4104 + [ a r:Fact; r:gives {((2 0 3 9) "=<") list:sort (0 2 3 9)}] + [ a r:Fact; r:gives {((2 0 3 9) ">=") list:sort (9 3 2 0)}] + skolem:lemma4105 + skolem:lemma4106 + [ a r:Fact; r:gives {(9320 239) math:difference 9081}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9081 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 9081 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2039]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2040 a r:Inference; + r:gives { + 2040 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2040 math:notEqualTo 0}] + skolem:lemma4107 + [ a r:Fact; r:gives {((2 0 4 0) "=<") list:sort (0 0 2 4)}] + [ a r:Fact; r:gives {((2 0 4 0) ">=") list:sort (4 2 0 0)}] + skolem:lemma4012 + skolem:lemma4013 + [ a r:Fact; r:gives {(4200 24) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2040]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 4 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2041 a r:Inference; + r:gives { + 2041 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2041 math:notEqualTo 0}] + skolem:lemma4108 + [ a r:Fact; r:gives {((2 0 4 1) "=<") list:sort (0 1 2 4)}] + [ a r:Fact; r:gives {((2 0 4 1) ">=") list:sort (4 2 1 0)}] + skolem:lemma4040 + skolem:lemma4041 + [ a r:Fact; r:gives {(4210 124) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2041]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 4 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2042 a r:Inference; + r:gives { + 2042 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2042 math:notEqualTo 0}] + skolem:lemma4109 + [ a r:Fact; r:gives {((2 0 4 2) "=<") list:sort (0 2 2 4)}] + [ a r:Fact; r:gives {((2 0 4 2) ">=") list:sort (4 2 2 0)}] + skolem:lemma4066 + skolem:lemma4067 + [ a r:Fact; r:gives {(4220 224) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2042]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2043 a r:Inference; + r:gives { + 2043 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2043 math:notEqualTo 0}] + skolem:lemma4110 + [ a r:Fact; r:gives {((2 0 4 3) "=<") list:sort (0 2 3 4)}] + [ a r:Fact; r:gives {((2 0 4 3) ">=") list:sort (4 3 2 0)}] + skolem:lemma4090 + skolem:lemma4091 + [ a r:Fact; r:gives {(4320 234) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2043]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2044 a r:Inference; + r:gives { + 2044 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2044 math:notEqualTo 0}] + skolem:lemma4111 + [ a r:Fact; r:gives {((2 0 4 4) "=<") list:sort (0 2 4 4)}] + [ a r:Fact; r:gives {((2 0 4 4) ">=") list:sort (4 4 2 0)}] + skolem:lemma4112 + skolem:lemma4113 + [ a r:Fact; r:gives {(4420 244) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2044]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2045 a r:Inference; + r:gives { + 2045 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2045 math:notEqualTo 0}] + skolem:lemma4114 + [ a r:Fact; r:gives {((2 0 4 5) "=<") list:sort (0 2 4 5)}] + [ a r:Fact; r:gives {((2 0 4 5) ">=") list:sort (5 4 2 0)}] + skolem:lemma4115 + skolem:lemma4116 + [ a r:Fact; r:gives {(5420 245) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2045]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2046 a r:Inference; + r:gives { + 2046 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2046 math:notEqualTo 0}] + skolem:lemma4117 + [ a r:Fact; r:gives {((2 0 4 6) "=<") list:sort (0 2 4 6)}] + [ a r:Fact; r:gives {((2 0 4 6) ">=") list:sort (6 4 2 0)}] + skolem:lemma4118 + skolem:lemma4119 + [ a r:Fact; r:gives {(6420 246) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2046]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2047 a r:Inference; + r:gives { + 2047 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2047 math:notEqualTo 0}] + skolem:lemma4120 + [ a r:Fact; r:gives {((2 0 4 7) "=<") list:sort (0 2 4 7)}] + [ a r:Fact; r:gives {((2 0 4 7) ">=") list:sort (7 4 2 0)}] + skolem:lemma4121 + skolem:lemma4122 + [ a r:Fact; r:gives {(7420 247) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2047]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2048 a r:Inference; + r:gives { + 2048 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2048 math:notEqualTo 0}] + skolem:lemma4123 + [ a r:Fact; r:gives {((2 0 4 8) "=<") list:sort (0 2 4 8)}] + [ a r:Fact; r:gives {((2 0 4 8) ">=") list:sort (8 4 2 0)}] + skolem:lemma4124 + skolem:lemma4125 + [ a r:Fact; r:gives {(8420 248) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2048]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2049 a r:Inference; + r:gives { + 2049 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2049 math:notEqualTo 0}] + skolem:lemma4126 + [ a r:Fact; r:gives {((2 0 4 9) "=<") list:sort (0 2 4 9)}] + [ a r:Fact; r:gives {((2 0 4 9) ">=") list:sort (9 4 2 0)}] + skolem:lemma4127 + skolem:lemma4128 + [ a r:Fact; r:gives {(9420 249) math:difference 9171}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9171 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9171 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2049]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2050 a r:Inference; + r:gives { + 2050 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2050 math:notEqualTo 0}] + skolem:lemma4129 + [ a r:Fact; r:gives {((2 0 5 0) "=<") list:sort (0 0 2 5)}] + [ a r:Fact; r:gives {((2 0 5 0) ">=") list:sort (5 2 0 0)}] + skolem:lemma4015 + skolem:lemma4016 + [ a r:Fact; r:gives {(5200 25) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2050]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 5 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2051 a r:Inference; + r:gives { + 2051 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2051 math:notEqualTo 0}] + skolem:lemma4130 + [ a r:Fact; r:gives {((2 0 5 1) "=<") list:sort (0 1 2 5)}] + [ a r:Fact; r:gives {((2 0 5 1) ">=") list:sort (5 2 1 0)}] + skolem:lemma4043 + skolem:lemma4044 + [ a r:Fact; r:gives {(5210 125) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2051]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 5 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2052 a r:Inference; + r:gives { + 2052 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2052 math:notEqualTo 0}] + skolem:lemma4131 + [ a r:Fact; r:gives {((2 0 5 2) "=<") list:sort (0 2 2 5)}] + [ a r:Fact; r:gives {((2 0 5 2) ">=") list:sort (5 2 2 0)}] + skolem:lemma4069 + skolem:lemma4070 + [ a r:Fact; r:gives {(5220 225) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2052]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2053 a r:Inference; + r:gives { + 2053 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2053 math:notEqualTo 0}] + skolem:lemma4132 + [ a r:Fact; r:gives {((2 0 5 3) "=<") list:sort (0 2 3 5)}] + [ a r:Fact; r:gives {((2 0 5 3) ">=") list:sort (5 3 2 0)}] + skolem:lemma4093 + skolem:lemma4094 + [ a r:Fact; r:gives {(5320 235) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2053]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2054 a r:Inference; + r:gives { + 2054 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2054 math:notEqualTo 0}] + skolem:lemma4133 + [ a r:Fact; r:gives {((2 0 5 4) "=<") list:sort (0 2 4 5)}] + [ a r:Fact; r:gives {((2 0 5 4) ">=") list:sort (5 4 2 0)}] + skolem:lemma4115 + skolem:lemma4116 + [ a r:Fact; r:gives {(5420 245) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2054]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 5 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2055 a r:Inference; + r:gives { + 2055 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2055 math:notEqualTo 0}] + skolem:lemma4134 + [ a r:Fact; r:gives {((2 0 5 5) "=<") list:sort (0 2 5 5)}] + [ a r:Fact; r:gives {((2 0 5 5) ">=") list:sort (5 5 2 0)}] + skolem:lemma4135 + skolem:lemma4136 + [ a r:Fact; r:gives {(5520 255) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2055]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2056 a r:Inference; + r:gives { + 2056 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2056 math:notEqualTo 0}] + skolem:lemma4137 + [ a r:Fact; r:gives {((2 0 5 6) "=<") list:sort (0 2 5 6)}] + [ a r:Fact; r:gives {((2 0 5 6) ">=") list:sort (6 5 2 0)}] + skolem:lemma4138 + skolem:lemma4139 + [ a r:Fact; r:gives {(6520 256) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2056]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2057 a r:Inference; + r:gives { + 2057 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2057 math:notEqualTo 0}] + skolem:lemma4140 + [ a r:Fact; r:gives {((2 0 5 7) "=<") list:sort (0 2 5 7)}] + [ a r:Fact; r:gives {((2 0 5 7) ">=") list:sort (7 5 2 0)}] + skolem:lemma4141 + skolem:lemma4142 + [ a r:Fact; r:gives {(7520 257) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2057]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2058 a r:Inference; + r:gives { + 2058 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2058 math:notEqualTo 0}] + skolem:lemma4143 + [ a r:Fact; r:gives {((2 0 5 8) "=<") list:sort (0 2 5 8)}] + [ a r:Fact; r:gives {((2 0 5 8) ">=") list:sort (8 5 2 0)}] + skolem:lemma4144 + skolem:lemma4145 + [ a r:Fact; r:gives {(8520 258) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2058]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2059 a r:Inference; + r:gives { + 2059 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2059 math:notEqualTo 0}] + skolem:lemma4146 + [ a r:Fact; r:gives {((2 0 5 9) "=<") list:sort (0 2 5 9)}] + [ a r:Fact; r:gives {((2 0 5 9) ">=") list:sort (9 5 2 0)}] + skolem:lemma4147 + skolem:lemma4148 + [ a r:Fact; r:gives {(9520 259) math:difference 9261}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9261 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9261 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2059]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9261]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2060 a r:Inference; + r:gives { + 2060 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2060 math:notEqualTo 0}] + skolem:lemma4149 + [ a r:Fact; r:gives {((2 0 6 0) "=<") list:sort (0 0 2 6)}] + [ a r:Fact; r:gives {((2 0 6 0) ">=") list:sort (6 2 0 0)}] + skolem:lemma4018 + skolem:lemma4019 + [ a r:Fact; r:gives {(6200 26) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2060]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 6 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2061 a r:Inference; + r:gives { + 2061 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2061 math:notEqualTo 0}] + skolem:lemma4150 + [ a r:Fact; r:gives {((2 0 6 1) "=<") list:sort (0 1 2 6)}] + [ a r:Fact; r:gives {((2 0 6 1) ">=") list:sort (6 2 1 0)}] + skolem:lemma4046 + skolem:lemma4047 + [ a r:Fact; r:gives {(6210 126) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2061]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 6 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2062 a r:Inference; + r:gives { + 2062 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2062 math:notEqualTo 0}] + skolem:lemma4151 + [ a r:Fact; r:gives {((2 0 6 2) "=<") list:sort (0 2 2 6)}] + [ a r:Fact; r:gives {((2 0 6 2) ">=") list:sort (6 2 2 0)}] + skolem:lemma4072 + skolem:lemma4073 + [ a r:Fact; r:gives {(6220 226) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2062]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2063 a r:Inference; + r:gives { + 2063 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2063 math:notEqualTo 0}] + skolem:lemma4152 + [ a r:Fact; r:gives {((2 0 6 3) "=<") list:sort (0 2 3 6)}] + [ a r:Fact; r:gives {((2 0 6 3) ">=") list:sort (6 3 2 0)}] + skolem:lemma4096 + skolem:lemma4097 + [ a r:Fact; r:gives {(6320 236) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2063]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2064 a r:Inference; + r:gives { + 2064 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2064 math:notEqualTo 0}] + skolem:lemma4153 + [ a r:Fact; r:gives {((2 0 6 4) "=<") list:sort (0 2 4 6)}] + [ a r:Fact; r:gives {((2 0 6 4) ">=") list:sort (6 4 2 0)}] + skolem:lemma4118 + skolem:lemma4119 + [ a r:Fact; r:gives {(6420 246) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2064]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 6 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2065 a r:Inference; + r:gives { + 2065 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2065 math:notEqualTo 0}] + skolem:lemma4154 + [ a r:Fact; r:gives {((2 0 6 5) "=<") list:sort (0 2 5 6)}] + [ a r:Fact; r:gives {((2 0 6 5) ">=") list:sort (6 5 2 0)}] + skolem:lemma4138 + skolem:lemma4139 + [ a r:Fact; r:gives {(6520 256) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2065]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 6 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2066 a r:Inference; + r:gives { + 2066 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2066 math:notEqualTo 0}] + skolem:lemma4155 + [ a r:Fact; r:gives {((2 0 6 6) "=<") list:sort (0 2 6 6)}] + [ a r:Fact; r:gives {((2 0 6 6) ">=") list:sort (6 6 2 0)}] + skolem:lemma4156 + skolem:lemma4157 + [ a r:Fact; r:gives {(6620 266) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2066]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2067 a r:Inference; + r:gives { + 2067 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2067 math:notEqualTo 0}] + skolem:lemma4158 + [ a r:Fact; r:gives {((2 0 6 7) "=<") list:sort (0 2 6 7)}] + [ a r:Fact; r:gives {((2 0 6 7) ">=") list:sort (7 6 2 0)}] + skolem:lemma4159 + skolem:lemma4160 + [ a r:Fact; r:gives {(7620 267) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2067]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2068 a r:Inference; + r:gives { + 2068 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2068 math:notEqualTo 0}] + skolem:lemma4161 + [ a r:Fact; r:gives {((2 0 6 8) "=<") list:sort (0 2 6 8)}] + [ a r:Fact; r:gives {((2 0 6 8) ">=") list:sort (8 6 2 0)}] + skolem:lemma4162 + skolem:lemma4163 + [ a r:Fact; r:gives {(8620 268) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2068]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2069 a r:Inference; + r:gives { + 2069 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2069 math:notEqualTo 0}] + skolem:lemma4164 + [ a r:Fact; r:gives {((2 0 6 9) "=<") list:sort (0 2 6 9)}] + [ a r:Fact; r:gives {((2 0 6 9) ">=") list:sort (9 6 2 0)}] + skolem:lemma4165 + skolem:lemma4166 + [ a r:Fact; r:gives {(9620 269) math:difference 9351}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9351 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9351 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2069]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9351]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2070 a r:Inference; + r:gives { + 2070 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2070 math:notEqualTo 0}] + skolem:lemma4167 + [ a r:Fact; r:gives {((2 0 7 0) "=<") list:sort (0 0 2 7)}] + [ a r:Fact; r:gives {((2 0 7 0) ">=") list:sort (7 2 0 0)}] + skolem:lemma4021 + skolem:lemma4022 + [ a r:Fact; r:gives {(7200 27) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2070]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 7 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2071 a r:Inference; + r:gives { + 2071 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2071 math:notEqualTo 0}] + skolem:lemma4168 + [ a r:Fact; r:gives {((2 0 7 1) "=<") list:sort (0 1 2 7)}] + [ a r:Fact; r:gives {((2 0 7 1) ">=") list:sort (7 2 1 0)}] + skolem:lemma4049 + skolem:lemma4050 + [ a r:Fact; r:gives {(7210 127) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2071]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 7 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2072 a r:Inference; + r:gives { + 2072 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2072 math:notEqualTo 0}] + skolem:lemma4169 + [ a r:Fact; r:gives {((2 0 7 2) "=<") list:sort (0 2 2 7)}] + [ a r:Fact; r:gives {((2 0 7 2) ">=") list:sort (7 2 2 0)}] + skolem:lemma4075 + skolem:lemma4076 + [ a r:Fact; r:gives {(7220 227) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2072]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2073 a r:Inference; + r:gives { + 2073 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2073 math:notEqualTo 0}] + skolem:lemma4170 + [ a r:Fact; r:gives {((2 0 7 3) "=<") list:sort (0 2 3 7)}] + [ a r:Fact; r:gives {((2 0 7 3) ">=") list:sort (7 3 2 0)}] + skolem:lemma4099 + skolem:lemma4100 + [ a r:Fact; r:gives {(7320 237) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2073]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2074 a r:Inference; + r:gives { + 2074 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2074 math:notEqualTo 0}] + skolem:lemma4171 + [ a r:Fact; r:gives {((2 0 7 4) "=<") list:sort (0 2 4 7)}] + [ a r:Fact; r:gives {((2 0 7 4) ">=") list:sort (7 4 2 0)}] + skolem:lemma4121 + skolem:lemma4122 + [ a r:Fact; r:gives {(7420 247) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2074]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 7 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2075 a r:Inference; + r:gives { + 2075 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2075 math:notEqualTo 0}] + skolem:lemma4172 + [ a r:Fact; r:gives {((2 0 7 5) "=<") list:sort (0 2 5 7)}] + [ a r:Fact; r:gives {((2 0 7 5) ">=") list:sort (7 5 2 0)}] + skolem:lemma4141 + skolem:lemma4142 + [ a r:Fact; r:gives {(7520 257) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2075]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 7 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2076 a r:Inference; + r:gives { + 2076 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2076 math:notEqualTo 0}] + skolem:lemma4173 + [ a r:Fact; r:gives {((2 0 7 6) "=<") list:sort (0 2 6 7)}] + [ a r:Fact; r:gives {((2 0 7 6) ">=") list:sort (7 6 2 0)}] + skolem:lemma4159 + skolem:lemma4160 + [ a r:Fact; r:gives {(7620 267) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2076]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 7 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2077 a r:Inference; + r:gives { + 2077 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2077 math:notEqualTo 0}] + skolem:lemma4174 + [ a r:Fact; r:gives {((2 0 7 7) "=<") list:sort (0 2 7 7)}] + [ a r:Fact; r:gives {((2 0 7 7) ">=") list:sort (7 7 2 0)}] + skolem:lemma4175 + skolem:lemma4176 + [ a r:Fact; r:gives {(7720 277) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2077]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 277]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2078 a r:Inference; + r:gives { + 2078 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2078 math:notEqualTo 0}] + skolem:lemma4177 + [ a r:Fact; r:gives {((2 0 7 8) "=<") list:sort (0 2 7 8)}] + [ a r:Fact; r:gives {((2 0 7 8) ">=") list:sort (8 7 2 0)}] + skolem:lemma4178 + skolem:lemma4179 + [ a r:Fact; r:gives {(8720 278) math:difference 8442}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8442 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 8442 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2078]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2079 a r:Inference; + r:gives { + 2079 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2079 math:notEqualTo 0}] + skolem:lemma4180 + [ a r:Fact; r:gives {((2 0 7 9) "=<") list:sort (0 2 7 9)}] + [ a r:Fact; r:gives {((2 0 7 9) ">=") list:sort (9 7 2 0)}] + skolem:lemma4181 + skolem:lemma4182 + [ a r:Fact; r:gives {(9720 279) math:difference 9441}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9441 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9441 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2079]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9441]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2080 a r:Inference; + r:gives { + 2080 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2080 math:notEqualTo 0}] + skolem:lemma4183 + [ a r:Fact; r:gives {((2 0 8 0) "=<") list:sort (0 0 2 8)}] + [ a r:Fact; r:gives {((2 0 8 0) ">=") list:sort (8 2 0 0)}] + skolem:lemma4024 + skolem:lemma4025 + [ a r:Fact; r:gives {(8200 28) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2080]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 8 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2081 a r:Inference; + r:gives { + 2081 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2081 math:notEqualTo 0}] + skolem:lemma4184 + [ a r:Fact; r:gives {((2 0 8 1) "=<") list:sort (0 1 2 8)}] + [ a r:Fact; r:gives {((2 0 8 1) ">=") list:sort (8 2 1 0)}] + skolem:lemma4052 + skolem:lemma4053 + [ a r:Fact; r:gives {(8210 128) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 8 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2082 a r:Inference; + r:gives { + 2082 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2082 math:notEqualTo 0}] + skolem:lemma4185 + [ a r:Fact; r:gives {((2 0 8 2) "=<") list:sort (0 2 2 8)}] + [ a r:Fact; r:gives {((2 0 8 2) ">=") list:sort (8 2 2 0)}] + skolem:lemma4078 + skolem:lemma4079 + [ a r:Fact; r:gives {(8220 228) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2083 a r:Inference; + r:gives { + 2083 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2083 math:notEqualTo 0}] + skolem:lemma4186 + [ a r:Fact; r:gives {((2 0 8 3) "=<") list:sort (0 2 3 8)}] + [ a r:Fact; r:gives {((2 0 8 3) ">=") list:sort (8 3 2 0)}] + skolem:lemma4102 + skolem:lemma4103 + [ a r:Fact; r:gives {(8320 238) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2084 a r:Inference; + r:gives { + 2084 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2084 math:notEqualTo 0}] + skolem:lemma4187 + [ a r:Fact; r:gives {((2 0 8 4) "=<") list:sort (0 2 4 8)}] + [ a r:Fact; r:gives {((2 0 8 4) ">=") list:sort (8 4 2 0)}] + skolem:lemma4124 + skolem:lemma4125 + [ a r:Fact; r:gives {(8420 248) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 8 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2085 a r:Inference; + r:gives { + 2085 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2085 math:notEqualTo 0}] + skolem:lemma4188 + [ a r:Fact; r:gives {((2 0 8 5) "=<") list:sort (0 2 5 8)}] + [ a r:Fact; r:gives {((2 0 8 5) ">=") list:sort (8 5 2 0)}] + skolem:lemma4144 + skolem:lemma4145 + [ a r:Fact; r:gives {(8520 258) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 8 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2086 a r:Inference; + r:gives { + 2086 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2086 math:notEqualTo 0}] + skolem:lemma4189 + [ a r:Fact; r:gives {((2 0 8 6) "=<") list:sort (0 2 6 8)}] + [ a r:Fact; r:gives {((2 0 8 6) ">=") list:sort (8 6 2 0)}] + skolem:lemma4162 + skolem:lemma4163 + [ a r:Fact; r:gives {(8620 268) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 8 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2087 a r:Inference; + r:gives { + 2087 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2087 math:notEqualTo 0}] + skolem:lemma4190 + [ a r:Fact; r:gives {((2 0 8 7) "=<") list:sort (0 2 7 8)}] + [ a r:Fact; r:gives {((2 0 8 7) ">=") list:sort (8 7 2 0)}] + skolem:lemma4178 + skolem:lemma4179 + [ a r:Fact; r:gives {(8720 278) math:difference 8442}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8442 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 8442 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 8 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2088 a r:Inference; + r:gives { + 2088 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2088 math:notEqualTo 0}] + skolem:lemma4191 + [ a r:Fact; r:gives {((2 0 8 8) "=<") list:sort (0 2 8 8)}] + [ a r:Fact; r:gives {((2 0 8 8) ">=") list:sort (8 8 2 0)}] + skolem:lemma4192 + skolem:lemma4193 + [ a r:Fact; r:gives {(8820 288) math:difference 8532}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8532 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8532 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 288]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8820]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2089 a r:Inference; + r:gives { + 2089 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2089 math:notEqualTo 0}] + skolem:lemma4194 + [ a r:Fact; r:gives {((2 0 8 9) "=<") list:sort (0 2 8 9)}] + [ a r:Fact; r:gives {((2 0 8 9) ">=") list:sort (9 8 2 0)}] + skolem:lemma4195 + skolem:lemma4196 + [ a r:Fact; r:gives {(9820 289) math:difference 9531}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9531 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9531 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2089]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9820]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2090 a r:Inference; + r:gives { + 2090 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2090 math:notEqualTo 0}] + skolem:lemma4197 + [ a r:Fact; r:gives {((2 0 9 0) "=<") list:sort (0 0 2 9)}] + [ a r:Fact; r:gives {((2 0 9 0) ">=") list:sort (9 2 0 0)}] + skolem:lemma4027 + skolem:lemma4028 + [ a r:Fact; r:gives {(9200 29) math:difference 9171}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9171 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9171 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2090]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 9 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2091 a r:Inference; + r:gives { + 2091 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2091 math:notEqualTo 0}] + skolem:lemma4198 + [ a r:Fact; r:gives {((2 0 9 1) "=<") list:sort (0 1 2 9)}] + [ a r:Fact; r:gives {((2 0 9 1) ">=") list:sort (9 2 1 0)}] + skolem:lemma4055 + skolem:lemma4056 + [ a r:Fact; r:gives {(9210 129) math:difference 9081}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9081 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 9081 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2091]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 9 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2092 a r:Inference; + r:gives { + 2092 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2092 math:notEqualTo 0}] + skolem:lemma4199 + [ a r:Fact; r:gives {((2 0 9 2) "=<") list:sort (0 2 2 9)}] + [ a r:Fact; r:gives {((2 0 9 2) ">=") list:sort (9 2 2 0)}] + skolem:lemma4081 + skolem:lemma4082 + [ a r:Fact; r:gives {(9220 229) math:difference 8991}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8991 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 8991 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2092]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 9 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8991]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2093 a r:Inference; + r:gives { + 2093 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2093 math:notEqualTo 0}] + skolem:lemma4200 + [ a r:Fact; r:gives {((2 0 9 3) "=<") list:sort (0 2 3 9)}] + [ a r:Fact; r:gives {((2 0 9 3) ">=") list:sort (9 3 2 0)}] + skolem:lemma4105 + skolem:lemma4106 + [ a r:Fact; r:gives {(9320 239) math:difference 9081}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9081 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 9081 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2093]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 9 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2094 a r:Inference; + r:gives { + 2094 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2094 math:notEqualTo 0}] + skolem:lemma4201 + [ a r:Fact; r:gives {((2 0 9 4) "=<") list:sort (0 2 4 9)}] + [ a r:Fact; r:gives {((2 0 9 4) ">=") list:sort (9 4 2 0)}] + skolem:lemma4127 + skolem:lemma4128 + [ a r:Fact; r:gives {(9420 249) math:difference 9171}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9171 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9171 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2094]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 9 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2095 a r:Inference; + r:gives { + 2095 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2095 math:notEqualTo 0}] + skolem:lemma4202 + [ a r:Fact; r:gives {((2 0 9 5) "=<") list:sort (0 2 5 9)}] + [ a r:Fact; r:gives {((2 0 9 5) ">=") list:sort (9 5 2 0)}] + skolem:lemma4147 + skolem:lemma4148 + [ a r:Fact; r:gives {(9520 259) math:difference 9261}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9261 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9261 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2095]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 9 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9261]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2096 a r:Inference; + r:gives { + 2096 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2096 math:notEqualTo 0}] + skolem:lemma4203 + [ a r:Fact; r:gives {((2 0 9 6) "=<") list:sort (0 2 6 9)}] + [ a r:Fact; r:gives {((2 0 9 6) ">=") list:sort (9 6 2 0)}] + skolem:lemma4165 + skolem:lemma4166 + [ a r:Fact; r:gives {(9620 269) math:difference 9351}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9351 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9351 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2096]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 9 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9351]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2097 a r:Inference; + r:gives { + 2097 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2097 math:notEqualTo 0}] + skolem:lemma4204 + [ a r:Fact; r:gives {((2 0 9 7) "=<") list:sort (0 2 7 9)}] + [ a r:Fact; r:gives {((2 0 9 7) ">=") list:sort (9 7 2 0)}] + skolem:lemma4181 + skolem:lemma4182 + [ a r:Fact; r:gives {(9720 279) math:difference 9441}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9441 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9441 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2097]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 9 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9441]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2098 a r:Inference; + r:gives { + 2098 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2098 math:notEqualTo 0}] + skolem:lemma4205 + [ a r:Fact; r:gives {((2 0 9 8) "=<") list:sort (0 2 8 9)}] + [ a r:Fact; r:gives {((2 0 9 8) ">=") list:sort (9 8 2 0)}] + skolem:lemma4195 + skolem:lemma4196 + [ a r:Fact; r:gives {(9820 289) math:difference 9531}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9531 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9531 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2098]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 9 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9820]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2099 a r:Inference; + r:gives { + 2099 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2099 math:notEqualTo 0}] + skolem:lemma4206 + [ a r:Fact; r:gives {((2 0 9 9) "=<") list:sort (0 2 9 9)}] + [ a r:Fact; r:gives {((2 0 9 9) ">=") list:sort (9 9 2 0)}] + skolem:lemma4207 + skolem:lemma4208 + [ a r:Fact; r:gives {(9920 299) math:difference 9621}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9621 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9621 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2099]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 0 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9920]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2100 a r:Inference; + r:gives { + 2100 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2100 math:notEqualTo 0}] + skolem:lemma4209 + [ a r:Fact; r:gives {((2 1 0 0) "=<") list:sort (0 0 1 2)}] + [ a r:Fact; r:gives {((2 1 0 0) ">=") list:sort (2 1 0 0)}] + skolem:lemma4003 + skolem:lemma4004 + [ a r:Fact; r:gives {(2100 12) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2101 a r:Inference; + r:gives { + 2101 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2101 math:notEqualTo 0}] + skolem:lemma4210 + [ a r:Fact; r:gives {((2 1 0 1) "=<") list:sort (0 1 1 2)}] + [ a r:Fact; r:gives {((2 1 0 1) ">=") list:sort (2 1 1 0)}] + skolem:lemma4031 + skolem:lemma4032 + [ a r:Fact; r:gives {(2110 112) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2101]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 0 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 112]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2110]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2102 a r:Inference; + r:gives { + 2102 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2102 math:notEqualTo 0}] + skolem:lemma4211 + [ a r:Fact; r:gives {((2 1 0 2) "=<") list:sort (0 1 2 2)}] + [ a r:Fact; r:gives {((2 1 0 2) ">=") list:sort (2 2 1 0)}] + skolem:lemma4034 + skolem:lemma4035 + [ a r:Fact; r:gives {(2210 122) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2102]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 0 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 122]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2103 a r:Inference; + r:gives { + 2103 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2103 math:notEqualTo 0}] + skolem:lemma4212 + [ a r:Fact; r:gives {((2 1 0 3) "=<") list:sort (0 1 2 3)}] + [ a r:Fact; r:gives {((2 1 0 3) ">=") list:sort (3 2 1 0)}] + skolem:lemma4037 + skolem:lemma4038 + [ a r:Fact; r:gives {(3210 123) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2103]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 0 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2104 a r:Inference; + r:gives { + 2104 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2104 math:notEqualTo 0}] + skolem:lemma4213 + [ a r:Fact; r:gives {((2 1 0 4) "=<") list:sort (0 1 2 4)}] + [ a r:Fact; r:gives {((2 1 0 4) ">=") list:sort (4 2 1 0)}] + skolem:lemma4040 + skolem:lemma4041 + [ a r:Fact; r:gives {(4210 124) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2104]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 0 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2105 a r:Inference; + r:gives { + 2105 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2105 math:notEqualTo 0}] + skolem:lemma4214 + [ a r:Fact; r:gives {((2 1 0 5) "=<") list:sort (0 1 2 5)}] + [ a r:Fact; r:gives {((2 1 0 5) ">=") list:sort (5 2 1 0)}] + skolem:lemma4043 + skolem:lemma4044 + [ a r:Fact; r:gives {(5210 125) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2105]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 0 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2106 a r:Inference; + r:gives { + 2106 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2106 math:notEqualTo 0}] + skolem:lemma4215 + [ a r:Fact; r:gives {((2 1 0 6) "=<") list:sort (0 1 2 6)}] + [ a r:Fact; r:gives {((2 1 0 6) ">=") list:sort (6 2 1 0)}] + skolem:lemma4046 + skolem:lemma4047 + [ a r:Fact; r:gives {(6210 126) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2106]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 0 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2107 a r:Inference; + r:gives { + 2107 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2107 math:notEqualTo 0}] + skolem:lemma4216 + [ a r:Fact; r:gives {((2 1 0 7) "=<") list:sort (0 1 2 7)}] + [ a r:Fact; r:gives {((2 1 0 7) ">=") list:sort (7 2 1 0)}] + skolem:lemma4049 + skolem:lemma4050 + [ a r:Fact; r:gives {(7210 127) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2107]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 0 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2108 a r:Inference; + r:gives { + 2108 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2108 math:notEqualTo 0}] + skolem:lemma4217 + [ a r:Fact; r:gives {((2 1 0 8) "=<") list:sort (0 1 2 8)}] + [ a r:Fact; r:gives {((2 1 0 8) ">=") list:sort (8 2 1 0)}] + skolem:lemma4052 + skolem:lemma4053 + [ a r:Fact; r:gives {(8210 128) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2108]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 0 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2109 a r:Inference; + r:gives { + 2109 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2109 math:notEqualTo 0}] + skolem:lemma4218 + [ a r:Fact; r:gives {((2 1 0 9) "=<") list:sort (0 1 2 9)}] + [ a r:Fact; r:gives {((2 1 0 9) ">=") list:sort (9 2 1 0)}] + skolem:lemma4055 + skolem:lemma4056 + [ a r:Fact; r:gives {(9210 129) math:difference 9081}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9081 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 9081 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2109]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 0 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2110 a r:Inference; + r:gives { + 2110 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2110 math:notEqualTo 0}] + skolem:lemma4219 + [ a r:Fact; r:gives {((2 1 1 0) "=<") list:sort (0 1 1 2)}] + [ a r:Fact; r:gives {((2 1 1 0) ">=") list:sort (2 1 1 0)}] + skolem:lemma4031 + skolem:lemma4032 + [ a r:Fact; r:gives {(2110 112) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2110]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 112]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2110]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2111 a r:Inference; + r:gives { + 2111 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2111 math:notEqualTo 0}] + skolem:lemma4220 + [ a r:Fact; r:gives {((2 1 1 1) "=<") list:sort (1 1 1 2)}] + [ a r:Fact; r:gives {((2 1 1 1) ">=") list:sort (2 1 1 1)}] + skolem:lemma4221 + skolem:lemma4222 + [ a r:Fact; r:gives {(2111 1112) math:difference 999}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 999 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 999 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2111]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 1 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1112]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2111]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2112 a r:Inference; + r:gives { + 2112 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2112 math:notEqualTo 0}] + skolem:lemma4223 + [ a r:Fact; r:gives {((2 1 1 2) "=<") list:sort (1 1 2 2)}] + [ a r:Fact; r:gives {((2 1 1 2) ">=") list:sort (2 2 1 1)}] + skolem:lemma4224 + skolem:lemma4225 + [ a r:Fact; r:gives {(2211 1122) math:difference 1089}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1089 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1089 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2112]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1122]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1089]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2113 a r:Inference; + r:gives { + 2113 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2113 math:notEqualTo 0}] + skolem:lemma4226 + [ a r:Fact; r:gives {((2 1 1 3) "=<") list:sort (1 1 2 3)}] + [ a r:Fact; r:gives {((2 1 1 3) ">=") list:sort (3 2 1 1)}] + skolem:lemma4227 + skolem:lemma4228 + [ a r:Fact; r:gives {(3211 1123) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2113]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2114 a r:Inference; + r:gives { + 2114 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2114 math:notEqualTo 0}] + skolem:lemma4229 + [ a r:Fact; r:gives {((2 1 1 4) "=<") list:sort (1 1 2 4)}] + [ a r:Fact; r:gives {((2 1 1 4) ">=") list:sort (4 2 1 1)}] + skolem:lemma4230 + skolem:lemma4231 + [ a r:Fact; r:gives {(4211 1124) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2114]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 1 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2115 a r:Inference; + r:gives { + 2115 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2115 math:notEqualTo 0}] + skolem:lemma4232 + [ a r:Fact; r:gives {((2 1 1 5) "=<") list:sort (1 1 2 5)}] + [ a r:Fact; r:gives {((2 1 1 5) ">=") list:sort (5 2 1 1)}] + skolem:lemma4233 + skolem:lemma4234 + [ a r:Fact; r:gives {(5211 1125) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2115]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 1 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2116 a r:Inference; + r:gives { + 2116 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2116 math:notEqualTo 0}] + skolem:lemma4235 + [ a r:Fact; r:gives {((2 1 1 6) "=<") list:sort (1 1 2 6)}] + [ a r:Fact; r:gives {((2 1 1 6) ">=") list:sort (6 2 1 1)}] + skolem:lemma4236 + skolem:lemma4237 + [ a r:Fact; r:gives {(6211 1126) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2116]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 1 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2117 a r:Inference; + r:gives { + 2117 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2117 math:notEqualTo 0}] + skolem:lemma4238 + [ a r:Fact; r:gives {((2 1 1 7) "=<") list:sort (1 1 2 7)}] + [ a r:Fact; r:gives {((2 1 1 7) ">=") list:sort (7 2 1 1)}] + skolem:lemma4239 + skolem:lemma4240 + [ a r:Fact; r:gives {(7211 1127) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2117]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 1 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2118 a r:Inference; + r:gives { + 2118 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2118 math:notEqualTo 0}] + skolem:lemma4241 + [ a r:Fact; r:gives {((2 1 1 8) "=<") list:sort (1 1 2 8)}] + [ a r:Fact; r:gives {((2 1 1 8) ">=") list:sort (8 2 1 1)}] + skolem:lemma4242 + skolem:lemma4243 + [ a r:Fact; r:gives {(8211 1128) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2118]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 1 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2119 a r:Inference; + r:gives { + 2119 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2119 math:notEqualTo 0}] + skolem:lemma4244 + [ a r:Fact; r:gives {((2 1 1 9) "=<") list:sort (1 1 2 9)}] + [ a r:Fact; r:gives {((2 1 1 9) ">=") list:sort (9 2 1 1)}] + skolem:lemma4245 + skolem:lemma4246 + [ a r:Fact; r:gives {(9211 1129) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2119]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 1 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2120 a r:Inference; + r:gives { + 2120 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2120 math:notEqualTo 0}] + skolem:lemma4247 + [ a r:Fact; r:gives {((2 1 2 0) "=<") list:sort (0 1 2 2)}] + [ a r:Fact; r:gives {((2 1 2 0) ">=") list:sort (2 2 1 0)}] + skolem:lemma4034 + skolem:lemma4035 + [ a r:Fact; r:gives {(2210 122) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2120]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 122]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2121 a r:Inference; + r:gives { + 2121 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2121 math:notEqualTo 0}] + skolem:lemma4248 + [ a r:Fact; r:gives {((2 1 2 1) "=<") list:sort (1 1 2 2)}] + [ a r:Fact; r:gives {((2 1 2 1) ">=") list:sort (2 2 1 1)}] + skolem:lemma4224 + skolem:lemma4225 + [ a r:Fact; r:gives {(2211 1122) math:difference 1089}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1089 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1089 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2121]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1122]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1089]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2122 a r:Inference; + r:gives { + 2122 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2122 math:notEqualTo 0}] + skolem:lemma4249 + [ a r:Fact; r:gives {((2 1 2 2) "=<") list:sort (1 2 2 2)}] + [ a r:Fact; r:gives {((2 1 2 2) ">=") list:sort (2 2 2 1)}] + skolem:lemma4250 + skolem:lemma4251 + [ a r:Fact; r:gives {(2221 1222) math:difference 999}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 999 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 999 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2122]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2123 a r:Inference; + r:gives { + 2123 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2123 math:notEqualTo 0}] + skolem:lemma4252 + [ a r:Fact; r:gives {((2 1 2 3) "=<") list:sort (1 2 2 3)}] + [ a r:Fact; r:gives {((2 1 2 3) ">=") list:sort (3 2 2 1)}] + skolem:lemma4253 + skolem:lemma4254 + [ a r:Fact; r:gives {(3221 1223) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2124 a r:Inference; + r:gives { + 2124 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2124 math:notEqualTo 0}] + skolem:lemma4255 + [ a r:Fact; r:gives {((2 1 2 4) "=<") list:sort (1 2 2 4)}] + [ a r:Fact; r:gives {((2 1 2 4) ">=") list:sort (4 2 2 1)}] + skolem:lemma4256 + skolem:lemma4257 + [ a r:Fact; r:gives {(4221 1224) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2125 a r:Inference; + r:gives { + 2125 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2125 math:notEqualTo 0}] + skolem:lemma4258 + [ a r:Fact; r:gives {((2 1 2 5) "=<") list:sort (1 2 2 5)}] + [ a r:Fact; r:gives {((2 1 2 5) ">=") list:sort (5 2 2 1)}] + skolem:lemma4259 + skolem:lemma4260 + [ a r:Fact; r:gives {(5221 1225) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2126 a r:Inference; + r:gives { + 2126 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2126 math:notEqualTo 0}] + skolem:lemma4261 + [ a r:Fact; r:gives {((2 1 2 6) "=<") list:sort (1 2 2 6)}] + [ a r:Fact; r:gives {((2 1 2 6) ">=") list:sort (6 2 2 1)}] + skolem:lemma4262 + skolem:lemma4263 + [ a r:Fact; r:gives {(6221 1226) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2127 a r:Inference; + r:gives { + 2127 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2127 math:notEqualTo 0}] + skolem:lemma4264 + [ a r:Fact; r:gives {((2 1 2 7) "=<") list:sort (1 2 2 7)}] + [ a r:Fact; r:gives {((2 1 2 7) ">=") list:sort (7 2 2 1)}] + skolem:lemma4265 + skolem:lemma4266 + [ a r:Fact; r:gives {(7221 1227) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2128 a r:Inference; + r:gives { + 2128 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2128 math:notEqualTo 0}] + skolem:lemma4267 + [ a r:Fact; r:gives {((2 1 2 8) "=<") list:sort (1 2 2 8)}] + [ a r:Fact; r:gives {((2 1 2 8) ">=") list:sort (8 2 2 1)}] + skolem:lemma4268 + skolem:lemma4269 + [ a r:Fact; r:gives {(8221 1228) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2129 a r:Inference; + r:gives { + 2129 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2129 math:notEqualTo 0}] + skolem:lemma4270 + [ a r:Fact; r:gives {((2 1 2 9) "=<") list:sort (1 2 2 9)}] + [ a r:Fact; r:gives {((2 1 2 9) ">=") list:sort (9 2 2 1)}] + skolem:lemma4271 + skolem:lemma4272 + [ a r:Fact; r:gives {(9221 1229) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2130 a r:Inference; + r:gives { + 2130 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2130 math:notEqualTo 0}] + skolem:lemma4273 + [ a r:Fact; r:gives {((2 1 3 0) "=<") list:sort (0 1 2 3)}] + [ a r:Fact; r:gives {((2 1 3 0) ">=") list:sort (3 2 1 0)}] + skolem:lemma4037 + skolem:lemma4038 + [ a r:Fact; r:gives {(3210 123) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2130]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2131 a r:Inference; + r:gives { + 2131 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2131 math:notEqualTo 0}] + skolem:lemma4274 + [ a r:Fact; r:gives {((2 1 3 1) "=<") list:sort (1 1 2 3)}] + [ a r:Fact; r:gives {((2 1 3 1) ">=") list:sort (3 2 1 1)}] + skolem:lemma4227 + skolem:lemma4228 + [ a r:Fact; r:gives {(3211 1123) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2131]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2132 a r:Inference; + r:gives { + 2132 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2132 math:notEqualTo 0}] + skolem:lemma4275 + [ a r:Fact; r:gives {((2 1 3 2) "=<") list:sort (1 2 2 3)}] + [ a r:Fact; r:gives {((2 1 3 2) ">=") list:sort (3 2 2 1)}] + skolem:lemma4253 + skolem:lemma4254 + [ a r:Fact; r:gives {(3221 1223) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2132]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2133 a r:Inference; + r:gives { + 2133 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2133 math:notEqualTo 0}] + skolem:lemma4276 + [ a r:Fact; r:gives {((2 1 3 3) "=<") list:sort (1 2 3 3)}] + [ a r:Fact; r:gives {((2 1 3 3) ">=") list:sort (3 3 2 1)}] + skolem:lemma4277 + skolem:lemma4278 + [ a r:Fact; r:gives {(3321 1233) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2133]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2134 a r:Inference; + r:gives { + 2134 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2134 math:notEqualTo 0}] + skolem:lemma4279 + [ a r:Fact; r:gives {((2 1 3 4) "=<") list:sort (1 2 3 4)}] + [ a r:Fact; r:gives {((2 1 3 4) ">=") list:sort (4 3 2 1)}] + skolem:lemma4280 + skolem:lemma4281 + [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2134]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2135 a r:Inference; + r:gives { + 2135 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2135 math:notEqualTo 0}] + skolem:lemma4282 + [ a r:Fact; r:gives {((2 1 3 5) "=<") list:sort (1 2 3 5)}] + [ a r:Fact; r:gives {((2 1 3 5) ">=") list:sort (5 3 2 1)}] + skolem:lemma4283 + skolem:lemma4284 + [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2135]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2136 a r:Inference; + r:gives { + 2136 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2136 math:notEqualTo 0}] + skolem:lemma4285 + [ a r:Fact; r:gives {((2 1 3 6) "=<") list:sort (1 2 3 6)}] + [ a r:Fact; r:gives {((2 1 3 6) ">=") list:sort (6 3 2 1)}] + skolem:lemma4286 + skolem:lemma4287 + [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2136]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2137 a r:Inference; + r:gives { + 2137 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2137 math:notEqualTo 0}] + skolem:lemma4288 + [ a r:Fact; r:gives {((2 1 3 7) "=<") list:sort (1 2 3 7)}] + [ a r:Fact; r:gives {((2 1 3 7) ">=") list:sort (7 3 2 1)}] + skolem:lemma4289 + skolem:lemma4290 + [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2137]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2138 a r:Inference; + r:gives { + 2138 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2138 math:notEqualTo 0}] + skolem:lemma4291 + [ a r:Fact; r:gives {((2 1 3 8) "=<") list:sort (1 2 3 8)}] + [ a r:Fact; r:gives {((2 1 3 8) ">=") list:sort (8 3 2 1)}] + skolem:lemma4292 + skolem:lemma4293 + [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2138]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2139 a r:Inference; + r:gives { + 2139 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2139 math:notEqualTo 0}] + skolem:lemma4294 + [ a r:Fact; r:gives {((2 1 3 9) "=<") list:sort (1 2 3 9)}] + [ a r:Fact; r:gives {((2 1 3 9) ">=") list:sort (9 3 2 1)}] + skolem:lemma4295 + skolem:lemma4296 + [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2139]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2140 a r:Inference; + r:gives { + 2140 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2140 math:notEqualTo 0}] + skolem:lemma4297 + [ a r:Fact; r:gives {((2 1 4 0) "=<") list:sort (0 1 2 4)}] + [ a r:Fact; r:gives {((2 1 4 0) ">=") list:sort (4 2 1 0)}] + skolem:lemma4040 + skolem:lemma4041 + [ a r:Fact; r:gives {(4210 124) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2140]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 4 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2141 a r:Inference; + r:gives { + 2141 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2141 math:notEqualTo 0}] + skolem:lemma4298 + [ a r:Fact; r:gives {((2 1 4 1) "=<") list:sort (1 1 2 4)}] + [ a r:Fact; r:gives {((2 1 4 1) ">=") list:sort (4 2 1 1)}] + skolem:lemma4230 + skolem:lemma4231 + [ a r:Fact; r:gives {(4211 1124) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2141]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 4 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2142 a r:Inference; + r:gives { + 2142 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2142 math:notEqualTo 0}] + skolem:lemma4299 + [ a r:Fact; r:gives {((2 1 4 2) "=<") list:sort (1 2 2 4)}] + [ a r:Fact; r:gives {((2 1 4 2) ">=") list:sort (4 2 2 1)}] + skolem:lemma4256 + skolem:lemma4257 + [ a r:Fact; r:gives {(4221 1224) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2142]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2143 a r:Inference; + r:gives { + 2143 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2143 math:notEqualTo 0}] + skolem:lemma4300 + [ a r:Fact; r:gives {((2 1 4 3) "=<") list:sort (1 2 3 4)}] + [ a r:Fact; r:gives {((2 1 4 3) ">=") list:sort (4 3 2 1)}] + skolem:lemma4280 + skolem:lemma4281 + [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2143]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2144 a r:Inference; + r:gives { + 2144 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2144 math:notEqualTo 0}] + skolem:lemma4301 + [ a r:Fact; r:gives {((2 1 4 4) "=<") list:sort (1 2 4 4)}] + [ a r:Fact; r:gives {((2 1 4 4) ">=") list:sort (4 4 2 1)}] + skolem:lemma4302 + skolem:lemma4303 + [ a r:Fact; r:gives {(4421 1244) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2144]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2145 a r:Inference; + r:gives { + 2145 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2145 math:notEqualTo 0}] + skolem:lemma4304 + [ a r:Fact; r:gives {((2 1 4 5) "=<") list:sort (1 2 4 5)}] + [ a r:Fact; r:gives {((2 1 4 5) ">=") list:sort (5 4 2 1)}] + skolem:lemma4305 + skolem:lemma4306 + [ a r:Fact; r:gives {(5421 1245) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2145]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2146 a r:Inference; + r:gives { + 2146 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2146 math:notEqualTo 0}] + skolem:lemma4307 + [ a r:Fact; r:gives {((2 1 4 6) "=<") list:sort (1 2 4 6)}] + [ a r:Fact; r:gives {((2 1 4 6) ">=") list:sort (6 4 2 1)}] + skolem:lemma4308 + skolem:lemma4309 + [ a r:Fact; r:gives {(6421 1246) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2146]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2147 a r:Inference; + r:gives { + 2147 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2147 math:notEqualTo 0}] + skolem:lemma4310 + [ a r:Fact; r:gives {((2 1 4 7) "=<") list:sort (1 2 4 7)}] + [ a r:Fact; r:gives {((2 1 4 7) ">=") list:sort (7 4 2 1)}] + skolem:lemma4311 + skolem:lemma4312 + [ a r:Fact; r:gives {(7421 1247) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2147]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2148 a r:Inference; + r:gives { + 2148 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2148 math:notEqualTo 0}] + skolem:lemma4313 + [ a r:Fact; r:gives {((2 1 4 8) "=<") list:sort (1 2 4 8)}] + [ a r:Fact; r:gives {((2 1 4 8) ">=") list:sort (8 4 2 1)}] + skolem:lemma4314 + skolem:lemma4315 + [ a r:Fact; r:gives {(8421 1248) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2148]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2149 a r:Inference; + r:gives { + 2149 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2149 math:notEqualTo 0}] + skolem:lemma4316 + [ a r:Fact; r:gives {((2 1 4 9) "=<") list:sort (1 2 4 9)}] + [ a r:Fact; r:gives {((2 1 4 9) ">=") list:sort (9 4 2 1)}] + skolem:lemma4317 + skolem:lemma4318 + [ a r:Fact; r:gives {(9421 1249) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2149]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2150 a r:Inference; + r:gives { + 2150 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2150 math:notEqualTo 0}] + skolem:lemma4319 + [ a r:Fact; r:gives {((2 1 5 0) "=<") list:sort (0 1 2 5)}] + [ a r:Fact; r:gives {((2 1 5 0) ">=") list:sort (5 2 1 0)}] + skolem:lemma4043 + skolem:lemma4044 + [ a r:Fact; r:gives {(5210 125) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2150]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 5 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2151 a r:Inference; + r:gives { + 2151 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2151 math:notEqualTo 0}] + skolem:lemma4320 + [ a r:Fact; r:gives {((2 1 5 1) "=<") list:sort (1 1 2 5)}] + [ a r:Fact; r:gives {((2 1 5 1) ">=") list:sort (5 2 1 1)}] + skolem:lemma4233 + skolem:lemma4234 + [ a r:Fact; r:gives {(5211 1125) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2151]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 5 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2152 a r:Inference; + r:gives { + 2152 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2152 math:notEqualTo 0}] + skolem:lemma4321 + [ a r:Fact; r:gives {((2 1 5 2) "=<") list:sort (1 2 2 5)}] + [ a r:Fact; r:gives {((2 1 5 2) ">=") list:sort (5 2 2 1)}] + skolem:lemma4259 + skolem:lemma4260 + [ a r:Fact; r:gives {(5221 1225) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2152]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2153 a r:Inference; + r:gives { + 2153 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2153 math:notEqualTo 0}] + skolem:lemma4322 + [ a r:Fact; r:gives {((2 1 5 3) "=<") list:sort (1 2 3 5)}] + [ a r:Fact; r:gives {((2 1 5 3) ">=") list:sort (5 3 2 1)}] + skolem:lemma4283 + skolem:lemma4284 + [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2153]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2154 a r:Inference; + r:gives { + 2154 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2154 math:notEqualTo 0}] + skolem:lemma4323 + [ a r:Fact; r:gives {((2 1 5 4) "=<") list:sort (1 2 4 5)}] + [ a r:Fact; r:gives {((2 1 5 4) ">=") list:sort (5 4 2 1)}] + skolem:lemma4305 + skolem:lemma4306 + [ a r:Fact; r:gives {(5421 1245) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2154]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 5 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2155 a r:Inference; + r:gives { + 2155 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2155 math:notEqualTo 0}] + skolem:lemma4324 + [ a r:Fact; r:gives {((2 1 5 5) "=<") list:sort (1 2 5 5)}] + [ a r:Fact; r:gives {((2 1 5 5) ">=") list:sort (5 5 2 1)}] + skolem:lemma4325 + skolem:lemma4326 + [ a r:Fact; r:gives {(5521 1255) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2155]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2156 a r:Inference; + r:gives { + 2156 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2156 math:notEqualTo 0}] + skolem:lemma4327 + [ a r:Fact; r:gives {((2 1 5 6) "=<") list:sort (1 2 5 6)}] + [ a r:Fact; r:gives {((2 1 5 6) ">=") list:sort (6 5 2 1)}] + skolem:lemma4328 + skolem:lemma4329 + [ a r:Fact; r:gives {(6521 1256) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2156]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2157 a r:Inference; + r:gives { + 2157 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2157 math:notEqualTo 0}] + skolem:lemma4330 + [ a r:Fact; r:gives {((2 1 5 7) "=<") list:sort (1 2 5 7)}] + [ a r:Fact; r:gives {((2 1 5 7) ">=") list:sort (7 5 2 1)}] + skolem:lemma4331 + skolem:lemma4332 + [ a r:Fact; r:gives {(7521 1257) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2157]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2158 a r:Inference; + r:gives { + 2158 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2158 math:notEqualTo 0}] + skolem:lemma4333 + [ a r:Fact; r:gives {((2 1 5 8) "=<") list:sort (1 2 5 8)}] + [ a r:Fact; r:gives {((2 1 5 8) ">=") list:sort (8 5 2 1)}] + skolem:lemma4334 + skolem:lemma4335 + [ a r:Fact; r:gives {(8521 1258) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2158]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2159 a r:Inference; + r:gives { + 2159 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2159 math:notEqualTo 0}] + skolem:lemma4336 + [ a r:Fact; r:gives {((2 1 5 9) "=<") list:sort (1 2 5 9)}] + [ a r:Fact; r:gives {((2 1 5 9) ">=") list:sort (9 5 2 1)}] + skolem:lemma4337 + skolem:lemma4338 + [ a r:Fact; r:gives {(9521 1259) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2159]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2160 a r:Inference; + r:gives { + 2160 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2160 math:notEqualTo 0}] + skolem:lemma4339 + [ a r:Fact; r:gives {((2 1 6 0) "=<") list:sort (0 1 2 6)}] + [ a r:Fact; r:gives {((2 1 6 0) ">=") list:sort (6 2 1 0)}] + skolem:lemma4046 + skolem:lemma4047 + [ a r:Fact; r:gives {(6210 126) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2160]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 6 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2161 a r:Inference; + r:gives { + 2161 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2161 math:notEqualTo 0}] + skolem:lemma4340 + [ a r:Fact; r:gives {((2 1 6 1) "=<") list:sort (1 1 2 6)}] + [ a r:Fact; r:gives {((2 1 6 1) ">=") list:sort (6 2 1 1)}] + skolem:lemma4236 + skolem:lemma4237 + [ a r:Fact; r:gives {(6211 1126) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2161]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 6 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2162 a r:Inference; + r:gives { + 2162 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2162 math:notEqualTo 0}] + skolem:lemma4341 + [ a r:Fact; r:gives {((2 1 6 2) "=<") list:sort (1 2 2 6)}] + [ a r:Fact; r:gives {((2 1 6 2) ">=") list:sort (6 2 2 1)}] + skolem:lemma4262 + skolem:lemma4263 + [ a r:Fact; r:gives {(6221 1226) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2162]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2163 a r:Inference; + r:gives { + 2163 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2163 math:notEqualTo 0}] + skolem:lemma4342 + [ a r:Fact; r:gives {((2 1 6 3) "=<") list:sort (1 2 3 6)}] + [ a r:Fact; r:gives {((2 1 6 3) ">=") list:sort (6 3 2 1)}] + skolem:lemma4286 + skolem:lemma4287 + [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2163]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2164 a r:Inference; + r:gives { + 2164 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2164 math:notEqualTo 0}] + skolem:lemma4343 + [ a r:Fact; r:gives {((2 1 6 4) "=<") list:sort (1 2 4 6)}] + [ a r:Fact; r:gives {((2 1 6 4) ">=") list:sort (6 4 2 1)}] + skolem:lemma4308 + skolem:lemma4309 + [ a r:Fact; r:gives {(6421 1246) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2164]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 6 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2165 a r:Inference; + r:gives { + 2165 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2165 math:notEqualTo 0}] + skolem:lemma4344 + [ a r:Fact; r:gives {((2 1 6 5) "=<") list:sort (1 2 5 6)}] + [ a r:Fact; r:gives {((2 1 6 5) ">=") list:sort (6 5 2 1)}] + skolem:lemma4328 + skolem:lemma4329 + [ a r:Fact; r:gives {(6521 1256) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2165]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 6 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2166 a r:Inference; + r:gives { + 2166 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2166 math:notEqualTo 0}] + skolem:lemma4345 + [ a r:Fact; r:gives {((2 1 6 6) "=<") list:sort (1 2 6 6)}] + [ a r:Fact; r:gives {((2 1 6 6) ">=") list:sort (6 6 2 1)}] + skolem:lemma4346 + skolem:lemma4347 + [ a r:Fact; r:gives {(6621 1266) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2166]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2167 a r:Inference; + r:gives { + 2167 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2167 math:notEqualTo 0}] + skolem:lemma4348 + [ a r:Fact; r:gives {((2 1 6 7) "=<") list:sort (1 2 6 7)}] + [ a r:Fact; r:gives {((2 1 6 7) ">=") list:sort (7 6 2 1)}] + skolem:lemma4349 + skolem:lemma4350 + [ a r:Fact; r:gives {(7621 1267) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2167]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2168 a r:Inference; + r:gives { + 2168 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2168 math:notEqualTo 0}] + skolem:lemma4351 + [ a r:Fact; r:gives {((2 1 6 8) "=<") list:sort (1 2 6 8)}] + [ a r:Fact; r:gives {((2 1 6 8) ">=") list:sort (8 6 2 1)}] + skolem:lemma4352 + skolem:lemma4353 + [ a r:Fact; r:gives {(8621 1268) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2168]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2169 a r:Inference; + r:gives { + 2169 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2169 math:notEqualTo 0}] + skolem:lemma4354 + [ a r:Fact; r:gives {((2 1 6 9) "=<") list:sort (1 2 6 9)}] + [ a r:Fact; r:gives {((2 1 6 9) ">=") list:sort (9 6 2 1)}] + skolem:lemma4355 + skolem:lemma4356 + [ a r:Fact; r:gives {(9621 1269) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2169]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2170 a r:Inference; + r:gives { + 2170 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2170 math:notEqualTo 0}] + skolem:lemma4357 + [ a r:Fact; r:gives {((2 1 7 0) "=<") list:sort (0 1 2 7)}] + [ a r:Fact; r:gives {((2 1 7 0) ">=") list:sort (7 2 1 0)}] + skolem:lemma4049 + skolem:lemma4050 + [ a r:Fact; r:gives {(7210 127) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2170]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 7 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2171 a r:Inference; + r:gives { + 2171 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2171 math:notEqualTo 0}] + skolem:lemma4358 + [ a r:Fact; r:gives {((2 1 7 1) "=<") list:sort (1 1 2 7)}] + [ a r:Fact; r:gives {((2 1 7 1) ">=") list:sort (7 2 1 1)}] + skolem:lemma4239 + skolem:lemma4240 + [ a r:Fact; r:gives {(7211 1127) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 7 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2172 a r:Inference; + r:gives { + 2172 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2172 math:notEqualTo 0}] + skolem:lemma4359 + [ a r:Fact; r:gives {((2 1 7 2) "=<") list:sort (1 2 2 7)}] + [ a r:Fact; r:gives {((2 1 7 2) ">=") list:sort (7 2 2 1)}] + skolem:lemma4265 + skolem:lemma4266 + [ a r:Fact; r:gives {(7221 1227) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2173 a r:Inference; + r:gives { + 2173 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2173 math:notEqualTo 0}] + skolem:lemma4360 + [ a r:Fact; r:gives {((2 1 7 3) "=<") list:sort (1 2 3 7)}] + [ a r:Fact; r:gives {((2 1 7 3) ">=") list:sort (7 3 2 1)}] + skolem:lemma4289 + skolem:lemma4290 + [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2174 a r:Inference; + r:gives { + 2174 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2174 math:notEqualTo 0}] + skolem:lemma4361 + [ a r:Fact; r:gives {((2 1 7 4) "=<") list:sort (1 2 4 7)}] + [ a r:Fact; r:gives {((2 1 7 4) ">=") list:sort (7 4 2 1)}] + skolem:lemma4311 + skolem:lemma4312 + [ a r:Fact; r:gives {(7421 1247) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 7 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2175 a r:Inference; + r:gives { + 2175 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2175 math:notEqualTo 0}] + skolem:lemma4362 + [ a r:Fact; r:gives {((2 1 7 5) "=<") list:sort (1 2 5 7)}] + [ a r:Fact; r:gives {((2 1 7 5) ">=") list:sort (7 5 2 1)}] + skolem:lemma4331 + skolem:lemma4332 + [ a r:Fact; r:gives {(7521 1257) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 7 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2176 a r:Inference; + r:gives { + 2176 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2176 math:notEqualTo 0}] + skolem:lemma4363 + [ a r:Fact; r:gives {((2 1 7 6) "=<") list:sort (1 2 6 7)}] + [ a r:Fact; r:gives {((2 1 7 6) ">=") list:sort (7 6 2 1)}] + skolem:lemma4349 + skolem:lemma4350 + [ a r:Fact; r:gives {(7621 1267) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 7 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2177 a r:Inference; + r:gives { + 2177 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2177 math:notEqualTo 0}] + skolem:lemma4364 + [ a r:Fact; r:gives {((2 1 7 7) "=<") list:sort (1 2 7 7)}] + [ a r:Fact; r:gives {((2 1 7 7) ">=") list:sort (7 7 2 1)}] + skolem:lemma4365 + skolem:lemma4366 + [ a r:Fact; r:gives {(7721 1277) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1277]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2178 a r:Inference; + r:gives { + 2178 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2178 math:notEqualTo 0}] + skolem:lemma4367 + [ a r:Fact; r:gives {((2 1 7 8) "=<") list:sort (1 2 7 8)}] + [ a r:Fact; r:gives {((2 1 7 8) ">=") list:sort (8 7 2 1)}] + skolem:lemma4368 + skolem:lemma4369 + [ a r:Fact; r:gives {(8721 1278) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2178]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2179 a r:Inference; + r:gives { + 2179 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2179 math:notEqualTo 0}] + skolem:lemma4370 + [ a r:Fact; r:gives {((2 1 7 9) "=<") list:sort (1 2 7 9)}] + [ a r:Fact; r:gives {((2 1 7 9) ">=") list:sort (9 7 2 1)}] + skolem:lemma4371 + skolem:lemma4372 + [ a r:Fact; r:gives {(9721 1279) math:difference 8442}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8442 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 8442 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2179]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2180 a r:Inference; + r:gives { + 2180 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2180 math:notEqualTo 0}] + skolem:lemma4373 + [ a r:Fact; r:gives {((2 1 8 0) "=<") list:sort (0 1 2 8)}] + [ a r:Fact; r:gives {((2 1 8 0) ">=") list:sort (8 2 1 0)}] + skolem:lemma4052 + skolem:lemma4053 + [ a r:Fact; r:gives {(8210 128) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2180]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 8 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2181 a r:Inference; + r:gives { + 2181 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2181 math:notEqualTo 0}] + skolem:lemma4374 + [ a r:Fact; r:gives {((2 1 8 1) "=<") list:sort (1 1 2 8)}] + [ a r:Fact; r:gives {((2 1 8 1) ">=") list:sort (8 2 1 1)}] + skolem:lemma4242 + skolem:lemma4243 + [ a r:Fact; r:gives {(8211 1128) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2181]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 8 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2182 a r:Inference; + r:gives { + 2182 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2182 math:notEqualTo 0}] + skolem:lemma4375 + [ a r:Fact; r:gives {((2 1 8 2) "=<") list:sort (1 2 2 8)}] + [ a r:Fact; r:gives {((2 1 8 2) ">=") list:sort (8 2 2 1)}] + skolem:lemma4268 + skolem:lemma4269 + [ a r:Fact; r:gives {(8221 1228) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2182]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2183 a r:Inference; + r:gives { + 2183 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2183 math:notEqualTo 0}] + skolem:lemma4376 + [ a r:Fact; r:gives {((2 1 8 3) "=<") list:sort (1 2 3 8)}] + [ a r:Fact; r:gives {((2 1 8 3) ">=") list:sort (8 3 2 1)}] + skolem:lemma4292 + skolem:lemma4293 + [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2183]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2184 a r:Inference; + r:gives { + 2184 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2184 math:notEqualTo 0}] + skolem:lemma4377 + [ a r:Fact; r:gives {((2 1 8 4) "=<") list:sort (1 2 4 8)}] + [ a r:Fact; r:gives {((2 1 8 4) ">=") list:sort (8 4 2 1)}] + skolem:lemma4314 + skolem:lemma4315 + [ a r:Fact; r:gives {(8421 1248) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2184]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 8 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2185 a r:Inference; + r:gives { + 2185 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2185 math:notEqualTo 0}] + skolem:lemma4378 + [ a r:Fact; r:gives {((2 1 8 5) "=<") list:sort (1 2 5 8)}] + [ a r:Fact; r:gives {((2 1 8 5) ">=") list:sort (8 5 2 1)}] + skolem:lemma4334 + skolem:lemma4335 + [ a r:Fact; r:gives {(8521 1258) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2185]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 8 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2186 a r:Inference; + r:gives { + 2186 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2186 math:notEqualTo 0}] + skolem:lemma4379 + [ a r:Fact; r:gives {((2 1 8 6) "=<") list:sort (1 2 6 8)}] + [ a r:Fact; r:gives {((2 1 8 6) ">=") list:sort (8 6 2 1)}] + skolem:lemma4352 + skolem:lemma4353 + [ a r:Fact; r:gives {(8621 1268) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2186]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 8 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2187 a r:Inference; + r:gives { + 2187 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2187 math:notEqualTo 0}] + skolem:lemma4380 + [ a r:Fact; r:gives {((2 1 8 7) "=<") list:sort (1 2 7 8)}] + [ a r:Fact; r:gives {((2 1 8 7) ">=") list:sort (8 7 2 1)}] + skolem:lemma4368 + skolem:lemma4369 + [ a r:Fact; r:gives {(8721 1278) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2187]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 8 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2188 a r:Inference; + r:gives { + 2188 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2188 math:notEqualTo 0}] + skolem:lemma4381 + [ a r:Fact; r:gives {((2 1 8 8) "=<") list:sort (1 2 8 8)}] + [ a r:Fact; r:gives {((2 1 8 8) ">=") list:sort (8 8 2 1)}] + skolem:lemma4382 + skolem:lemma4383 + [ a r:Fact; r:gives {(8821 1288) math:difference 7533}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7533 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7533 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2188]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1288]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8821]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2189 a r:Inference; + r:gives { + 2189 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2189 math:notEqualTo 0}] + skolem:lemma4384 + [ a r:Fact; r:gives {((2 1 8 9) "=<") list:sort (1 2 8 9)}] + [ a r:Fact; r:gives {((2 1 8 9) ">=") list:sort (9 8 2 1)}] + skolem:lemma4385 + skolem:lemma4386 + [ a r:Fact; r:gives {(9821 1289) math:difference 8532}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8532 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8532 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2189]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9821]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2190 a r:Inference; + r:gives { + 2190 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2190 math:notEqualTo 0}] + skolem:lemma4387 + [ a r:Fact; r:gives {((2 1 9 0) "=<") list:sort (0 1 2 9)}] + [ a r:Fact; r:gives {((2 1 9 0) ">=") list:sort (9 2 1 0)}] + skolem:lemma4055 + skolem:lemma4056 + [ a r:Fact; r:gives {(9210 129) math:difference 9081}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9081 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 9081 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2190]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 9 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2191 a r:Inference; + r:gives { + 2191 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2191 math:notEqualTo 0}] + skolem:lemma4388 + [ a r:Fact; r:gives {((2 1 9 1) "=<") list:sort (1 1 2 9)}] + [ a r:Fact; r:gives {((2 1 9 1) ">=") list:sort (9 2 1 1)}] + skolem:lemma4245 + skolem:lemma4246 + [ a r:Fact; r:gives {(9211 1129) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2191]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 9 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2192 a r:Inference; + r:gives { + 2192 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2192 math:notEqualTo 0}] + skolem:lemma4389 + [ a r:Fact; r:gives {((2 1 9 2) "=<") list:sort (1 2 2 9)}] + [ a r:Fact; r:gives {((2 1 9 2) ">=") list:sort (9 2 2 1)}] + skolem:lemma4271 + skolem:lemma4272 + [ a r:Fact; r:gives {(9221 1229) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2192]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 9 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2193 a r:Inference; + r:gives { + 2193 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2193 math:notEqualTo 0}] + skolem:lemma4390 + [ a r:Fact; r:gives {((2 1 9 3) "=<") list:sort (1 2 3 9)}] + [ a r:Fact; r:gives {((2 1 9 3) ">=") list:sort (9 3 2 1)}] + skolem:lemma4295 + skolem:lemma4296 + [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2193]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 9 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2194 a r:Inference; + r:gives { + 2194 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2194 math:notEqualTo 0}] + skolem:lemma4391 + [ a r:Fact; r:gives {((2 1 9 4) "=<") list:sort (1 2 4 9)}] + [ a r:Fact; r:gives {((2 1 9 4) ">=") list:sort (9 4 2 1)}] + skolem:lemma4317 + skolem:lemma4318 + [ a r:Fact; r:gives {(9421 1249) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2194]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 9 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2195 a r:Inference; + r:gives { + 2195 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2195 math:notEqualTo 0}] + skolem:lemma4392 + [ a r:Fact; r:gives {((2 1 9 5) "=<") list:sort (1 2 5 9)}] + [ a r:Fact; r:gives {((2 1 9 5) ">=") list:sort (9 5 2 1)}] + skolem:lemma4337 + skolem:lemma4338 + [ a r:Fact; r:gives {(9521 1259) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2195]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 9 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2196 a r:Inference; + r:gives { + 2196 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2196 math:notEqualTo 0}] + skolem:lemma4393 + [ a r:Fact; r:gives {((2 1 9 6) "=<") list:sort (1 2 6 9)}] + [ a r:Fact; r:gives {((2 1 9 6) ">=") list:sort (9 6 2 1)}] + skolem:lemma4355 + skolem:lemma4356 + [ a r:Fact; r:gives {(9621 1269) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2196]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 9 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2197 a r:Inference; + r:gives { + 2197 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2197 math:notEqualTo 0}] + skolem:lemma4394 + [ a r:Fact; r:gives {((2 1 9 7) "=<") list:sort (1 2 7 9)}] + [ a r:Fact; r:gives {((2 1 9 7) ">=") list:sort (9 7 2 1)}] + skolem:lemma4371 + skolem:lemma4372 + [ a r:Fact; r:gives {(9721 1279) math:difference 8442}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8442 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 8442 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2197]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 9 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2198 a r:Inference; + r:gives { + 2198 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2198 math:notEqualTo 0}] + skolem:lemma4395 + [ a r:Fact; r:gives {((2 1 9 8) "=<") list:sort (1 2 8 9)}] + [ a r:Fact; r:gives {((2 1 9 8) ">=") list:sort (9 8 2 1)}] + skolem:lemma4385 + skolem:lemma4386 + [ a r:Fact; r:gives {(9821 1289) math:difference 8532}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8532 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8532 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2198]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 9 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9821]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2199 a r:Inference; + r:gives { + 2199 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2199 math:notEqualTo 0}] + skolem:lemma4396 + [ a r:Fact; r:gives {((2 1 9 9) "=<") list:sort (1 2 9 9)}] + [ a r:Fact; r:gives {((2 1 9 9) ">=") list:sort (9 9 2 1)}] + skolem:lemma4397 + skolem:lemma4398 + [ a r:Fact; r:gives {(9921 1299) math:difference 8622}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8622 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8622 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2199]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 1 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9921]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2200 a r:Inference; + r:gives { + 2200 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2200 math:notEqualTo 0}] + skolem:lemma4399 + [ a r:Fact; r:gives {((2 2 0 0) "=<") list:sort (0 0 2 2)}] + [ a r:Fact; r:gives {((2 2 0 0) ">=") list:sort (2 2 0 0)}] + skolem:lemma4006 + skolem:lemma4007 + [ a r:Fact; r:gives {(2200 22) math:difference 2178}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2178 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2178 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2178]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2201 a r:Inference; + r:gives { + 2201 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2201 math:notEqualTo 0}] + skolem:lemma4400 + [ a r:Fact; r:gives {((2 2 0 1) "=<") list:sort (0 1 2 2)}] + [ a r:Fact; r:gives {((2 2 0 1) ">=") list:sort (2 2 1 0)}] + skolem:lemma4034 + skolem:lemma4035 + [ a r:Fact; r:gives {(2210 122) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2201]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 0 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 122]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2202 a r:Inference; + r:gives { + 2202 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2202 math:notEqualTo 0}] + skolem:lemma4401 + [ a r:Fact; r:gives {((2 2 0 2) "=<") list:sort (0 2 2 2)}] + [ a r:Fact; r:gives {((2 2 0 2) ">=") list:sort (2 2 2 0)}] + skolem:lemma4060 + skolem:lemma4061 + [ a r:Fact; r:gives {(2220 222) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2202]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 0 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2203 a r:Inference; + r:gives { + 2203 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2203 math:notEqualTo 0}] + skolem:lemma4402 + [ a r:Fact; r:gives {((2 2 0 3) "=<") list:sort (0 2 2 3)}] + [ a r:Fact; r:gives {((2 2 0 3) ">=") list:sort (3 2 2 0)}] + skolem:lemma4063 + skolem:lemma4064 + [ a r:Fact; r:gives {(3220 223) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2203]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 0 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2204 a r:Inference; + r:gives { + 2204 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2204 math:notEqualTo 0}] + skolem:lemma4403 + [ a r:Fact; r:gives {((2 2 0 4) "=<") list:sort (0 2 2 4)}] + [ a r:Fact; r:gives {((2 2 0 4) ">=") list:sort (4 2 2 0)}] + skolem:lemma4066 + skolem:lemma4067 + [ a r:Fact; r:gives {(4220 224) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2204]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 0 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2205 a r:Inference; + r:gives { + 2205 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2205 math:notEqualTo 0}] + skolem:lemma4404 + [ a r:Fact; r:gives {((2 2 0 5) "=<") list:sort (0 2 2 5)}] + [ a r:Fact; r:gives {((2 2 0 5) ">=") list:sort (5 2 2 0)}] + skolem:lemma4069 + skolem:lemma4070 + [ a r:Fact; r:gives {(5220 225) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2205]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 0 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2206 a r:Inference; + r:gives { + 2206 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2206 math:notEqualTo 0}] + skolem:lemma4405 + [ a r:Fact; r:gives {((2 2 0 6) "=<") list:sort (0 2 2 6)}] + [ a r:Fact; r:gives {((2 2 0 6) ">=") list:sort (6 2 2 0)}] + skolem:lemma4072 + skolem:lemma4073 + [ a r:Fact; r:gives {(6220 226) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2206]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 0 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2207 a r:Inference; + r:gives { + 2207 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2207 math:notEqualTo 0}] + skolem:lemma4406 + [ a r:Fact; r:gives {((2 2 0 7) "=<") list:sort (0 2 2 7)}] + [ a r:Fact; r:gives {((2 2 0 7) ">=") list:sort (7 2 2 0)}] + skolem:lemma4075 + skolem:lemma4076 + [ a r:Fact; r:gives {(7220 227) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2207]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 0 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2208 a r:Inference; + r:gives { + 2208 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2208 math:notEqualTo 0}] + skolem:lemma4407 + [ a r:Fact; r:gives {((2 2 0 8) "=<") list:sort (0 2 2 8)}] + [ a r:Fact; r:gives {((2 2 0 8) ">=") list:sort (8 2 2 0)}] + skolem:lemma4078 + skolem:lemma4079 + [ a r:Fact; r:gives {(8220 228) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2208]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 0 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2209 a r:Inference; + r:gives { + 2209 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2209 math:notEqualTo 0}] + skolem:lemma4408 + [ a r:Fact; r:gives {((2 2 0 9) "=<") list:sort (0 2 2 9)}] + [ a r:Fact; r:gives {((2 2 0 9) ">=") list:sort (9 2 2 0)}] + skolem:lemma4081 + skolem:lemma4082 + [ a r:Fact; r:gives {(9220 229) math:difference 8991}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8991 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 8991 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2209]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 0 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8991]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2210 a r:Inference; + r:gives { + 2210 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2210 math:notEqualTo 0}] + skolem:lemma4409 + [ a r:Fact; r:gives {((2 2 1 0) "=<") list:sort (0 1 2 2)}] + [ a r:Fact; r:gives {((2 2 1 0) ">=") list:sort (2 2 1 0)}] + skolem:lemma4034 + skolem:lemma4035 + [ a r:Fact; r:gives {(2210 122) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 122]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2211 a r:Inference; + r:gives { + 2211 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2211 math:notEqualTo 0}] + skolem:lemma4410 + [ a r:Fact; r:gives {((2 2 1 1) "=<") list:sort (1 1 2 2)}] + [ a r:Fact; r:gives {((2 2 1 1) ">=") list:sort (2 2 1 1)}] + skolem:lemma4224 + skolem:lemma4225 + [ a r:Fact; r:gives {(2211 1122) math:difference 1089}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1089 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1089 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1122]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1089]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2212 a r:Inference; + r:gives { + 2212 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2212 math:notEqualTo 0}] + skolem:lemma4411 + [ a r:Fact; r:gives {((2 2 1 2) "=<") list:sort (1 2 2 2)}] + [ a r:Fact; r:gives {((2 2 1 2) ">=") list:sort (2 2 2 1)}] + skolem:lemma4250 + skolem:lemma4251 + [ a r:Fact; r:gives {(2221 1222) math:difference 999}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 999 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 999 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2212]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2213 a r:Inference; + r:gives { + 2213 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2213 math:notEqualTo 0}] + skolem:lemma4412 + [ a r:Fact; r:gives {((2 2 1 3) "=<") list:sort (1 2 2 3)}] + [ a r:Fact; r:gives {((2 2 1 3) ">=") list:sort (3 2 2 1)}] + skolem:lemma4253 + skolem:lemma4254 + [ a r:Fact; r:gives {(3221 1223) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2213]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2214 a r:Inference; + r:gives { + 2214 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2214 math:notEqualTo 0}] + skolem:lemma4413 + [ a r:Fact; r:gives {((2 2 1 4) "=<") list:sort (1 2 2 4)}] + [ a r:Fact; r:gives {((2 2 1 4) ">=") list:sort (4 2 2 1)}] + skolem:lemma4256 + skolem:lemma4257 + [ a r:Fact; r:gives {(4221 1224) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2214]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 1 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2215 a r:Inference; + r:gives { + 2215 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2215 math:notEqualTo 0}] + skolem:lemma4414 + [ a r:Fact; r:gives {((2 2 1 5) "=<") list:sort (1 2 2 5)}] + [ a r:Fact; r:gives {((2 2 1 5) ">=") list:sort (5 2 2 1)}] + skolem:lemma4259 + skolem:lemma4260 + [ a r:Fact; r:gives {(5221 1225) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2215]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 1 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2216 a r:Inference; + r:gives { + 2216 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2216 math:notEqualTo 0}] + skolem:lemma4415 + [ a r:Fact; r:gives {((2 2 1 6) "=<") list:sort (1 2 2 6)}] + [ a r:Fact; r:gives {((2 2 1 6) ">=") list:sort (6 2 2 1)}] + skolem:lemma4262 + skolem:lemma4263 + [ a r:Fact; r:gives {(6221 1226) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2216]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 1 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2217 a r:Inference; + r:gives { + 2217 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2217 math:notEqualTo 0}] + skolem:lemma4416 + [ a r:Fact; r:gives {((2 2 1 7) "=<") list:sort (1 2 2 7)}] + [ a r:Fact; r:gives {((2 2 1 7) ">=") list:sort (7 2 2 1)}] + skolem:lemma4265 + skolem:lemma4266 + [ a r:Fact; r:gives {(7221 1227) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2217]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 1 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2218 a r:Inference; + r:gives { + 2218 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2218 math:notEqualTo 0}] + skolem:lemma4417 + [ a r:Fact; r:gives {((2 2 1 8) "=<") list:sort (1 2 2 8)}] + [ a r:Fact; r:gives {((2 2 1 8) ">=") list:sort (8 2 2 1)}] + skolem:lemma4268 + skolem:lemma4269 + [ a r:Fact; r:gives {(8221 1228) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2218]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 1 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2219 a r:Inference; + r:gives { + 2219 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2219 math:notEqualTo 0}] + skolem:lemma4418 + [ a r:Fact; r:gives {((2 2 1 9) "=<") list:sort (1 2 2 9)}] + [ a r:Fact; r:gives {((2 2 1 9) ">=") list:sort (9 2 2 1)}] + skolem:lemma4271 + skolem:lemma4272 + [ a r:Fact; r:gives {(9221 1229) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2219]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 1 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2220 a r:Inference; + r:gives { + 2220 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2220 math:notEqualTo 0}] + skolem:lemma4419 + [ a r:Fact; r:gives {((2 2 2 0) "=<") list:sort (0 2 2 2)}] + [ a r:Fact; r:gives {((2 2 2 0) ">=") list:sort (2 2 2 0)}] + skolem:lemma4060 + skolem:lemma4061 + [ a r:Fact; r:gives {(2220 222) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2221 a r:Inference; + r:gives { + 2221 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2221 math:notEqualTo 0}] + skolem:lemma4420 + [ a r:Fact; r:gives {((2 2 2 1) "=<") list:sort (1 2 2 2)}] + [ a r:Fact; r:gives {((2 2 2 1) ">=") list:sort (2 2 2 1)}] + skolem:lemma4250 + skolem:lemma4251 + [ a r:Fact; r:gives {(2221 1222) math:difference 999}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 999 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 999 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (2 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2222 a r:Inference; + r:gives { + 2223 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2223 math:notEqualTo 0}] + skolem:lemma4421 + [ a r:Fact; r:gives {((2 2 2 3) "=<") list:sort (2 2 2 3)}] + [ a r:Fact; r:gives {((2 2 2 3) ">=") list:sort (3 2 2 2)}] + skolem:lemma4422 + skolem:lemma4423 + [ a r:Fact; r:gives {(3222 2223) math:difference 999}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 999 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 999 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2223 a r:Inference; + r:gives { + 2224 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2224 math:notEqualTo 0}] + skolem:lemma4424 + [ a r:Fact; r:gives {((2 2 2 4) "=<") list:sort (2 2 2 4)}] + [ a r:Fact; r:gives {((2 2 2 4) ">=") list:sort (4 2 2 2)}] + skolem:lemma4425 + skolem:lemma4426 + [ a r:Fact; r:gives {(4222 2224) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2224 a r:Inference; + r:gives { + 2225 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2225 math:notEqualTo 0}] + skolem:lemma4427 + [ a r:Fact; r:gives {((2 2 2 5) "=<") list:sort (2 2 2 5)}] + [ a r:Fact; r:gives {((2 2 2 5) ">=") list:sort (5 2 2 2)}] + skolem:lemma4428 + skolem:lemma4429 + [ a r:Fact; r:gives {(5222 2225) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2225 a r:Inference; + r:gives { + 2226 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2226 math:notEqualTo 0}] + skolem:lemma4430 + [ a r:Fact; r:gives {((2 2 2 6) "=<") list:sort (2 2 2 6)}] + [ a r:Fact; r:gives {((2 2 2 6) ">=") list:sort (6 2 2 2)}] + skolem:lemma4431 + skolem:lemma4432 + [ a r:Fact; r:gives {(6222 2226) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2226 a r:Inference; + r:gives { + 2227 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2227 math:notEqualTo 0}] + skolem:lemma4433 + [ a r:Fact; r:gives {((2 2 2 7) "=<") list:sort (2 2 2 7)}] + [ a r:Fact; r:gives {((2 2 2 7) ">=") list:sort (7 2 2 2)}] + skolem:lemma4434 + skolem:lemma4435 + [ a r:Fact; r:gives {(7222 2227) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2227 a r:Inference; + r:gives { + 2228 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2228 math:notEqualTo 0}] + skolem:lemma4436 + [ a r:Fact; r:gives {((2 2 2 8) "=<") list:sort (2 2 2 8)}] + [ a r:Fact; r:gives {((2 2 2 8) ">=") list:sort (8 2 2 2)}] + skolem:lemma4437 + skolem:lemma4438 + [ a r:Fact; r:gives {(8222 2228) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2228 a r:Inference; + r:gives { + 2229 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2229 math:notEqualTo 0}] + skolem:lemma4439 + [ a r:Fact; r:gives {((2 2 2 9) "=<") list:sort (2 2 2 9)}] + [ a r:Fact; r:gives {((2 2 2 9) ">=") list:sort (9 2 2 2)}] + skolem:lemma4440 + skolem:lemma4441 + [ a r:Fact; r:gives {(9222 2229) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2229 a r:Inference; + r:gives { + 2230 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2230 math:notEqualTo 0}] + skolem:lemma4442 + [ a r:Fact; r:gives {((2 2 3 0) "=<") list:sort (0 2 2 3)}] + [ a r:Fact; r:gives {((2 2 3 0) ">=") list:sort (3 2 2 0)}] + skolem:lemma4063 + skolem:lemma4064 + [ a r:Fact; r:gives {(3220 223) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2230]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2230 a r:Inference; + r:gives { + 2231 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2231 math:notEqualTo 0}] + skolem:lemma4443 + [ a r:Fact; r:gives {((2 2 3 1) "=<") list:sort (1 2 2 3)}] + [ a r:Fact; r:gives {((2 2 3 1) ">=") list:sort (3 2 2 1)}] + skolem:lemma4253 + skolem:lemma4254 + [ a r:Fact; r:gives {(3221 1223) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2231]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2231 a r:Inference; + r:gives { + 2232 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2232 math:notEqualTo 0}] + skolem:lemma4444 + [ a r:Fact; r:gives {((2 2 3 2) "=<") list:sort (2 2 2 3)}] + [ a r:Fact; r:gives {((2 2 3 2) ">=") list:sort (3 2 2 2)}] + skolem:lemma4422 + skolem:lemma4423 + [ a r:Fact; r:gives {(3222 2223) math:difference 999}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 999 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 999 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2232]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2232 a r:Inference; + r:gives { + 2233 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2233 math:notEqualTo 0}] + skolem:lemma4445 + [ a r:Fact; r:gives {((2 2 3 3) "=<") list:sort (2 2 3 3)}] + [ a r:Fact; r:gives {((2 2 3 3) ">=") list:sort (3 3 2 2)}] + skolem:lemma4446 + skolem:lemma4447 + [ a r:Fact; r:gives {(3322 2233) math:difference 1089}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1089 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1089 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1089]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2233 a r:Inference; + r:gives { + 2234 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2234 math:notEqualTo 0}] + skolem:lemma4448 + [ a r:Fact; r:gives {((2 2 3 4) "=<") list:sort (2 2 3 4)}] + [ a r:Fact; r:gives {((2 2 3 4) ">=") list:sort (4 3 2 2)}] + skolem:lemma4449 + skolem:lemma4450 + [ a r:Fact; r:gives {(4322 2234) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2234 a r:Inference; + r:gives { + 2235 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2235 math:notEqualTo 0}] + skolem:lemma4451 + [ a r:Fact; r:gives {((2 2 3 5) "=<") list:sort (2 2 3 5)}] + [ a r:Fact; r:gives {((2 2 3 5) ">=") list:sort (5 3 2 2)}] + skolem:lemma4452 + skolem:lemma4453 + [ a r:Fact; r:gives {(5322 2235) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2235 a r:Inference; + r:gives { + 2236 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2236 math:notEqualTo 0}] + skolem:lemma4454 + [ a r:Fact; r:gives {((2 2 3 6) "=<") list:sort (2 2 3 6)}] + [ a r:Fact; r:gives {((2 2 3 6) ">=") list:sort (6 3 2 2)}] + skolem:lemma4455 + skolem:lemma4456 + [ a r:Fact; r:gives {(6322 2236) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2236 a r:Inference; + r:gives { + 2237 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2237 math:notEqualTo 0}] + skolem:lemma4457 + [ a r:Fact; r:gives {((2 2 3 7) "=<") list:sort (2 2 3 7)}] + [ a r:Fact; r:gives {((2 2 3 7) ">=") list:sort (7 3 2 2)}] + skolem:lemma4458 + skolem:lemma4459 + [ a r:Fact; r:gives {(7322 2237) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2237 a r:Inference; + r:gives { + 2238 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2238 math:notEqualTo 0}] + skolem:lemma4460 + [ a r:Fact; r:gives {((2 2 3 8) "=<") list:sort (2 2 3 8)}] + [ a r:Fact; r:gives {((2 2 3 8) ">=") list:sort (8 3 2 2)}] + skolem:lemma4461 + skolem:lemma4462 + [ a r:Fact; r:gives {(8322 2238) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2238 a r:Inference; + r:gives { + 2239 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2239 math:notEqualTo 0}] + skolem:lemma4463 + [ a r:Fact; r:gives {((2 2 3 9) "=<") list:sort (2 2 3 9)}] + [ a r:Fact; r:gives {((2 2 3 9) ">=") list:sort (9 3 2 2)}] + skolem:lemma4464 + skolem:lemma4465 + [ a r:Fact; r:gives {(9322 2239) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2239 a r:Inference; + r:gives { + 2240 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2240 math:notEqualTo 0}] + skolem:lemma4466 + [ a r:Fact; r:gives {((2 2 4 0) "=<") list:sort (0 2 2 4)}] + [ a r:Fact; r:gives {((2 2 4 0) ">=") list:sort (4 2 2 0)}] + skolem:lemma4066 + skolem:lemma4067 + [ a r:Fact; r:gives {(4220 224) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2240]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 4 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2240 a r:Inference; + r:gives { + 2241 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2241 math:notEqualTo 0}] + skolem:lemma4467 + [ a r:Fact; r:gives {((2 2 4 1) "=<") list:sort (1 2 2 4)}] + [ a r:Fact; r:gives {((2 2 4 1) ">=") list:sort (4 2 2 1)}] + skolem:lemma4256 + skolem:lemma4257 + [ a r:Fact; r:gives {(4221 1224) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2241]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 4 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2241 a r:Inference; + r:gives { + 2242 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2242 math:notEqualTo 0}] + skolem:lemma4468 + [ a r:Fact; r:gives {((2 2 4 2) "=<") list:sort (2 2 2 4)}] + [ a r:Fact; r:gives {((2 2 4 2) ">=") list:sort (4 2 2 2)}] + skolem:lemma4425 + skolem:lemma4426 + [ a r:Fact; r:gives {(4222 2224) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2242]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2242 a r:Inference; + r:gives { + 2243 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2243 math:notEqualTo 0}] + skolem:lemma4469 + [ a r:Fact; r:gives {((2 2 4 3) "=<") list:sort (2 2 3 4)}] + [ a r:Fact; r:gives {((2 2 4 3) ">=") list:sort (4 3 2 2)}] + skolem:lemma4449 + skolem:lemma4450 + [ a r:Fact; r:gives {(4322 2234) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2243]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2243 a r:Inference; + r:gives { + 2244 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2244 math:notEqualTo 0}] + skolem:lemma4470 + [ a r:Fact; r:gives {((2 2 4 4) "=<") list:sort (2 2 4 4)}] + [ a r:Fact; r:gives {((2 2 4 4) ">=") list:sort (4 4 2 2)}] + skolem:lemma4471 + skolem:lemma4472 + [ a r:Fact; r:gives {(4422 2244) math:difference 2178}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2178 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2178 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2178]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2244 a r:Inference; + r:gives { + 2245 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2245 math:notEqualTo 0}] + skolem:lemma4473 + [ a r:Fact; r:gives {((2 2 4 5) "=<") list:sort (2 2 4 5)}] + [ a r:Fact; r:gives {((2 2 4 5) ">=") list:sort (5 4 2 2)}] + skolem:lemma4474 + skolem:lemma4475 + [ a r:Fact; r:gives {(5422 2245) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2245 a r:Inference; + r:gives { + 2246 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2246 math:notEqualTo 0}] + skolem:lemma4476 + [ a r:Fact; r:gives {((2 2 4 6) "=<") list:sort (2 2 4 6)}] + [ a r:Fact; r:gives {((2 2 4 6) ">=") list:sort (6 4 2 2)}] + skolem:lemma4477 + skolem:lemma4478 + [ a r:Fact; r:gives {(6422 2246) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2246 a r:Inference; + r:gives { + 2247 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2247 math:notEqualTo 0}] + skolem:lemma4479 + [ a r:Fact; r:gives {((2 2 4 7) "=<") list:sort (2 2 4 7)}] + [ a r:Fact; r:gives {((2 2 4 7) ">=") list:sort (7 4 2 2)}] + skolem:lemma4480 + skolem:lemma4481 + [ a r:Fact; r:gives {(7422 2247) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2247 a r:Inference; + r:gives { + 2248 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2248 math:notEqualTo 0}] + skolem:lemma4482 + [ a r:Fact; r:gives {((2 2 4 8) "=<") list:sort (2 2 4 8)}] + [ a r:Fact; r:gives {((2 2 4 8) ">=") list:sort (8 4 2 2)}] + skolem:lemma4483 + skolem:lemma4484 + [ a r:Fact; r:gives {(8422 2248) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2248 a r:Inference; + r:gives { + 2249 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2249 math:notEqualTo 0}] + skolem:lemma4485 + [ a r:Fact; r:gives {((2 2 4 9) "=<") list:sort (2 2 4 9)}] + [ a r:Fact; r:gives {((2 2 4 9) ">=") list:sort (9 4 2 2)}] + skolem:lemma4486 + skolem:lemma4487 + [ a r:Fact; r:gives {(9422 2249) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2249 a r:Inference; + r:gives { + 2250 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2250 math:notEqualTo 0}] + skolem:lemma4488 + [ a r:Fact; r:gives {((2 2 5 0) "=<") list:sort (0 2 2 5)}] + [ a r:Fact; r:gives {((2 2 5 0) ">=") list:sort (5 2 2 0)}] + skolem:lemma4069 + skolem:lemma4070 + [ a r:Fact; r:gives {(5220 225) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2250]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 5 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2250 a r:Inference; + r:gives { + 2251 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2251 math:notEqualTo 0}] + skolem:lemma4489 + [ a r:Fact; r:gives {((2 2 5 1) "=<") list:sort (1 2 2 5)}] + [ a r:Fact; r:gives {((2 2 5 1) ">=") list:sort (5 2 2 1)}] + skolem:lemma4259 + skolem:lemma4260 + [ a r:Fact; r:gives {(5221 1225) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2251]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 5 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2251 a r:Inference; + r:gives { + 2252 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2252 math:notEqualTo 0}] + skolem:lemma4490 + [ a r:Fact; r:gives {((2 2 5 2) "=<") list:sort (2 2 2 5)}] + [ a r:Fact; r:gives {((2 2 5 2) ">=") list:sort (5 2 2 2)}] + skolem:lemma4428 + skolem:lemma4429 + [ a r:Fact; r:gives {(5222 2225) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2252]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2252 a r:Inference; + r:gives { + 2253 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2253 math:notEqualTo 0}] + skolem:lemma4491 + [ a r:Fact; r:gives {((2 2 5 3) "=<") list:sort (2 2 3 5)}] + [ a r:Fact; r:gives {((2 2 5 3) ">=") list:sort (5 3 2 2)}] + skolem:lemma4452 + skolem:lemma4453 + [ a r:Fact; r:gives {(5322 2235) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2253]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2253 a r:Inference; + r:gives { + 2254 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2254 math:notEqualTo 0}] + skolem:lemma4492 + [ a r:Fact; r:gives {((2 2 5 4) "=<") list:sort (2 2 4 5)}] + [ a r:Fact; r:gives {((2 2 5 4) ">=") list:sort (5 4 2 2)}] + skolem:lemma4474 + skolem:lemma4475 + [ a r:Fact; r:gives {(5422 2245) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2254]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 5 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2254 a r:Inference; + r:gives { + 2255 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2255 math:notEqualTo 0}] + skolem:lemma4493 + [ a r:Fact; r:gives {((2 2 5 5) "=<") list:sort (2 2 5 5)}] + [ a r:Fact; r:gives {((2 2 5 5) ">=") list:sort (5 5 2 2)}] + skolem:lemma4494 + skolem:lemma4495 + [ a r:Fact; r:gives {(5522 2255) math:difference 3267}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3267 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 3267 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2255 a r:Inference; + r:gives { + 2256 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2256 math:notEqualTo 0}] + skolem:lemma4496 + [ a r:Fact; r:gives {((2 2 5 6) "=<") list:sort (2 2 5 6)}] + [ a r:Fact; r:gives {((2 2 5 6) ">=") list:sort (6 5 2 2)}] + skolem:lemma4497 + skolem:lemma4498 + [ a r:Fact; r:gives {(6522 2256) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2256 a r:Inference; + r:gives { + 2257 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2257 math:notEqualTo 0}] + skolem:lemma4499 + [ a r:Fact; r:gives {((2 2 5 7) "=<") list:sort (2 2 5 7)}] + [ a r:Fact; r:gives {((2 2 5 7) ">=") list:sort (7 5 2 2)}] + skolem:lemma4500 + skolem:lemma4501 + [ a r:Fact; r:gives {(7522 2257) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2257 a r:Inference; + r:gives { + 2258 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2258 math:notEqualTo 0}] + skolem:lemma4502 + [ a r:Fact; r:gives {((2 2 5 8) "=<") list:sort (2 2 5 8)}] + [ a r:Fact; r:gives {((2 2 5 8) ">=") list:sort (8 5 2 2)}] + skolem:lemma4503 + skolem:lemma4504 + [ a r:Fact; r:gives {(8522 2258) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2258 a r:Inference; + r:gives { + 2259 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2259 math:notEqualTo 0}] + skolem:lemma4505 + [ a r:Fact; r:gives {((2 2 5 9) "=<") list:sort (2 2 5 9)}] + [ a r:Fact; r:gives {((2 2 5 9) ">=") list:sort (9 5 2 2)}] + skolem:lemma4506 + skolem:lemma4507 + [ a r:Fact; r:gives {(9522 2259) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2259 a r:Inference; + r:gives { + 2260 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2260 math:notEqualTo 0}] + skolem:lemma4508 + [ a r:Fact; r:gives {((2 2 6 0) "=<") list:sort (0 2 2 6)}] + [ a r:Fact; r:gives {((2 2 6 0) ">=") list:sort (6 2 2 0)}] + skolem:lemma4072 + skolem:lemma4073 + [ a r:Fact; r:gives {(6220 226) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2260]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 6 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2260 a r:Inference; + r:gives { + 2261 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2261 math:notEqualTo 0}] + skolem:lemma4509 + [ a r:Fact; r:gives {((2 2 6 1) "=<") list:sort (1 2 2 6)}] + [ a r:Fact; r:gives {((2 2 6 1) ">=") list:sort (6 2 2 1)}] + skolem:lemma4262 + skolem:lemma4263 + [ a r:Fact; r:gives {(6221 1226) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2261]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 6 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2261 a r:Inference; + r:gives { + 2262 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2262 math:notEqualTo 0}] + skolem:lemma4510 + [ a r:Fact; r:gives {((2 2 6 2) "=<") list:sort (2 2 2 6)}] + [ a r:Fact; r:gives {((2 2 6 2) ">=") list:sort (6 2 2 2)}] + skolem:lemma4431 + skolem:lemma4432 + [ a r:Fact; r:gives {(6222 2226) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2262 a r:Inference; + r:gives { + 2263 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2263 math:notEqualTo 0}] + skolem:lemma4511 + [ a r:Fact; r:gives {((2 2 6 3) "=<") list:sort (2 2 3 6)}] + [ a r:Fact; r:gives {((2 2 6 3) ">=") list:sort (6 3 2 2)}] + skolem:lemma4455 + skolem:lemma4456 + [ a r:Fact; r:gives {(6322 2236) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2263 a r:Inference; + r:gives { + 2264 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2264 math:notEqualTo 0}] + skolem:lemma4512 + [ a r:Fact; r:gives {((2 2 6 4) "=<") list:sort (2 2 4 6)}] + [ a r:Fact; r:gives {((2 2 6 4) ">=") list:sort (6 4 2 2)}] + skolem:lemma4477 + skolem:lemma4478 + [ a r:Fact; r:gives {(6422 2246) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 6 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2264 a r:Inference; + r:gives { + 2265 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2265 math:notEqualTo 0}] + skolem:lemma4513 + [ a r:Fact; r:gives {((2 2 6 5) "=<") list:sort (2 2 5 6)}] + [ a r:Fact; r:gives {((2 2 6 5) ">=") list:sort (6 5 2 2)}] + skolem:lemma4497 + skolem:lemma4498 + [ a r:Fact; r:gives {(6522 2256) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 6 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2265 a r:Inference; + r:gives { + 2266 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2266 math:notEqualTo 0}] + skolem:lemma4514 + [ a r:Fact; r:gives {((2 2 6 6) "=<") list:sort (2 2 6 6)}] + [ a r:Fact; r:gives {((2 2 6 6) ">=") list:sort (6 6 2 2)}] + skolem:lemma4515 + skolem:lemma4516 + [ a r:Fact; r:gives {(6622 2266) math:difference 4356}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4356 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 4356 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2266 a r:Inference; + r:gives { + 2267 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2267 math:notEqualTo 0}] + skolem:lemma4517 + [ a r:Fact; r:gives {((2 2 6 7) "=<") list:sort (2 2 6 7)}] + [ a r:Fact; r:gives {((2 2 6 7) ">=") list:sort (7 6 2 2)}] + skolem:lemma4518 + skolem:lemma4519 + [ a r:Fact; r:gives {(7622 2267) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2267 a r:Inference; + r:gives { + 2268 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2268 math:notEqualTo 0}] + skolem:lemma4520 + [ a r:Fact; r:gives {((2 2 6 8) "=<") list:sort (2 2 6 8)}] + [ a r:Fact; r:gives {((2 2 6 8) ">=") list:sort (8 6 2 2)}] + skolem:lemma4521 + skolem:lemma4522 + [ a r:Fact; r:gives {(8622 2268) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2268 a r:Inference; + r:gives { + 2269 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2269 math:notEqualTo 0}] + skolem:lemma4523 + [ a r:Fact; r:gives {((2 2 6 9) "=<") list:sort (2 2 6 9)}] + [ a r:Fact; r:gives {((2 2 6 9) ">=") list:sort (9 6 2 2)}] + skolem:lemma4524 + skolem:lemma4525 + [ a r:Fact; r:gives {(9622 2269) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2269 a r:Inference; + r:gives { + 2270 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2270 math:notEqualTo 0}] + skolem:lemma4526 + [ a r:Fact; r:gives {((2 2 7 0) "=<") list:sort (0 2 2 7)}] + [ a r:Fact; r:gives {((2 2 7 0) ">=") list:sort (7 2 2 0)}] + skolem:lemma4075 + skolem:lemma4076 + [ a r:Fact; r:gives {(7220 227) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2270]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 7 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2270 a r:Inference; + r:gives { + 2271 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2271 math:notEqualTo 0}] + skolem:lemma4527 + [ a r:Fact; r:gives {((2 2 7 1) "=<") list:sort (1 2 2 7)}] + [ a r:Fact; r:gives {((2 2 7 1) ">=") list:sort (7 2 2 1)}] + skolem:lemma4265 + skolem:lemma4266 + [ a r:Fact; r:gives {(7221 1227) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2271]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 7 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2271 a r:Inference; + r:gives { + 2272 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2272 math:notEqualTo 0}] + skolem:lemma4528 + [ a r:Fact; r:gives {((2 2 7 2) "=<") list:sort (2 2 2 7)}] + [ a r:Fact; r:gives {((2 2 7 2) ">=") list:sort (7 2 2 2)}] + skolem:lemma4434 + skolem:lemma4435 + [ a r:Fact; r:gives {(7222 2227) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2272]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2272 a r:Inference; + r:gives { + 2273 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2273 math:notEqualTo 0}] + skolem:lemma4529 + [ a r:Fact; r:gives {((2 2 7 3) "=<") list:sort (2 2 3 7)}] + [ a r:Fact; r:gives {((2 2 7 3) ">=") list:sort (7 3 2 2)}] + skolem:lemma4458 + skolem:lemma4459 + [ a r:Fact; r:gives {(7322 2237) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2273]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2273 a r:Inference; + r:gives { + 2274 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2274 math:notEqualTo 0}] + skolem:lemma4530 + [ a r:Fact; r:gives {((2 2 7 4) "=<") list:sort (2 2 4 7)}] + [ a r:Fact; r:gives {((2 2 7 4) ">=") list:sort (7 4 2 2)}] + skolem:lemma4480 + skolem:lemma4481 + [ a r:Fact; r:gives {(7422 2247) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2274]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 7 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2274 a r:Inference; + r:gives { + 2275 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2275 math:notEqualTo 0}] + skolem:lemma4531 + [ a r:Fact; r:gives {((2 2 7 5) "=<") list:sort (2 2 5 7)}] + [ a r:Fact; r:gives {((2 2 7 5) ">=") list:sort (7 5 2 2)}] + skolem:lemma4500 + skolem:lemma4501 + [ a r:Fact; r:gives {(7522 2257) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2275]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 7 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2275 a r:Inference; + r:gives { + 2276 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2276 math:notEqualTo 0}] + skolem:lemma4532 + [ a r:Fact; r:gives {((2 2 7 6) "=<") list:sort (2 2 6 7)}] + [ a r:Fact; r:gives {((2 2 7 6) ">=") list:sort (7 6 2 2)}] + skolem:lemma4518 + skolem:lemma4519 + [ a r:Fact; r:gives {(7622 2267) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2276]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 7 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2276 a r:Inference; + r:gives { + 2277 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2277 math:notEqualTo 0}] + skolem:lemma4533 + [ a r:Fact; r:gives {((2 2 7 7) "=<") list:sort (2 2 7 7)}] + [ a r:Fact; r:gives {((2 2 7 7) ">=") list:sort (7 7 2 2)}] + skolem:lemma4534 + skolem:lemma4535 + [ a r:Fact; r:gives {(7722 2277) math:difference 5445}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5445 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5445 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2277]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2277]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5445]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2277 a r:Inference; + r:gives { + 2278 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2278 math:notEqualTo 0}] + skolem:lemma4536 + [ a r:Fact; r:gives {((2 2 7 8) "=<") list:sort (2 2 7 8)}] + [ a r:Fact; r:gives {((2 2 7 8) ">=") list:sort (8 7 2 2)}] + skolem:lemma4537 + skolem:lemma4538 + [ a r:Fact; r:gives {(8722 2278) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2278 a r:Inference; + r:gives { + 2279 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2279 math:notEqualTo 0}] + skolem:lemma4539 + [ a r:Fact; r:gives {((2 2 7 9) "=<") list:sort (2 2 7 9)}] + [ a r:Fact; r:gives {((2 2 7 9) ">=") list:sort (9 7 2 2)}] + skolem:lemma4540 + skolem:lemma4541 + [ a r:Fact; r:gives {(9722 2279) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2279 a r:Inference; + r:gives { + 2280 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2280 math:notEqualTo 0}] + skolem:lemma4542 + [ a r:Fact; r:gives {((2 2 8 0) "=<") list:sort (0 2 2 8)}] + [ a r:Fact; r:gives {((2 2 8 0) ">=") list:sort (8 2 2 0)}] + skolem:lemma4078 + skolem:lemma4079 + [ a r:Fact; r:gives {(8220 228) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2280]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 8 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2280 a r:Inference; + r:gives { + 2281 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2281 math:notEqualTo 0}] + skolem:lemma4543 + [ a r:Fact; r:gives {((2 2 8 1) "=<") list:sort (1 2 2 8)}] + [ a r:Fact; r:gives {((2 2 8 1) ">=") list:sort (8 2 2 1)}] + skolem:lemma4268 + skolem:lemma4269 + [ a r:Fact; r:gives {(8221 1228) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2281]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 8 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2281 a r:Inference; + r:gives { + 2282 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2282 math:notEqualTo 0}] + skolem:lemma4544 + [ a r:Fact; r:gives {((2 2 8 2) "=<") list:sort (2 2 2 8)}] + [ a r:Fact; r:gives {((2 2 8 2) ">=") list:sort (8 2 2 2)}] + skolem:lemma4437 + skolem:lemma4438 + [ a r:Fact; r:gives {(8222 2228) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2282]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2282 a r:Inference; + r:gives { + 2283 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2283 math:notEqualTo 0}] + skolem:lemma4545 + [ a r:Fact; r:gives {((2 2 8 3) "=<") list:sort (2 2 3 8)}] + [ a r:Fact; r:gives {((2 2 8 3) ">=") list:sort (8 3 2 2)}] + skolem:lemma4461 + skolem:lemma4462 + [ a r:Fact; r:gives {(8322 2238) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2283]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2283 a r:Inference; + r:gives { + 2284 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2284 math:notEqualTo 0}] + skolem:lemma4546 + [ a r:Fact; r:gives {((2 2 8 4) "=<") list:sort (2 2 4 8)}] + [ a r:Fact; r:gives {((2 2 8 4) ">=") list:sort (8 4 2 2)}] + skolem:lemma4483 + skolem:lemma4484 + [ a r:Fact; r:gives {(8422 2248) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2284]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 8 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2284 a r:Inference; + r:gives { + 2285 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2285 math:notEqualTo 0}] + skolem:lemma4547 + [ a r:Fact; r:gives {((2 2 8 5) "=<") list:sort (2 2 5 8)}] + [ a r:Fact; r:gives {((2 2 8 5) ">=") list:sort (8 5 2 2)}] + skolem:lemma4503 + skolem:lemma4504 + [ a r:Fact; r:gives {(8522 2258) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2285]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 8 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2285 a r:Inference; + r:gives { + 2286 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2286 math:notEqualTo 0}] + skolem:lemma4548 + [ a r:Fact; r:gives {((2 2 8 6) "=<") list:sort (2 2 6 8)}] + [ a r:Fact; r:gives {((2 2 8 6) ">=") list:sort (8 6 2 2)}] + skolem:lemma4521 + skolem:lemma4522 + [ a r:Fact; r:gives {(8622 2268) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2286]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 8 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2286 a r:Inference; + r:gives { + 2287 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2287 math:notEqualTo 0}] + skolem:lemma4549 + [ a r:Fact; r:gives {((2 2 8 7) "=<") list:sort (2 2 7 8)}] + [ a r:Fact; r:gives {((2 2 8 7) ">=") list:sort (8 7 2 2)}] + skolem:lemma4537 + skolem:lemma4538 + [ a r:Fact; r:gives {(8722 2278) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2287]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 8 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2287 a r:Inference; + r:gives { + 2288 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2288 math:notEqualTo 0}] + skolem:lemma4550 + [ a r:Fact; r:gives {((2 2 8 8) "=<") list:sort (2 2 8 8)}] + [ a r:Fact; r:gives {((2 2 8 8) ">=") list:sort (8 8 2 2)}] + skolem:lemma4551 + skolem:lemma4552 + [ a r:Fact; r:gives {(8822 2288) math:difference 6534}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6534 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6534 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2288]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2288]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8822]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6534]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2288 a r:Inference; + r:gives { + 2289 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2289 math:notEqualTo 0}] + skolem:lemma4553 + [ a r:Fact; r:gives {((2 2 8 9) "=<") list:sort (2 2 8 9)}] + [ a r:Fact; r:gives {((2 2 8 9) ">=") list:sort (9 8 2 2)}] + skolem:lemma4554 + skolem:lemma4555 + [ a r:Fact; r:gives {(9822 2289) math:difference 7533}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7533 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7533 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9822]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2289 a r:Inference; + r:gives { + 2290 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2290 math:notEqualTo 0}] + skolem:lemma4556 + [ a r:Fact; r:gives {((2 2 9 0) "=<") list:sort (0 2 2 9)}] + [ a r:Fact; r:gives {((2 2 9 0) ">=") list:sort (9 2 2 0)}] + skolem:lemma4081 + skolem:lemma4082 + [ a r:Fact; r:gives {(9220 229) math:difference 8991}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8991 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 8991 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2290]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 9 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8991]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2290 a r:Inference; + r:gives { + 2291 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2291 math:notEqualTo 0}] + skolem:lemma4557 + [ a r:Fact; r:gives {((2 2 9 1) "=<") list:sort (1 2 2 9)}] + [ a r:Fact; r:gives {((2 2 9 1) ">=") list:sort (9 2 2 1)}] + skolem:lemma4271 + skolem:lemma4272 + [ a r:Fact; r:gives {(9221 1229) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2291]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 9 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2291 a r:Inference; + r:gives { + 2292 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2292 math:notEqualTo 0}] + skolem:lemma4558 + [ a r:Fact; r:gives {((2 2 9 2) "=<") list:sort (2 2 2 9)}] + [ a r:Fact; r:gives {((2 2 9 2) ">=") list:sort (9 2 2 2)}] + skolem:lemma4440 + skolem:lemma4441 + [ a r:Fact; r:gives {(9222 2229) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2292]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 9 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2292 a r:Inference; + r:gives { + 2293 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2293 math:notEqualTo 0}] + skolem:lemma4559 + [ a r:Fact; r:gives {((2 2 9 3) "=<") list:sort (2 2 3 9)}] + [ a r:Fact; r:gives {((2 2 9 3) ">=") list:sort (9 3 2 2)}] + skolem:lemma4464 + skolem:lemma4465 + [ a r:Fact; r:gives {(9322 2239) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2293]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 9 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2293 a r:Inference; + r:gives { + 2294 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2294 math:notEqualTo 0}] + skolem:lemma4560 + [ a r:Fact; r:gives {((2 2 9 4) "=<") list:sort (2 2 4 9)}] + [ a r:Fact; r:gives {((2 2 9 4) ">=") list:sort (9 4 2 2)}] + skolem:lemma4486 + skolem:lemma4487 + [ a r:Fact; r:gives {(9422 2249) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2294]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 9 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2294 a r:Inference; + r:gives { + 2295 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2295 math:notEqualTo 0}] + skolem:lemma4561 + [ a r:Fact; r:gives {((2 2 9 5) "=<") list:sort (2 2 5 9)}] + [ a r:Fact; r:gives {((2 2 9 5) ">=") list:sort (9 5 2 2)}] + skolem:lemma4506 + skolem:lemma4507 + [ a r:Fact; r:gives {(9522 2259) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2295]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 9 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2295 a r:Inference; + r:gives { + 2296 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2296 math:notEqualTo 0}] + skolem:lemma4562 + [ a r:Fact; r:gives {((2 2 9 6) "=<") list:sort (2 2 6 9)}] + [ a r:Fact; r:gives {((2 2 9 6) ">=") list:sort (9 6 2 2)}] + skolem:lemma4524 + skolem:lemma4525 + [ a r:Fact; r:gives {(9622 2269) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2296]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 9 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2296 a r:Inference; + r:gives { + 2297 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2297 math:notEqualTo 0}] + skolem:lemma4563 + [ a r:Fact; r:gives {((2 2 9 7) "=<") list:sort (2 2 7 9)}] + [ a r:Fact; r:gives {((2 2 9 7) ">=") list:sort (9 7 2 2)}] + skolem:lemma4540 + skolem:lemma4541 + [ a r:Fact; r:gives {(9722 2279) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2297]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 9 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2297 a r:Inference; + r:gives { + 2298 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2298 math:notEqualTo 0}] + skolem:lemma4564 + [ a r:Fact; r:gives {((2 2 9 8) "=<") list:sort (2 2 8 9)}] + [ a r:Fact; r:gives {((2 2 9 8) ">=") list:sort (9 8 2 2)}] + skolem:lemma4554 + skolem:lemma4555 + [ a r:Fact; r:gives {(9822 2289) math:difference 7533}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7533 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7533 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2298]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 9 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9822]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2298 a r:Inference; + r:gives { + 2299 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2299 math:notEqualTo 0}] + skolem:lemma4565 + [ a r:Fact; r:gives {((2 2 9 9) "=<") list:sort (2 2 9 9)}] + [ a r:Fact; r:gives {((2 2 9 9) ">=") list:sort (9 9 2 2)}] + skolem:lemma4566 + skolem:lemma4567 + [ a r:Fact; r:gives {(9922 2299) math:difference 7623}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7623 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7623 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 2 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9922]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7623]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2299 a r:Inference; + r:gives { + 2300 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2300 math:notEqualTo 0}] + skolem:lemma4568 + [ a r:Fact; r:gives {((2 3 0 0) "=<") list:sort (0 0 2 3)}] + [ a r:Fact; r:gives {((2 3 0 0) ">=") list:sort (3 2 0 0)}] + skolem:lemma4009 + skolem:lemma4010 + [ a r:Fact; r:gives {(3200 23) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2300 a r:Inference; + r:gives { + 2301 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2301 math:notEqualTo 0}] + skolem:lemma4569 + [ a r:Fact; r:gives {((2 3 0 1) "=<") list:sort (0 1 2 3)}] + [ a r:Fact; r:gives {((2 3 0 1) ">=") list:sort (3 2 1 0)}] + skolem:lemma4037 + skolem:lemma4038 + [ a r:Fact; r:gives {(3210 123) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2301]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 0 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2301 a r:Inference; + r:gives { + 2302 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2302 math:notEqualTo 0}] + skolem:lemma4570 + [ a r:Fact; r:gives {((2 3 0 2) "=<") list:sort (0 2 2 3)}] + [ a r:Fact; r:gives {((2 3 0 2) ">=") list:sort (3 2 2 0)}] + skolem:lemma4063 + skolem:lemma4064 + [ a r:Fact; r:gives {(3220 223) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2302]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 0 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2302 a r:Inference; + r:gives { + 2303 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2303 math:notEqualTo 0}] + skolem:lemma4571 + [ a r:Fact; r:gives {((2 3 0 3) "=<") list:sort (0 2 3 3)}] + [ a r:Fact; r:gives {((2 3 0 3) ">=") list:sort (3 3 2 0)}] + skolem:lemma4087 + skolem:lemma4088 + [ a r:Fact; r:gives {(3320 233) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2303]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 0 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2303 a r:Inference; + r:gives { + 2304 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2304 math:notEqualTo 0}] + skolem:lemma4572 + [ a r:Fact; r:gives {((2 3 0 4) "=<") list:sort (0 2 3 4)}] + [ a r:Fact; r:gives {((2 3 0 4) ">=") list:sort (4 3 2 0)}] + skolem:lemma4090 + skolem:lemma4091 + [ a r:Fact; r:gives {(4320 234) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2304]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 0 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2304 a r:Inference; + r:gives { + 2305 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2305 math:notEqualTo 0}] + skolem:lemma4573 + [ a r:Fact; r:gives {((2 3 0 5) "=<") list:sort (0 2 3 5)}] + [ a r:Fact; r:gives {((2 3 0 5) ">=") list:sort (5 3 2 0)}] + skolem:lemma4093 + skolem:lemma4094 + [ a r:Fact; r:gives {(5320 235) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2305]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 0 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2305 a r:Inference; + r:gives { + 2306 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2306 math:notEqualTo 0}] + skolem:lemma4574 + [ a r:Fact; r:gives {((2 3 0 6) "=<") list:sort (0 2 3 6)}] + [ a r:Fact; r:gives {((2 3 0 6) ">=") list:sort (6 3 2 0)}] + skolem:lemma4096 + skolem:lemma4097 + [ a r:Fact; r:gives {(6320 236) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2306]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 0 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2306 a r:Inference; + r:gives { + 2307 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2307 math:notEqualTo 0}] + skolem:lemma4575 + [ a r:Fact; r:gives {((2 3 0 7) "=<") list:sort (0 2 3 7)}] + [ a r:Fact; r:gives {((2 3 0 7) ">=") list:sort (7 3 2 0)}] + skolem:lemma4099 + skolem:lemma4100 + [ a r:Fact; r:gives {(7320 237) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2307]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 0 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2307 a r:Inference; + r:gives { + 2308 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2308 math:notEqualTo 0}] + skolem:lemma4576 + [ a r:Fact; r:gives {((2 3 0 8) "=<") list:sort (0 2 3 8)}] + [ a r:Fact; r:gives {((2 3 0 8) ">=") list:sort (8 3 2 0)}] + skolem:lemma4102 + skolem:lemma4103 + [ a r:Fact; r:gives {(8320 238) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2308]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 0 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2308 a r:Inference; + r:gives { + 2309 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2309 math:notEqualTo 0}] + skolem:lemma4577 + [ a r:Fact; r:gives {((2 3 0 9) "=<") list:sort (0 2 3 9)}] + [ a r:Fact; r:gives {((2 3 0 9) ">=") list:sort (9 3 2 0)}] + skolem:lemma4105 + skolem:lemma4106 + [ a r:Fact; r:gives {(9320 239) math:difference 9081}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9081 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 9081 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2309]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 0 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2309 a r:Inference; + r:gives { + 2310 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2310 math:notEqualTo 0}] + skolem:lemma4578 + [ a r:Fact; r:gives {((2 3 1 0) "=<") list:sort (0 1 2 3)}] + [ a r:Fact; r:gives {((2 3 1 0) ">=") list:sort (3 2 1 0)}] + skolem:lemma4037 + skolem:lemma4038 + [ a r:Fact; r:gives {(3210 123) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2310 a r:Inference; + r:gives { + 2311 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2311 math:notEqualTo 0}] + skolem:lemma4579 + [ a r:Fact; r:gives {((2 3 1 1) "=<") list:sort (1 1 2 3)}] + [ a r:Fact; r:gives {((2 3 1 1) ">=") list:sort (3 2 1 1)}] + skolem:lemma4227 + skolem:lemma4228 + [ a r:Fact; r:gives {(3211 1123) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2311 a r:Inference; + r:gives { + 2312 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2312 math:notEqualTo 0}] + skolem:lemma4580 + [ a r:Fact; r:gives {((2 3 1 2) "=<") list:sort (1 2 2 3)}] + [ a r:Fact; r:gives {((2 3 1 2) ">=") list:sort (3 2 2 1)}] + skolem:lemma4253 + skolem:lemma4254 + [ a r:Fact; r:gives {(3221 1223) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2312]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2312 a r:Inference; + r:gives { + 2313 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2313 math:notEqualTo 0}] + skolem:lemma4581 + [ a r:Fact; r:gives {((2 3 1 3) "=<") list:sort (1 2 3 3)}] + [ a r:Fact; r:gives {((2 3 1 3) ">=") list:sort (3 3 2 1)}] + skolem:lemma4277 + skolem:lemma4278 + [ a r:Fact; r:gives {(3321 1233) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2313]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2313 a r:Inference; + r:gives { + 2314 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2314 math:notEqualTo 0}] + skolem:lemma4582 + [ a r:Fact; r:gives {((2 3 1 4) "=<") list:sort (1 2 3 4)}] + [ a r:Fact; r:gives {((2 3 1 4) ">=") list:sort (4 3 2 1)}] + skolem:lemma4280 + skolem:lemma4281 + [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2314]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 1 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2314 a r:Inference; + r:gives { + 2315 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2315 math:notEqualTo 0}] + skolem:lemma4583 + [ a r:Fact; r:gives {((2 3 1 5) "=<") list:sort (1 2 3 5)}] + [ a r:Fact; r:gives {((2 3 1 5) ">=") list:sort (5 3 2 1)}] + skolem:lemma4283 + skolem:lemma4284 + [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2315]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 1 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2315 a r:Inference; + r:gives { + 2316 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2316 math:notEqualTo 0}] + skolem:lemma4584 + [ a r:Fact; r:gives {((2 3 1 6) "=<") list:sort (1 2 3 6)}] + [ a r:Fact; r:gives {((2 3 1 6) ">=") list:sort (6 3 2 1)}] + skolem:lemma4286 + skolem:lemma4287 + [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2316]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 1 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2316 a r:Inference; + r:gives { + 2317 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2317 math:notEqualTo 0}] + skolem:lemma4585 + [ a r:Fact; r:gives {((2 3 1 7) "=<") list:sort (1 2 3 7)}] + [ a r:Fact; r:gives {((2 3 1 7) ">=") list:sort (7 3 2 1)}] + skolem:lemma4289 + skolem:lemma4290 + [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2317]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 1 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2317 a r:Inference; + r:gives { + 2318 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2318 math:notEqualTo 0}] + skolem:lemma4586 + [ a r:Fact; r:gives {((2 3 1 8) "=<") list:sort (1 2 3 8)}] + [ a r:Fact; r:gives {((2 3 1 8) ">=") list:sort (8 3 2 1)}] + skolem:lemma4292 + skolem:lemma4293 + [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2318]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 1 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2318 a r:Inference; + r:gives { + 2319 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2319 math:notEqualTo 0}] + skolem:lemma4587 + [ a r:Fact; r:gives {((2 3 1 9) "=<") list:sort (1 2 3 9)}] + [ a r:Fact; r:gives {((2 3 1 9) ">=") list:sort (9 3 2 1)}] + skolem:lemma4295 + skolem:lemma4296 + [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2319]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 1 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2319 a r:Inference; + r:gives { + 2320 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2320 math:notEqualTo 0}] + skolem:lemma4588 + [ a r:Fact; r:gives {((2 3 2 0) "=<") list:sort (0 2 2 3)}] + [ a r:Fact; r:gives {((2 3 2 0) ">=") list:sort (3 2 2 0)}] + skolem:lemma4063 + skolem:lemma4064 + [ a r:Fact; r:gives {(3220 223) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2320 a r:Inference; + r:gives { + 2321 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2321 math:notEqualTo 0}] + skolem:lemma4589 + [ a r:Fact; r:gives {((2 3 2 1) "=<") list:sort (1 2 2 3)}] + [ a r:Fact; r:gives {((2 3 2 1) ">=") list:sort (3 2 2 1)}] + skolem:lemma4253 + skolem:lemma4254 + [ a r:Fact; r:gives {(3221 1223) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2321 a r:Inference; + r:gives { + 2322 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2322 math:notEqualTo 0}] + skolem:lemma4590 + [ a r:Fact; r:gives {((2 3 2 2) "=<") list:sort (2 2 2 3)}] + [ a r:Fact; r:gives {((2 3 2 2) ">=") list:sort (3 2 2 2)}] + skolem:lemma4422 + skolem:lemma4423 + [ a r:Fact; r:gives {(3222 2223) math:difference 999}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 999 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 999 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2322 a r:Inference; + r:gives { + 2323 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2323 math:notEqualTo 0}] + skolem:lemma4591 + [ a r:Fact; r:gives {((2 3 2 3) "=<") list:sort (2 2 3 3)}] + [ a r:Fact; r:gives {((2 3 2 3) ">=") list:sort (3 3 2 2)}] + skolem:lemma4446 + skolem:lemma4447 + [ a r:Fact; r:gives {(3322 2233) math:difference 1089}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1089 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1089 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2323]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1089]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2323 a r:Inference; + r:gives { + 2324 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2324 math:notEqualTo 0}] + skolem:lemma4592 + [ a r:Fact; r:gives {((2 3 2 4) "=<") list:sort (2 2 3 4)}] + [ a r:Fact; r:gives {((2 3 2 4) ">=") list:sort (4 3 2 2)}] + skolem:lemma4449 + skolem:lemma4450 + [ a r:Fact; r:gives {(4322 2234) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2324]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2324 a r:Inference; + r:gives { + 2325 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2325 math:notEqualTo 0}] + skolem:lemma4593 + [ a r:Fact; r:gives {((2 3 2 5) "=<") list:sort (2 2 3 5)}] + [ a r:Fact; r:gives {((2 3 2 5) ">=") list:sort (5 3 2 2)}] + skolem:lemma4452 + skolem:lemma4453 + [ a r:Fact; r:gives {(5322 2235) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2325]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2325 a r:Inference; + r:gives { + 2326 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2326 math:notEqualTo 0}] + skolem:lemma4594 + [ a r:Fact; r:gives {((2 3 2 6) "=<") list:sort (2 2 3 6)}] + [ a r:Fact; r:gives {((2 3 2 6) ">=") list:sort (6 3 2 2)}] + skolem:lemma4455 + skolem:lemma4456 + [ a r:Fact; r:gives {(6322 2236) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2326]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2326 a r:Inference; + r:gives { + 2327 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2327 math:notEqualTo 0}] + skolem:lemma4595 + [ a r:Fact; r:gives {((2 3 2 7) "=<") list:sort (2 2 3 7)}] + [ a r:Fact; r:gives {((2 3 2 7) ">=") list:sort (7 3 2 2)}] + skolem:lemma4458 + skolem:lemma4459 + [ a r:Fact; r:gives {(7322 2237) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2327]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2327 a r:Inference; + r:gives { + 2328 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2328 math:notEqualTo 0}] + skolem:lemma4596 + [ a r:Fact; r:gives {((2 3 2 8) "=<") list:sort (2 2 3 8)}] + [ a r:Fact; r:gives {((2 3 2 8) ">=") list:sort (8 3 2 2)}] + skolem:lemma4461 + skolem:lemma4462 + [ a r:Fact; r:gives {(8322 2238) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2328]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2328 a r:Inference; + r:gives { + 2329 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2329 math:notEqualTo 0}] + skolem:lemma4597 + [ a r:Fact; r:gives {((2 3 2 9) "=<") list:sort (2 2 3 9)}] + [ a r:Fact; r:gives {((2 3 2 9) ">=") list:sort (9 3 2 2)}] + skolem:lemma4464 + skolem:lemma4465 + [ a r:Fact; r:gives {(9322 2239) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2329]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2329 a r:Inference; + r:gives { + 2330 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2330 math:notEqualTo 0}] + skolem:lemma4598 + [ a r:Fact; r:gives {((2 3 3 0) "=<") list:sort (0 2 3 3)}] + [ a r:Fact; r:gives {((2 3 3 0) ">=") list:sort (3 3 2 0)}] + skolem:lemma4087 + skolem:lemma4088 + [ a r:Fact; r:gives {(3320 233) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2330 a r:Inference; + r:gives { + 2331 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2331 math:notEqualTo 0}] + skolem:lemma4599 + [ a r:Fact; r:gives {((2 3 3 1) "=<") list:sort (1 2 3 3)}] + [ a r:Fact; r:gives {((2 3 3 1) ">=") list:sort (3 3 2 1)}] + skolem:lemma4277 + skolem:lemma4278 + [ a r:Fact; r:gives {(3321 1233) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2331 a r:Inference; + r:gives { + 2332 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2332 math:notEqualTo 0}] + skolem:lemma4600 + [ a r:Fact; r:gives {((2 3 3 2) "=<") list:sort (2 2 3 3)}] + [ a r:Fact; r:gives {((2 3 3 2) ">=") list:sort (3 3 2 2)}] + skolem:lemma4446 + skolem:lemma4447 + [ a r:Fact; r:gives {(3322 2233) math:difference 1089}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1089 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1089 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1089]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2332 a r:Inference; + r:gives { + 2333 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2333 math:notEqualTo 0}] + skolem:lemma4601 + [ a r:Fact; r:gives {((2 3 3 3) "=<") list:sort (2 3 3 3)}] + [ a r:Fact; r:gives {((2 3 3 3) ">=") list:sort (3 3 3 2)}] + skolem:lemma4602 + skolem:lemma4603 + [ a r:Fact; r:gives {(3332 2333) math:difference 999}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 999 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 999 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2333 a r:Inference; + r:gives { + 2334 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2334 math:notEqualTo 0}] + skolem:lemma4604 + [ a r:Fact; r:gives {((2 3 3 4) "=<") list:sort (2 3 3 4)}] + [ a r:Fact; r:gives {((2 3 3 4) ">=") list:sort (4 3 3 2)}] + skolem:lemma4605 + skolem:lemma4606 + [ a r:Fact; r:gives {(4332 2334) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2334 a r:Inference; + r:gives { + 2335 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2335 math:notEqualTo 0}] + skolem:lemma4607 + [ a r:Fact; r:gives {((2 3 3 5) "=<") list:sort (2 3 3 5)}] + [ a r:Fact; r:gives {((2 3 3 5) ">=") list:sort (5 3 3 2)}] + skolem:lemma4608 + skolem:lemma4609 + [ a r:Fact; r:gives {(5332 2335) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2335 a r:Inference; + r:gives { + 2336 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2336 math:notEqualTo 0}] + skolem:lemma4610 + [ a r:Fact; r:gives {((2 3 3 6) "=<") list:sort (2 3 3 6)}] + [ a r:Fact; r:gives {((2 3 3 6) ">=") list:sort (6 3 3 2)}] + skolem:lemma4611 + skolem:lemma4612 + [ a r:Fact; r:gives {(6332 2336) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2336 a r:Inference; + r:gives { + 2337 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2337 math:notEqualTo 0}] + skolem:lemma4613 + [ a r:Fact; r:gives {((2 3 3 7) "=<") list:sort (2 3 3 7)}] + [ a r:Fact; r:gives {((2 3 3 7) ">=") list:sort (7 3 3 2)}] + skolem:lemma4614 + skolem:lemma4615 + [ a r:Fact; r:gives {(7332 2337) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2337 a r:Inference; + r:gives { + 2338 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2338 math:notEqualTo 0}] + skolem:lemma4616 + [ a r:Fact; r:gives {((2 3 3 8) "=<") list:sort (2 3 3 8)}] + [ a r:Fact; r:gives {((2 3 3 8) ">=") list:sort (8 3 3 2)}] + skolem:lemma4617 + skolem:lemma4618 + [ a r:Fact; r:gives {(8332 2338) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2338 a r:Inference; + r:gives { + 2339 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2339 math:notEqualTo 0}] + skolem:lemma4619 + [ a r:Fact; r:gives {((2 3 3 9) "=<") list:sort (2 3 3 9)}] + [ a r:Fact; r:gives {((2 3 3 9) ">=") list:sort (9 3 3 2)}] + skolem:lemma4620 + skolem:lemma4621 + [ a r:Fact; r:gives {(9332 2339) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2339 a r:Inference; + r:gives { + 2340 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2340 math:notEqualTo 0}] + skolem:lemma4622 + [ a r:Fact; r:gives {((2 3 4 0) "=<") list:sort (0 2 3 4)}] + [ a r:Fact; r:gives {((2 3 4 0) ">=") list:sort (4 3 2 0)}] + skolem:lemma4090 + skolem:lemma4091 + [ a r:Fact; r:gives {(4320 234) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2340]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 4 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2340 a r:Inference; + r:gives { + 2341 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2341 math:notEqualTo 0}] + skolem:lemma4623 + [ a r:Fact; r:gives {((2 3 4 1) "=<") list:sort (1 2 3 4)}] + [ a r:Fact; r:gives {((2 3 4 1) ">=") list:sort (4 3 2 1)}] + skolem:lemma4280 + skolem:lemma4281 + [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2341]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 4 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2341 a r:Inference; + r:gives { + 2342 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2342 math:notEqualTo 0}] + skolem:lemma4624 + [ a r:Fact; r:gives {((2 3 4 2) "=<") list:sort (2 2 3 4)}] + [ a r:Fact; r:gives {((2 3 4 2) ">=") list:sort (4 3 2 2)}] + skolem:lemma4449 + skolem:lemma4450 + [ a r:Fact; r:gives {(4322 2234) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2342]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2342 a r:Inference; + r:gives { + 2343 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2343 math:notEqualTo 0}] + skolem:lemma4625 + [ a r:Fact; r:gives {((2 3 4 3) "=<") list:sort (2 3 3 4)}] + [ a r:Fact; r:gives {((2 3 4 3) ">=") list:sort (4 3 3 2)}] + skolem:lemma4605 + skolem:lemma4606 + [ a r:Fact; r:gives {(4332 2334) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2343]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2343 a r:Inference; + r:gives { + 2344 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2344 math:notEqualTo 0}] + skolem:lemma4626 + [ a r:Fact; r:gives {((2 3 4 4) "=<") list:sort (2 3 4 4)}] + [ a r:Fact; r:gives {((2 3 4 4) ">=") list:sort (4 4 3 2)}] + skolem:lemma4627 + skolem:lemma4628 + [ a r:Fact; r:gives {(4432 2344) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2344 a r:Inference; + r:gives { + 2345 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2345 math:notEqualTo 0}] + skolem:lemma4629 + [ a r:Fact; r:gives {((2 3 4 5) "=<") list:sort (2 3 4 5)}] + [ a r:Fact; r:gives {((2 3 4 5) ">=") list:sort (5 4 3 2)}] + skolem:lemma4630 + skolem:lemma4631 + [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2345 a r:Inference; + r:gives { + 2346 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2346 math:notEqualTo 0}] + skolem:lemma4632 + [ a r:Fact; r:gives {((2 3 4 6) "=<") list:sort (2 3 4 6)}] + [ a r:Fact; r:gives {((2 3 4 6) ">=") list:sort (6 4 3 2)}] + skolem:lemma4633 + skolem:lemma4634 + [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2346 a r:Inference; + r:gives { + 2347 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2347 math:notEqualTo 0}] + skolem:lemma4635 + [ a r:Fact; r:gives {((2 3 4 7) "=<") list:sort (2 3 4 7)}] + [ a r:Fact; r:gives {((2 3 4 7) ">=") list:sort (7 4 3 2)}] + skolem:lemma4636 + skolem:lemma4637 + [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2347 a r:Inference; + r:gives { + 2348 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2348 math:notEqualTo 0}] + skolem:lemma4638 + [ a r:Fact; r:gives {((2 3 4 8) "=<") list:sort (2 3 4 8)}] + [ a r:Fact; r:gives {((2 3 4 8) ">=") list:sort (8 4 3 2)}] + skolem:lemma4639 + skolem:lemma4640 + [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2348 a r:Inference; + r:gives { + 2349 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2349 math:notEqualTo 0}] + skolem:lemma4641 + [ a r:Fact; r:gives {((2 3 4 9) "=<") list:sort (2 3 4 9)}] + [ a r:Fact; r:gives {((2 3 4 9) ">=") list:sort (9 4 3 2)}] + skolem:lemma4642 + skolem:lemma4643 + [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2349 a r:Inference; + r:gives { + 2350 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2350 math:notEqualTo 0}] + skolem:lemma4644 + [ a r:Fact; r:gives {((2 3 5 0) "=<") list:sort (0 2 3 5)}] + [ a r:Fact; r:gives {((2 3 5 0) ">=") list:sort (5 3 2 0)}] + skolem:lemma4093 + skolem:lemma4094 + [ a r:Fact; r:gives {(5320 235) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2350]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 5 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2350 a r:Inference; + r:gives { + 2351 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2351 math:notEqualTo 0}] + skolem:lemma4645 + [ a r:Fact; r:gives {((2 3 5 1) "=<") list:sort (1 2 3 5)}] + [ a r:Fact; r:gives {((2 3 5 1) ">=") list:sort (5 3 2 1)}] + skolem:lemma4283 + skolem:lemma4284 + [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2351]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 5 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2351 a r:Inference; + r:gives { + 2352 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2352 math:notEqualTo 0}] + skolem:lemma4646 + [ a r:Fact; r:gives {((2 3 5 2) "=<") list:sort (2 2 3 5)}] + [ a r:Fact; r:gives {((2 3 5 2) ">=") list:sort (5 3 2 2)}] + skolem:lemma4452 + skolem:lemma4453 + [ a r:Fact; r:gives {(5322 2235) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2352 a r:Inference; + r:gives { + 2353 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2353 math:notEqualTo 0}] + skolem:lemma4647 + [ a r:Fact; r:gives {((2 3 5 3) "=<") list:sort (2 3 3 5)}] + [ a r:Fact; r:gives {((2 3 5 3) ">=") list:sort (5 3 3 2)}] + skolem:lemma4608 + skolem:lemma4609 + [ a r:Fact; r:gives {(5332 2335) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2353 a r:Inference; + r:gives { + 2354 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2354 math:notEqualTo 0}] + skolem:lemma4648 + [ a r:Fact; r:gives {((2 3 5 4) "=<") list:sort (2 3 4 5)}] + [ a r:Fact; r:gives {((2 3 5 4) ">=") list:sort (5 4 3 2)}] + skolem:lemma4630 + skolem:lemma4631 + [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 5 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2354 a r:Inference; + r:gives { + 2355 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2355 math:notEqualTo 0}] + skolem:lemma4649 + [ a r:Fact; r:gives {((2 3 5 5) "=<") list:sort (2 3 5 5)}] + [ a r:Fact; r:gives {((2 3 5 5) ">=") list:sort (5 5 3 2)}] + skolem:lemma4650 + skolem:lemma4651 + [ a r:Fact; r:gives {(5532 2355) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2355 a r:Inference; + r:gives { + 2356 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2356 math:notEqualTo 0}] + skolem:lemma4652 + [ a r:Fact; r:gives {((2 3 5 6) "=<") list:sort (2 3 5 6)}] + [ a r:Fact; r:gives {((2 3 5 6) ">=") list:sort (6 5 3 2)}] + skolem:lemma4653 + skolem:lemma4654 + [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2356 a r:Inference; + r:gives { + 2357 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2357 math:notEqualTo 0}] + skolem:lemma4655 + [ a r:Fact; r:gives {((2 3 5 7) "=<") list:sort (2 3 5 7)}] + [ a r:Fact; r:gives {((2 3 5 7) ">=") list:sort (7 5 3 2)}] + skolem:lemma4656 + skolem:lemma4657 + [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2357 a r:Inference; + r:gives { + 2358 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2358 math:notEqualTo 0}] + skolem:lemma4658 + [ a r:Fact; r:gives {((2 3 5 8) "=<") list:sort (2 3 5 8)}] + [ a r:Fact; r:gives {((2 3 5 8) ">=") list:sort (8 5 3 2)}] + skolem:lemma4659 + skolem:lemma4660 + [ a r:Fact; r:gives {(8532 2358) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2358 a r:Inference; + r:gives { + 2359 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2359 math:notEqualTo 0}] + skolem:lemma4661 + [ a r:Fact; r:gives {((2 3 5 9) "=<") list:sort (2 3 5 9)}] + [ a r:Fact; r:gives {((2 3 5 9) ">=") list:sort (9 5 3 2)}] + skolem:lemma4662 + skolem:lemma4663 + [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2359 a r:Inference; + r:gives { + 2360 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2360 math:notEqualTo 0}] + skolem:lemma4664 + [ a r:Fact; r:gives {((2 3 6 0) "=<") list:sort (0 2 3 6)}] + [ a r:Fact; r:gives {((2 3 6 0) ">=") list:sort (6 3 2 0)}] + skolem:lemma4096 + skolem:lemma4097 + [ a r:Fact; r:gives {(6320 236) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2360]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 6 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2360 a r:Inference; + r:gives { + 2361 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2361 math:notEqualTo 0}] + skolem:lemma4665 + [ a r:Fact; r:gives {((2 3 6 1) "=<") list:sort (1 2 3 6)}] + [ a r:Fact; r:gives {((2 3 6 1) ">=") list:sort (6 3 2 1)}] + skolem:lemma4286 + skolem:lemma4287 + [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2361]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 6 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2361 a r:Inference; + r:gives { + 2362 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2362 math:notEqualTo 0}] + skolem:lemma4666 + [ a r:Fact; r:gives {((2 3 6 2) "=<") list:sort (2 2 3 6)}] + [ a r:Fact; r:gives {((2 3 6 2) ">=") list:sort (6 3 2 2)}] + skolem:lemma4455 + skolem:lemma4456 + [ a r:Fact; r:gives {(6322 2236) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2362]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2362 a r:Inference; + r:gives { + 2363 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2363 math:notEqualTo 0}] + skolem:lemma4667 + [ a r:Fact; r:gives {((2 3 6 3) "=<") list:sort (2 3 3 6)}] + [ a r:Fact; r:gives {((2 3 6 3) ">=") list:sort (6 3 3 2)}] + skolem:lemma4611 + skolem:lemma4612 + [ a r:Fact; r:gives {(6332 2336) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2363]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2363 a r:Inference; + r:gives { + 2364 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2364 math:notEqualTo 0}] + skolem:lemma4668 + [ a r:Fact; r:gives {((2 3 6 4) "=<") list:sort (2 3 4 6)}] + [ a r:Fact; r:gives {((2 3 6 4) ">=") list:sort (6 4 3 2)}] + skolem:lemma4633 + skolem:lemma4634 + [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2364]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 6 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2364 a r:Inference; + r:gives { + 2365 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2365 math:notEqualTo 0}] + skolem:lemma4669 + [ a r:Fact; r:gives {((2 3 6 5) "=<") list:sort (2 3 5 6)}] + [ a r:Fact; r:gives {((2 3 6 5) ">=") list:sort (6 5 3 2)}] + skolem:lemma4653 + skolem:lemma4654 + [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2365]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 6 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2365 a r:Inference; + r:gives { + 2366 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2366 math:notEqualTo 0}] + skolem:lemma4670 + [ a r:Fact; r:gives {((2 3 6 6) "=<") list:sort (2 3 6 6)}] + [ a r:Fact; r:gives {((2 3 6 6) ">=") list:sort (6 6 3 2)}] + skolem:lemma4671 + skolem:lemma4672 + [ a r:Fact; r:gives {(6632 2366) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2366 a r:Inference; + r:gives { + 2367 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2367 math:notEqualTo 0}] + skolem:lemma4673 + [ a r:Fact; r:gives {((2 3 6 7) "=<") list:sort (2 3 6 7)}] + [ a r:Fact; r:gives {((2 3 6 7) ">=") list:sort (7 6 3 2)}] + skolem:lemma4674 + skolem:lemma4675 + [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2367 a r:Inference; + r:gives { + 2368 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2368 math:notEqualTo 0}] + skolem:lemma4676 + [ a r:Fact; r:gives {((2 3 6 8) "=<") list:sort (2 3 6 8)}] + [ a r:Fact; r:gives {((2 3 6 8) ">=") list:sort (8 6 3 2)}] + skolem:lemma4677 + skolem:lemma4678 + [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2368 a r:Inference; + r:gives { + 2369 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2369 math:notEqualTo 0}] + skolem:lemma4679 + [ a r:Fact; r:gives {((2 3 6 9) "=<") list:sort (2 3 6 9)}] + [ a r:Fact; r:gives {((2 3 6 9) ">=") list:sort (9 6 3 2)}] + skolem:lemma4680 + skolem:lemma4681 + [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2369 a r:Inference; + r:gives { + 2370 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2370 math:notEqualTo 0}] + skolem:lemma4682 + [ a r:Fact; r:gives {((2 3 7 0) "=<") list:sort (0 2 3 7)}] + [ a r:Fact; r:gives {((2 3 7 0) ">=") list:sort (7 3 2 0)}] + skolem:lemma4099 + skolem:lemma4100 + [ a r:Fact; r:gives {(7320 237) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2370]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 7 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2370 a r:Inference; + r:gives { + 2371 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2371 math:notEqualTo 0}] + skolem:lemma4683 + [ a r:Fact; r:gives {((2 3 7 1) "=<") list:sort (1 2 3 7)}] + [ a r:Fact; r:gives {((2 3 7 1) ">=") list:sort (7 3 2 1)}] + skolem:lemma4289 + skolem:lemma4290 + [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2371]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 7 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2371 a r:Inference; + r:gives { + 2372 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2372 math:notEqualTo 0}] + skolem:lemma4684 + [ a r:Fact; r:gives {((2 3 7 2) "=<") list:sort (2 2 3 7)}] + [ a r:Fact; r:gives {((2 3 7 2) ">=") list:sort (7 3 2 2)}] + skolem:lemma4458 + skolem:lemma4459 + [ a r:Fact; r:gives {(7322 2237) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2372]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2372 a r:Inference; + r:gives { + 2373 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2373 math:notEqualTo 0}] + skolem:lemma4685 + [ a r:Fact; r:gives {((2 3 7 3) "=<") list:sort (2 3 3 7)}] + [ a r:Fact; r:gives {((2 3 7 3) ">=") list:sort (7 3 3 2)}] + skolem:lemma4614 + skolem:lemma4615 + [ a r:Fact; r:gives {(7332 2337) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2373]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2373 a r:Inference; + r:gives { + 2374 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2374 math:notEqualTo 0}] + skolem:lemma4686 + [ a r:Fact; r:gives {((2 3 7 4) "=<") list:sort (2 3 4 7)}] + [ a r:Fact; r:gives {((2 3 7 4) ">=") list:sort (7 4 3 2)}] + skolem:lemma4636 + skolem:lemma4637 + [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2374]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 7 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2374 a r:Inference; + r:gives { + 2375 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2375 math:notEqualTo 0}] + skolem:lemma4687 + [ a r:Fact; r:gives {((2 3 7 5) "=<") list:sort (2 3 5 7)}] + [ a r:Fact; r:gives {((2 3 7 5) ">=") list:sort (7 5 3 2)}] + skolem:lemma4656 + skolem:lemma4657 + [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2375]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 7 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2375 a r:Inference; + r:gives { + 2376 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2376 math:notEqualTo 0}] + skolem:lemma4688 + [ a r:Fact; r:gives {((2 3 7 6) "=<") list:sort (2 3 6 7)}] + [ a r:Fact; r:gives {((2 3 7 6) ">=") list:sort (7 6 3 2)}] + skolem:lemma4674 + skolem:lemma4675 + [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2376]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 7 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2376 a r:Inference; + r:gives { + 2377 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2377 math:notEqualTo 0}] + skolem:lemma4689 + [ a r:Fact; r:gives {((2 3 7 7) "=<") list:sort (2 3 7 7)}] + [ a r:Fact; r:gives {((2 3 7 7) ">=") list:sort (7 7 3 2)}] + skolem:lemma4690 + skolem:lemma4691 + [ a r:Fact; r:gives {(7732 2377) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2377 a r:Inference; + r:gives { + 2378 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2378 math:notEqualTo 0}] + skolem:lemma4692 + [ a r:Fact; r:gives {((2 3 7 8) "=<") list:sort (2 3 7 8)}] + [ a r:Fact; r:gives {((2 3 7 8) ">=") list:sort (8 7 3 2)}] + skolem:lemma4693 + skolem:lemma4694 + [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2378 a r:Inference; + r:gives { + 2379 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2379 math:notEqualTo 0}] + skolem:lemma4695 + [ a r:Fact; r:gives {((2 3 7 9) "=<") list:sort (2 3 7 9)}] + [ a r:Fact; r:gives {((2 3 7 9) ">=") list:sort (9 7 3 2)}] + skolem:lemma4696 + skolem:lemma4697 + [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2379 a r:Inference; + r:gives { + 2380 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2380 math:notEqualTo 0}] + skolem:lemma4698 + [ a r:Fact; r:gives {((2 3 8 0) "=<") list:sort (0 2 3 8)}] + [ a r:Fact; r:gives {((2 3 8 0) ">=") list:sort (8 3 2 0)}] + skolem:lemma4102 + skolem:lemma4103 + [ a r:Fact; r:gives {(8320 238) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2380]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 8 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2380 a r:Inference; + r:gives { + 2381 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2381 math:notEqualTo 0}] + skolem:lemma4699 + [ a r:Fact; r:gives {((2 3 8 1) "=<") list:sort (1 2 3 8)}] + [ a r:Fact; r:gives {((2 3 8 1) ">=") list:sort (8 3 2 1)}] + skolem:lemma4292 + skolem:lemma4293 + [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2381]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 8 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2381 a r:Inference; + r:gives { + 2382 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2382 math:notEqualTo 0}] + skolem:lemma4700 + [ a r:Fact; r:gives {((2 3 8 2) "=<") list:sort (2 2 3 8)}] + [ a r:Fact; r:gives {((2 3 8 2) ">=") list:sort (8 3 2 2)}] + skolem:lemma4461 + skolem:lemma4462 + [ a r:Fact; r:gives {(8322 2238) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2382]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2382 a r:Inference; + r:gives { + 2383 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2383 math:notEqualTo 0}] + skolem:lemma4701 + [ a r:Fact; r:gives {((2 3 8 3) "=<") list:sort (2 3 3 8)}] + [ a r:Fact; r:gives {((2 3 8 3) ">=") list:sort (8 3 3 2)}] + skolem:lemma4617 + skolem:lemma4618 + [ a r:Fact; r:gives {(8332 2338) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2383]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2383 a r:Inference; + r:gives { + 2384 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2384 math:notEqualTo 0}] + skolem:lemma4702 + [ a r:Fact; r:gives {((2 3 8 4) "=<") list:sort (2 3 4 8)}] + [ a r:Fact; r:gives {((2 3 8 4) ">=") list:sort (8 4 3 2)}] + skolem:lemma4639 + skolem:lemma4640 + [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2384]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 8 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2384 a r:Inference; + r:gives { + 2385 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2385 math:notEqualTo 0}] + skolem:lemma4703 + [ a r:Fact; r:gives {((2 3 8 5) "=<") list:sort (2 3 5 8)}] + [ a r:Fact; r:gives {((2 3 8 5) ">=") list:sort (8 5 3 2)}] + skolem:lemma4659 + skolem:lemma4660 + [ a r:Fact; r:gives {(8532 2358) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2385]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 8 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2385 a r:Inference; + r:gives { + 2386 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2386 math:notEqualTo 0}] + skolem:lemma4704 + [ a r:Fact; r:gives {((2 3 8 6) "=<") list:sort (2 3 6 8)}] + [ a r:Fact; r:gives {((2 3 8 6) ">=") list:sort (8 6 3 2)}] + skolem:lemma4677 + skolem:lemma4678 + [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2386]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 8 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2386 a r:Inference; + r:gives { + 2387 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2387 math:notEqualTo 0}] + skolem:lemma4705 + [ a r:Fact; r:gives {((2 3 8 7) "=<") list:sort (2 3 7 8)}] + [ a r:Fact; r:gives {((2 3 8 7) ">=") list:sort (8 7 3 2)}] + skolem:lemma4693 + skolem:lemma4694 + [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2387]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 8 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2387 a r:Inference; + r:gives { + 2388 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2388 math:notEqualTo 0}] + skolem:lemma4706 + [ a r:Fact; r:gives {((2 3 8 8) "=<") list:sort (2 3 8 8)}] + [ a r:Fact; r:gives {((2 3 8 8) ">=") list:sort (8 8 3 2)}] + skolem:lemma4707 + skolem:lemma4708 + [ a r:Fact; r:gives {(8832 2388) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2388 a r:Inference; + r:gives { + 2389 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2389 math:notEqualTo 0}] + skolem:lemma4709 + [ a r:Fact; r:gives {((2 3 8 9) "=<") list:sort (2 3 8 9)}] + [ a r:Fact; r:gives {((2 3 8 9) ">=") list:sort (9 8 3 2)}] + skolem:lemma4710 + skolem:lemma4711 + [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2389 a r:Inference; + r:gives { + 2390 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2390 math:notEqualTo 0}] + skolem:lemma4712 + [ a r:Fact; r:gives {((2 3 9 0) "=<") list:sort (0 2 3 9)}] + [ a r:Fact; r:gives {((2 3 9 0) ">=") list:sort (9 3 2 0)}] + skolem:lemma4105 + skolem:lemma4106 + [ a r:Fact; r:gives {(9320 239) math:difference 9081}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9081 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 9081 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2390]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 9 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2390 a r:Inference; + r:gives { + 2391 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2391 math:notEqualTo 0}] + skolem:lemma4713 + [ a r:Fact; r:gives {((2 3 9 1) "=<") list:sort (1 2 3 9)}] + [ a r:Fact; r:gives {((2 3 9 1) ">=") list:sort (9 3 2 1)}] + skolem:lemma4295 + skolem:lemma4296 + [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2391]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 9 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2391 a r:Inference; + r:gives { + 2392 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2392 math:notEqualTo 0}] + skolem:lemma4714 + [ a r:Fact; r:gives {((2 3 9 2) "=<") list:sort (2 2 3 9)}] + [ a r:Fact; r:gives {((2 3 9 2) ">=") list:sort (9 3 2 2)}] + skolem:lemma4464 + skolem:lemma4465 + [ a r:Fact; r:gives {(9322 2239) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2392]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 9 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2392 a r:Inference; + r:gives { + 2393 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2393 math:notEqualTo 0}] + skolem:lemma4715 + [ a r:Fact; r:gives {((2 3 9 3) "=<") list:sort (2 3 3 9)}] + [ a r:Fact; r:gives {((2 3 9 3) ">=") list:sort (9 3 3 2)}] + skolem:lemma4620 + skolem:lemma4621 + [ a r:Fact; r:gives {(9332 2339) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2393]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 9 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2393 a r:Inference; + r:gives { + 2394 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2394 math:notEqualTo 0}] + skolem:lemma4716 + [ a r:Fact; r:gives {((2 3 9 4) "=<") list:sort (2 3 4 9)}] + [ a r:Fact; r:gives {((2 3 9 4) ">=") list:sort (9 4 3 2)}] + skolem:lemma4642 + skolem:lemma4643 + [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2394]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 9 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2394 a r:Inference; + r:gives { + 2395 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2395 math:notEqualTo 0}] + skolem:lemma4717 + [ a r:Fact; r:gives {((2 3 9 5) "=<") list:sort (2 3 5 9)}] + [ a r:Fact; r:gives {((2 3 9 5) ">=") list:sort (9 5 3 2)}] + skolem:lemma4662 + skolem:lemma4663 + [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2395]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 9 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2395 a r:Inference; + r:gives { + 2396 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2396 math:notEqualTo 0}] + skolem:lemma4718 + [ a r:Fact; r:gives {((2 3 9 6) "=<") list:sort (2 3 6 9)}] + [ a r:Fact; r:gives {((2 3 9 6) ">=") list:sort (9 6 3 2)}] + skolem:lemma4680 + skolem:lemma4681 + [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2396]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 9 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2396 a r:Inference; + r:gives { + 2397 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2397 math:notEqualTo 0}] + skolem:lemma4719 + [ a r:Fact; r:gives {((2 3 9 7) "=<") list:sort (2 3 7 9)}] + [ a r:Fact; r:gives {((2 3 9 7) ">=") list:sort (9 7 3 2)}] + skolem:lemma4696 + skolem:lemma4697 + [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2397]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 9 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2397 a r:Inference; + r:gives { + 2398 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2398 math:notEqualTo 0}] + skolem:lemma4720 + [ a r:Fact; r:gives {((2 3 9 8) "=<") list:sort (2 3 8 9)}] + [ a r:Fact; r:gives {((2 3 9 8) ">=") list:sort (9 8 3 2)}] + skolem:lemma4710 + skolem:lemma4711 + [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2398]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 9 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2398 a r:Inference; + r:gives { + 2399 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2399 math:notEqualTo 0}] + skolem:lemma4721 + [ a r:Fact; r:gives {((2 3 9 9) "=<") list:sort (2 3 9 9)}] + [ a r:Fact; r:gives {((2 3 9 9) ">=") list:sort (9 9 3 2)}] + skolem:lemma4722 + skolem:lemma4723 + [ a r:Fact; r:gives {(9932 2399) math:difference 7533}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7533 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7533 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 3 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9932]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2399 a r:Inference; + r:gives { + 2400 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2400 math:notEqualTo 0}] + skolem:lemma4724 + [ a r:Fact; r:gives {((2 4 0 0) "=<") list:sort (0 0 2 4)}] + [ a r:Fact; r:gives {((2 4 0 0) ">=") list:sort (4 2 0 0)}] + skolem:lemma4012 + skolem:lemma4013 + [ a r:Fact; r:gives {(4200 24) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2400 a r:Inference; + r:gives { + 2401 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2401 math:notEqualTo 0}] + skolem:lemma4725 + [ a r:Fact; r:gives {((2 4 0 1) "=<") list:sort (0 1 2 4)}] + [ a r:Fact; r:gives {((2 4 0 1) ">=") list:sort (4 2 1 0)}] + skolem:lemma4040 + skolem:lemma4041 + [ a r:Fact; r:gives {(4210 124) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2401]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 0 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2401 a r:Inference; + r:gives { + 2402 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2402 math:notEqualTo 0}] + skolem:lemma4726 + [ a r:Fact; r:gives {((2 4 0 2) "=<") list:sort (0 2 2 4)}] + [ a r:Fact; r:gives {((2 4 0 2) ">=") list:sort (4 2 2 0)}] + skolem:lemma4066 + skolem:lemma4067 + [ a r:Fact; r:gives {(4220 224) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2402]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 0 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2402 a r:Inference; + r:gives { + 2403 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2403 math:notEqualTo 0}] + skolem:lemma4727 + [ a r:Fact; r:gives {((2 4 0 3) "=<") list:sort (0 2 3 4)}] + [ a r:Fact; r:gives {((2 4 0 3) ">=") list:sort (4 3 2 0)}] + skolem:lemma4090 + skolem:lemma4091 + [ a r:Fact; r:gives {(4320 234) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2403]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 0 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2403 a r:Inference; + r:gives { + 2404 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2404 math:notEqualTo 0}] + skolem:lemma4728 + [ a r:Fact; r:gives {((2 4 0 4) "=<") list:sort (0 2 4 4)}] + [ a r:Fact; r:gives {((2 4 0 4) ">=") list:sort (4 4 2 0)}] + skolem:lemma4112 + skolem:lemma4113 + [ a r:Fact; r:gives {(4420 244) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2404]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 0 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2404 a r:Inference; + r:gives { + 2405 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2405 math:notEqualTo 0}] + skolem:lemma4729 + [ a r:Fact; r:gives {((2 4 0 5) "=<") list:sort (0 2 4 5)}] + [ a r:Fact; r:gives {((2 4 0 5) ">=") list:sort (5 4 2 0)}] + skolem:lemma4115 + skolem:lemma4116 + [ a r:Fact; r:gives {(5420 245) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2405]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 0 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2405 a r:Inference; + r:gives { + 2406 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2406 math:notEqualTo 0}] + skolem:lemma4730 + [ a r:Fact; r:gives {((2 4 0 6) "=<") list:sort (0 2 4 6)}] + [ a r:Fact; r:gives {((2 4 0 6) ">=") list:sort (6 4 2 0)}] + skolem:lemma4118 + skolem:lemma4119 + [ a r:Fact; r:gives {(6420 246) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2406]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 0 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2406 a r:Inference; + r:gives { + 2407 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2407 math:notEqualTo 0}] + skolem:lemma4731 + [ a r:Fact; r:gives {((2 4 0 7) "=<") list:sort (0 2 4 7)}] + [ a r:Fact; r:gives {((2 4 0 7) ">=") list:sort (7 4 2 0)}] + skolem:lemma4121 + skolem:lemma4122 + [ a r:Fact; r:gives {(7420 247) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2407]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 0 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2407 a r:Inference; + r:gives { + 2408 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2408 math:notEqualTo 0}] + skolem:lemma4732 + [ a r:Fact; r:gives {((2 4 0 8) "=<") list:sort (0 2 4 8)}] + [ a r:Fact; r:gives {((2 4 0 8) ">=") list:sort (8 4 2 0)}] + skolem:lemma4124 + skolem:lemma4125 + [ a r:Fact; r:gives {(8420 248) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2408]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 0 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2408 a r:Inference; + r:gives { + 2409 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2409 math:notEqualTo 0}] + skolem:lemma4733 + [ a r:Fact; r:gives {((2 4 0 9) "=<") list:sort (0 2 4 9)}] + [ a r:Fact; r:gives {((2 4 0 9) ">=") list:sort (9 4 2 0)}] + skolem:lemma4127 + skolem:lemma4128 + [ a r:Fact; r:gives {(9420 249) math:difference 9171}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9171 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9171 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2409]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 0 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2409 a r:Inference; + r:gives { + 2410 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2410 math:notEqualTo 0}] + skolem:lemma4734 + [ a r:Fact; r:gives {((2 4 1 0) "=<") list:sort (0 1 2 4)}] + [ a r:Fact; r:gives {((2 4 1 0) ">=") list:sort (4 2 1 0)}] + skolem:lemma4040 + skolem:lemma4041 + [ a r:Fact; r:gives {(4210 124) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2410]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2410 a r:Inference; + r:gives { + 2411 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2411 math:notEqualTo 0}] + skolem:lemma4735 + [ a r:Fact; r:gives {((2 4 1 1) "=<") list:sort (1 1 2 4)}] + [ a r:Fact; r:gives {((2 4 1 1) ">=") list:sort (4 2 1 1)}] + skolem:lemma4230 + skolem:lemma4231 + [ a r:Fact; r:gives {(4211 1124) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2411]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2411 a r:Inference; + r:gives { + 2412 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2412 math:notEqualTo 0}] + skolem:lemma4736 + [ a r:Fact; r:gives {((2 4 1 2) "=<") list:sort (1 2 2 4)}] + [ a r:Fact; r:gives {((2 4 1 2) ">=") list:sort (4 2 2 1)}] + skolem:lemma4256 + skolem:lemma4257 + [ a r:Fact; r:gives {(4221 1224) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2412]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2412 a r:Inference; + r:gives { + 2413 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2413 math:notEqualTo 0}] + skolem:lemma4737 + [ a r:Fact; r:gives {((2 4 1 3) "=<") list:sort (1 2 3 4)}] + [ a r:Fact; r:gives {((2 4 1 3) ">=") list:sort (4 3 2 1)}] + skolem:lemma4280 + skolem:lemma4281 + [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2413]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2413 a r:Inference; + r:gives { + 2414 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2414 math:notEqualTo 0}] + skolem:lemma4738 + [ a r:Fact; r:gives {((2 4 1 4) "=<") list:sort (1 2 4 4)}] + [ a r:Fact; r:gives {((2 4 1 4) ">=") list:sort (4 4 2 1)}] + skolem:lemma4302 + skolem:lemma4303 + [ a r:Fact; r:gives {(4421 1244) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2414]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 1 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2414 a r:Inference; + r:gives { + 2415 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2415 math:notEqualTo 0}] + skolem:lemma4739 + [ a r:Fact; r:gives {((2 4 1 5) "=<") list:sort (1 2 4 5)}] + [ a r:Fact; r:gives {((2 4 1 5) ">=") list:sort (5 4 2 1)}] + skolem:lemma4305 + skolem:lemma4306 + [ a r:Fact; r:gives {(5421 1245) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2415]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 1 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2415 a r:Inference; + r:gives { + 2416 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2416 math:notEqualTo 0}] + skolem:lemma4740 + [ a r:Fact; r:gives {((2 4 1 6) "=<") list:sort (1 2 4 6)}] + [ a r:Fact; r:gives {((2 4 1 6) ">=") list:sort (6 4 2 1)}] + skolem:lemma4308 + skolem:lemma4309 + [ a r:Fact; r:gives {(6421 1246) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2416]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 1 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2416 a r:Inference; + r:gives { + 2417 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2417 math:notEqualTo 0}] + skolem:lemma4741 + [ a r:Fact; r:gives {((2 4 1 7) "=<") list:sort (1 2 4 7)}] + [ a r:Fact; r:gives {((2 4 1 7) ">=") list:sort (7 4 2 1)}] + skolem:lemma4311 + skolem:lemma4312 + [ a r:Fact; r:gives {(7421 1247) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2417]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 1 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2417 a r:Inference; + r:gives { + 2418 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2418 math:notEqualTo 0}] + skolem:lemma4742 + [ a r:Fact; r:gives {((2 4 1 8) "=<") list:sort (1 2 4 8)}] + [ a r:Fact; r:gives {((2 4 1 8) ">=") list:sort (8 4 2 1)}] + skolem:lemma4314 + skolem:lemma4315 + [ a r:Fact; r:gives {(8421 1248) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2418]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 1 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2418 a r:Inference; + r:gives { + 2419 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2419 math:notEqualTo 0}] + skolem:lemma4743 + [ a r:Fact; r:gives {((2 4 1 9) "=<") list:sort (1 2 4 9)}] + [ a r:Fact; r:gives {((2 4 1 9) ">=") list:sort (9 4 2 1)}] + skolem:lemma4317 + skolem:lemma4318 + [ a r:Fact; r:gives {(9421 1249) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2419]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 1 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2419 a r:Inference; + r:gives { + 2420 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2420 math:notEqualTo 0}] + skolem:lemma4744 + [ a r:Fact; r:gives {((2 4 2 0) "=<") list:sort (0 2 2 4)}] + [ a r:Fact; r:gives {((2 4 2 0) ">=") list:sort (4 2 2 0)}] + skolem:lemma4066 + skolem:lemma4067 + [ a r:Fact; r:gives {(4220 224) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2420 a r:Inference; + r:gives { + 2421 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2421 math:notEqualTo 0}] + skolem:lemma4745 + [ a r:Fact; r:gives {((2 4 2 1) "=<") list:sort (1 2 2 4)}] + [ a r:Fact; r:gives {((2 4 2 1) ">=") list:sort (4 2 2 1)}] + skolem:lemma4256 + skolem:lemma4257 + [ a r:Fact; r:gives {(4221 1224) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2421 a r:Inference; + r:gives { + 2422 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2422 math:notEqualTo 0}] + skolem:lemma4746 + [ a r:Fact; r:gives {((2 4 2 2) "=<") list:sort (2 2 2 4)}] + [ a r:Fact; r:gives {((2 4 2 2) ">=") list:sort (4 2 2 2)}] + skolem:lemma4425 + skolem:lemma4426 + [ a r:Fact; r:gives {(4222 2224) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2422 a r:Inference; + r:gives { + 2423 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2423 math:notEqualTo 0}] + skolem:lemma4747 + [ a r:Fact; r:gives {((2 4 2 3) "=<") list:sort (2 2 3 4)}] + [ a r:Fact; r:gives {((2 4 2 3) ">=") list:sort (4 3 2 2)}] + skolem:lemma4449 + skolem:lemma4450 + [ a r:Fact; r:gives {(4322 2234) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2423]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2423 a r:Inference; + r:gives { + 2424 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2424 math:notEqualTo 0}] + skolem:lemma4748 + [ a r:Fact; r:gives {((2 4 2 4) "=<") list:sort (2 2 4 4)}] + [ a r:Fact; r:gives {((2 4 2 4) ">=") list:sort (4 4 2 2)}] + skolem:lemma4471 + skolem:lemma4472 + [ a r:Fact; r:gives {(4422 2244) math:difference 2178}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2178 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2178 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2424]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2178]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2424 a r:Inference; + r:gives { + 2425 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2425 math:notEqualTo 0}] + skolem:lemma4749 + [ a r:Fact; r:gives {((2 4 2 5) "=<") list:sort (2 2 4 5)}] + [ a r:Fact; r:gives {((2 4 2 5) ">=") list:sort (5 4 2 2)}] + skolem:lemma4474 + skolem:lemma4475 + [ a r:Fact; r:gives {(5422 2245) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2425]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2425 a r:Inference; + r:gives { + 2426 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2426 math:notEqualTo 0}] + skolem:lemma4750 + [ a r:Fact; r:gives {((2 4 2 6) "=<") list:sort (2 2 4 6)}] + [ a r:Fact; r:gives {((2 4 2 6) ">=") list:sort (6 4 2 2)}] + skolem:lemma4477 + skolem:lemma4478 + [ a r:Fact; r:gives {(6422 2246) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2426]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2426 a r:Inference; + r:gives { + 2427 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2427 math:notEqualTo 0}] + skolem:lemma4751 + [ a r:Fact; r:gives {((2 4 2 7) "=<") list:sort (2 2 4 7)}] + [ a r:Fact; r:gives {((2 4 2 7) ">=") list:sort (7 4 2 2)}] + skolem:lemma4480 + skolem:lemma4481 + [ a r:Fact; r:gives {(7422 2247) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2427]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2427 a r:Inference; + r:gives { + 2428 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2428 math:notEqualTo 0}] + skolem:lemma4752 + [ a r:Fact; r:gives {((2 4 2 8) "=<") list:sort (2 2 4 8)}] + [ a r:Fact; r:gives {((2 4 2 8) ">=") list:sort (8 4 2 2)}] + skolem:lemma4483 + skolem:lemma4484 + [ a r:Fact; r:gives {(8422 2248) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2428]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2428 a r:Inference; + r:gives { + 2429 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2429 math:notEqualTo 0}] + skolem:lemma4753 + [ a r:Fact; r:gives {((2 4 2 9) "=<") list:sort (2 2 4 9)}] + [ a r:Fact; r:gives {((2 4 2 9) ">=") list:sort (9 4 2 2)}] + skolem:lemma4486 + skolem:lemma4487 + [ a r:Fact; r:gives {(9422 2249) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2429]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2429 a r:Inference; + r:gives { + 2430 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2430 math:notEqualTo 0}] + skolem:lemma4754 + [ a r:Fact; r:gives {((2 4 3 0) "=<") list:sort (0 2 3 4)}] + [ a r:Fact; r:gives {((2 4 3 0) ">=") list:sort (4 3 2 0)}] + skolem:lemma4090 + skolem:lemma4091 + [ a r:Fact; r:gives {(4320 234) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2430 a r:Inference; + r:gives { + 2431 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2431 math:notEqualTo 0}] + skolem:lemma4755 + [ a r:Fact; r:gives {((2 4 3 1) "=<") list:sort (1 2 3 4)}] + [ a r:Fact; r:gives {((2 4 3 1) ">=") list:sort (4 3 2 1)}] + skolem:lemma4280 + skolem:lemma4281 + [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2431 a r:Inference; + r:gives { + 2432 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2432 math:notEqualTo 0}] + skolem:lemma4756 + [ a r:Fact; r:gives {((2 4 3 2) "=<") list:sort (2 2 3 4)}] + [ a r:Fact; r:gives {((2 4 3 2) ">=") list:sort (4 3 2 2)}] + skolem:lemma4449 + skolem:lemma4450 + [ a r:Fact; r:gives {(4322 2234) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2432 a r:Inference; + r:gives { + 2433 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2433 math:notEqualTo 0}] + skolem:lemma4757 + [ a r:Fact; r:gives {((2 4 3 3) "=<") list:sort (2 3 3 4)}] + [ a r:Fact; r:gives {((2 4 3 3) ">=") list:sort (4 3 3 2)}] + skolem:lemma4605 + skolem:lemma4606 + [ a r:Fact; r:gives {(4332 2334) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2433 a r:Inference; + r:gives { + 2434 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2434 math:notEqualTo 0}] + skolem:lemma4758 + [ a r:Fact; r:gives {((2 4 3 4) "=<") list:sort (2 3 4 4)}] + [ a r:Fact; r:gives {((2 4 3 4) ">=") list:sort (4 4 3 2)}] + skolem:lemma4627 + skolem:lemma4628 + [ a r:Fact; r:gives {(4432 2344) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2434]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2434 a r:Inference; + r:gives { + 2435 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2435 math:notEqualTo 0}] + skolem:lemma4759 + [ a r:Fact; r:gives {((2 4 3 5) "=<") list:sort (2 3 4 5)}] + [ a r:Fact; r:gives {((2 4 3 5) ">=") list:sort (5 4 3 2)}] + skolem:lemma4630 + skolem:lemma4631 + [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2435]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2435 a r:Inference; + r:gives { + 2436 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2436 math:notEqualTo 0}] + skolem:lemma4760 + [ a r:Fact; r:gives {((2 4 3 6) "=<") list:sort (2 3 4 6)}] + [ a r:Fact; r:gives {((2 4 3 6) ">=") list:sort (6 4 3 2)}] + skolem:lemma4633 + skolem:lemma4634 + [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2436]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2436 a r:Inference; + r:gives { + 2437 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2437 math:notEqualTo 0}] + skolem:lemma4761 + [ a r:Fact; r:gives {((2 4 3 7) "=<") list:sort (2 3 4 7)}] + [ a r:Fact; r:gives {((2 4 3 7) ">=") list:sort (7 4 3 2)}] + skolem:lemma4636 + skolem:lemma4637 + [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2437]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2437 a r:Inference; + r:gives { + 2438 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2438 math:notEqualTo 0}] + skolem:lemma4762 + [ a r:Fact; r:gives {((2 4 3 8) "=<") list:sort (2 3 4 8)}] + [ a r:Fact; r:gives {((2 4 3 8) ">=") list:sort (8 4 3 2)}] + skolem:lemma4639 + skolem:lemma4640 + [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2438]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2438 a r:Inference; + r:gives { + 2439 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2439 math:notEqualTo 0}] + skolem:lemma4763 + [ a r:Fact; r:gives {((2 4 3 9) "=<") list:sort (2 3 4 9)}] + [ a r:Fact; r:gives {((2 4 3 9) ">=") list:sort (9 4 3 2)}] + skolem:lemma4642 + skolem:lemma4643 + [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2439]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2439 a r:Inference; + r:gives { + 2440 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2440 math:notEqualTo 0}] + skolem:lemma4764 + [ a r:Fact; r:gives {((2 4 4 0) "=<") list:sort (0 2 4 4)}] + [ a r:Fact; r:gives {((2 4 4 0) ">=") list:sort (4 4 2 0)}] + skolem:lemma4112 + skolem:lemma4113 + [ a r:Fact; r:gives {(4420 244) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2440]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 4 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2440 a r:Inference; + r:gives { + 2441 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2441 math:notEqualTo 0}] + skolem:lemma4765 + [ a r:Fact; r:gives {((2 4 4 1) "=<") list:sort (1 2 4 4)}] + [ a r:Fact; r:gives {((2 4 4 1) ">=") list:sort (4 4 2 1)}] + skolem:lemma4302 + skolem:lemma4303 + [ a r:Fact; r:gives {(4421 1244) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2441]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 4 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2441 a r:Inference; + r:gives { + 2442 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2442 math:notEqualTo 0}] + skolem:lemma4766 + [ a r:Fact; r:gives {((2 4 4 2) "=<") list:sort (2 2 4 4)}] + [ a r:Fact; r:gives {((2 4 4 2) ">=") list:sort (4 4 2 2)}] + skolem:lemma4471 + skolem:lemma4472 + [ a r:Fact; r:gives {(4422 2244) math:difference 2178}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2178 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2178 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2178]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2442 a r:Inference; + r:gives { + 2443 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2443 math:notEqualTo 0}] + skolem:lemma4767 + [ a r:Fact; r:gives {((2 4 4 3) "=<") list:sort (2 3 4 4)}] + [ a r:Fact; r:gives {((2 4 4 3) ">=") list:sort (4 4 3 2)}] + skolem:lemma4627 + skolem:lemma4628 + [ a r:Fact; r:gives {(4432 2344) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2443 a r:Inference; + r:gives { + 2444 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2444 math:notEqualTo 0}] + skolem:lemma4768 + [ a r:Fact; r:gives {((2 4 4 4) "=<") list:sort (2 4 4 4)}] + [ a r:Fact; r:gives {((2 4 4 4) ">=") list:sort (4 4 4 2)}] + skolem:lemma4769 + skolem:lemma4770 + [ a r:Fact; r:gives {(4442 2444) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2444 a r:Inference; + r:gives { + 2445 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2445 math:notEqualTo 0}] + skolem:lemma4771 + [ a r:Fact; r:gives {((2 4 4 5) "=<") list:sort (2 4 4 5)}] + [ a r:Fact; r:gives {((2 4 4 5) ">=") list:sort (5 4 4 2)}] + skolem:lemma4772 + skolem:lemma4773 + [ a r:Fact; r:gives {(5442 2445) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2445]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2445]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2445 a r:Inference; + r:gives { + 2446 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2446 math:notEqualTo 0}] + skolem:lemma4774 + [ a r:Fact; r:gives {((2 4 4 6) "=<") list:sort (2 4 4 6)}] + [ a r:Fact; r:gives {((2 4 4 6) ">=") list:sort (6 4 4 2)}] + skolem:lemma4775 + skolem:lemma4776 + [ a r:Fact; r:gives {(6442 2446) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2446]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2446]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2446 a r:Inference; + r:gives { + 2447 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2447 math:notEqualTo 0}] + skolem:lemma4777 + [ a r:Fact; r:gives {((2 4 4 7) "=<") list:sort (2 4 4 7)}] + [ a r:Fact; r:gives {((2 4 4 7) ">=") list:sort (7 4 4 2)}] + skolem:lemma4778 + skolem:lemma4779 + [ a r:Fact; r:gives {(7442 2447) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2447]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2447]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2447 a r:Inference; + r:gives { + 2448 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2448 math:notEqualTo 0}] + skolem:lemma4780 + [ a r:Fact; r:gives {((2 4 4 8) "=<") list:sort (2 4 4 8)}] + [ a r:Fact; r:gives {((2 4 4 8) ">=") list:sort (8 4 4 2)}] + skolem:lemma4781 + skolem:lemma4782 + [ a r:Fact; r:gives {(8442 2448) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2448]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2448]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2448 a r:Inference; + r:gives { + 2449 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2449 math:notEqualTo 0}] + skolem:lemma4783 + [ a r:Fact; r:gives {((2 4 4 9) "=<") list:sort (2 4 4 9)}] + [ a r:Fact; r:gives {((2 4 4 9) ">=") list:sort (9 4 4 2)}] + skolem:lemma4784 + skolem:lemma4785 + [ a r:Fact; r:gives {(9442 2449) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2449]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2449]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2449 a r:Inference; + r:gives { + 2450 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2450 math:notEqualTo 0}] + skolem:lemma4786 + [ a r:Fact; r:gives {((2 4 5 0) "=<") list:sort (0 2 4 5)}] + [ a r:Fact; r:gives {((2 4 5 0) ">=") list:sort (5 4 2 0)}] + skolem:lemma4115 + skolem:lemma4116 + [ a r:Fact; r:gives {(5420 245) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2450]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 5 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2450 a r:Inference; + r:gives { + 2451 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2451 math:notEqualTo 0}] + skolem:lemma4787 + [ a r:Fact; r:gives {((2 4 5 1) "=<") list:sort (1 2 4 5)}] + [ a r:Fact; r:gives {((2 4 5 1) ">=") list:sort (5 4 2 1)}] + skolem:lemma4305 + skolem:lemma4306 + [ a r:Fact; r:gives {(5421 1245) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2451]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 5 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2451 a r:Inference; + r:gives { + 2452 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2452 math:notEqualTo 0}] + skolem:lemma4788 + [ a r:Fact; r:gives {((2 4 5 2) "=<") list:sort (2 2 4 5)}] + [ a r:Fact; r:gives {((2 4 5 2) ">=") list:sort (5 4 2 2)}] + skolem:lemma4474 + skolem:lemma4475 + [ a r:Fact; r:gives {(5422 2245) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2452]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2452 a r:Inference; + r:gives { + 2453 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2453 math:notEqualTo 0}] + skolem:lemma4789 + [ a r:Fact; r:gives {((2 4 5 3) "=<") list:sort (2 3 4 5)}] + [ a r:Fact; r:gives {((2 4 5 3) ">=") list:sort (5 4 3 2)}] + skolem:lemma4630 + skolem:lemma4631 + [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2453]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2453 a r:Inference; + r:gives { + 2454 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2454 math:notEqualTo 0}] + skolem:lemma4790 + [ a r:Fact; r:gives {((2 4 5 4) "=<") list:sort (2 4 4 5)}] + [ a r:Fact; r:gives {((2 4 5 4) ">=") list:sort (5 4 4 2)}] + skolem:lemma4772 + skolem:lemma4773 + [ a r:Fact; r:gives {(5442 2445) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2454]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 5 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2445]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2454 a r:Inference; + r:gives { + 2455 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2455 math:notEqualTo 0}] + skolem:lemma4791 + [ a r:Fact; r:gives {((2 4 5 5) "=<") list:sort (2 4 5 5)}] + [ a r:Fact; r:gives {((2 4 5 5) ">=") list:sort (5 5 4 2)}] + skolem:lemma4792 + skolem:lemma4793 + [ a r:Fact; r:gives {(5542 2455) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2455]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2455]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2455 a r:Inference; + r:gives { + 2456 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2456 math:notEqualTo 0}] + skolem:lemma4794 + [ a r:Fact; r:gives {((2 4 5 6) "=<") list:sort (2 4 5 6)}] + [ a r:Fact; r:gives {((2 4 5 6) ">=") list:sort (6 5 4 2)}] + skolem:lemma4795 + skolem:lemma4796 + [ a r:Fact; r:gives {(6542 2456) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2456 a r:Inference; + r:gives { + 2457 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2457 math:notEqualTo 0}] + skolem:lemma4797 + [ a r:Fact; r:gives {((2 4 5 7) "=<") list:sort (2 4 5 7)}] + [ a r:Fact; r:gives {((2 4 5 7) ">=") list:sort (7 5 4 2)}] + skolem:lemma4798 + skolem:lemma4799 + [ a r:Fact; r:gives {(7542 2457) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2457]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2457]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2457 a r:Inference; + r:gives { + 2458 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2458 math:notEqualTo 0}] + skolem:lemma4800 + [ a r:Fact; r:gives {((2 4 5 8) "=<") list:sort (2 4 5 8)}] + [ a r:Fact; r:gives {((2 4 5 8) ">=") list:sort (8 5 4 2)}] + skolem:lemma4801 + skolem:lemma4802 + [ a r:Fact; r:gives {(8542 2458) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2458]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2458]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2458 a r:Inference; + r:gives { + 2459 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2459 math:notEqualTo 0}] + skolem:lemma4803 + [ a r:Fact; r:gives {((2 4 5 9) "=<") list:sort (2 4 5 9)}] + [ a r:Fact; r:gives {((2 4 5 9) ">=") list:sort (9 5 4 2)}] + skolem:lemma4804 + skolem:lemma4805 + [ a r:Fact; r:gives {(9542 2459) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2459]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2459]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2459 a r:Inference; + r:gives { + 2460 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2460 math:notEqualTo 0}] + skolem:lemma4806 + [ a r:Fact; r:gives {((2 4 6 0) "=<") list:sort (0 2 4 6)}] + [ a r:Fact; r:gives {((2 4 6 0) ">=") list:sort (6 4 2 0)}] + skolem:lemma4118 + skolem:lemma4119 + [ a r:Fact; r:gives {(6420 246) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2460]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 6 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2460 a r:Inference; + r:gives { + 2461 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2461 math:notEqualTo 0}] + skolem:lemma4807 + [ a r:Fact; r:gives {((2 4 6 1) "=<") list:sort (1 2 4 6)}] + [ a r:Fact; r:gives {((2 4 6 1) ">=") list:sort (6 4 2 1)}] + skolem:lemma4308 + skolem:lemma4309 + [ a r:Fact; r:gives {(6421 1246) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2461]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 6 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2461 a r:Inference; + r:gives { + 2462 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2462 math:notEqualTo 0}] + skolem:lemma4808 + [ a r:Fact; r:gives {((2 4 6 2) "=<") list:sort (2 2 4 6)}] + [ a r:Fact; r:gives {((2 4 6 2) ">=") list:sort (6 4 2 2)}] + skolem:lemma4477 + skolem:lemma4478 + [ a r:Fact; r:gives {(6422 2246) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2462]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2462 a r:Inference; + r:gives { + 2463 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2463 math:notEqualTo 0}] + skolem:lemma4809 + [ a r:Fact; r:gives {((2 4 6 3) "=<") list:sort (2 3 4 6)}] + [ a r:Fact; r:gives {((2 4 6 3) ">=") list:sort (6 4 3 2)}] + skolem:lemma4633 + skolem:lemma4634 + [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2463]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2463 a r:Inference; + r:gives { + 2464 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2464 math:notEqualTo 0}] + skolem:lemma4810 + [ a r:Fact; r:gives {((2 4 6 4) "=<") list:sort (2 4 4 6)}] + [ a r:Fact; r:gives {((2 4 6 4) ">=") list:sort (6 4 4 2)}] + skolem:lemma4775 + skolem:lemma4776 + [ a r:Fact; r:gives {(6442 2446) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2464]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 6 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2446]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2464 a r:Inference; + r:gives { + 2465 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2465 math:notEqualTo 0}] + skolem:lemma4811 + [ a r:Fact; r:gives {((2 4 6 5) "=<") list:sort (2 4 5 6)}] + [ a r:Fact; r:gives {((2 4 6 5) ">=") list:sort (6 5 4 2)}] + skolem:lemma4795 + skolem:lemma4796 + [ a r:Fact; r:gives {(6542 2456) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2465]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 6 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2465 a r:Inference; + r:gives { + 2466 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2466 math:notEqualTo 0}] + skolem:lemma4812 + [ a r:Fact; r:gives {((2 4 6 6) "=<") list:sort (2 4 6 6)}] + [ a r:Fact; r:gives {((2 4 6 6) ">=") list:sort (6 6 4 2)}] + skolem:lemma4813 + skolem:lemma4814 + [ a r:Fact; r:gives {(6642 2466) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2466]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2466]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2466 a r:Inference; + r:gives { + 2467 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2467 math:notEqualTo 0}] + skolem:lemma4815 + [ a r:Fact; r:gives {((2 4 6 7) "=<") list:sort (2 4 6 7)}] + [ a r:Fact; r:gives {((2 4 6 7) ">=") list:sort (7 6 4 2)}] + skolem:lemma4816 + skolem:lemma4817 + [ a r:Fact; r:gives {(7642 2467) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2467]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2467]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2467 a r:Inference; + r:gives { + 2468 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2468 math:notEqualTo 0}] + skolem:lemma4818 + [ a r:Fact; r:gives {((2 4 6 8) "=<") list:sort (2 4 6 8)}] + [ a r:Fact; r:gives {((2 4 6 8) ">=") list:sort (8 6 4 2)}] + skolem:lemma4819 + skolem:lemma4820 + [ a r:Fact; r:gives {(8642 2468) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2468]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2468]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2468 a r:Inference; + r:gives { + 2469 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2469 math:notEqualTo 0}] + skolem:lemma4821 + [ a r:Fact; r:gives {((2 4 6 9) "=<") list:sort (2 4 6 9)}] + [ a r:Fact; r:gives {((2 4 6 9) ">=") list:sort (9 6 4 2)}] + skolem:lemma4822 + skolem:lemma4823 + [ a r:Fact; r:gives {(9642 2469) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2469]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2469]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2469 a r:Inference; + r:gives { + 2470 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2470 math:notEqualTo 0}] + skolem:lemma4824 + [ a r:Fact; r:gives {((2 4 7 0) "=<") list:sort (0 2 4 7)}] + [ a r:Fact; r:gives {((2 4 7 0) ">=") list:sort (7 4 2 0)}] + skolem:lemma4121 + skolem:lemma4122 + [ a r:Fact; r:gives {(7420 247) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2470]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 7 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2470 a r:Inference; + r:gives { + 2471 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2471 math:notEqualTo 0}] + skolem:lemma4825 + [ a r:Fact; r:gives {((2 4 7 1) "=<") list:sort (1 2 4 7)}] + [ a r:Fact; r:gives {((2 4 7 1) ">=") list:sort (7 4 2 1)}] + skolem:lemma4311 + skolem:lemma4312 + [ a r:Fact; r:gives {(7421 1247) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2471]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 7 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2471 a r:Inference; + r:gives { + 2472 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2472 math:notEqualTo 0}] + skolem:lemma4826 + [ a r:Fact; r:gives {((2 4 7 2) "=<") list:sort (2 2 4 7)}] + [ a r:Fact; r:gives {((2 4 7 2) ">=") list:sort (7 4 2 2)}] + skolem:lemma4480 + skolem:lemma4481 + [ a r:Fact; r:gives {(7422 2247) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2472]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2472 a r:Inference; + r:gives { + 2473 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2473 math:notEqualTo 0}] + skolem:lemma4827 + [ a r:Fact; r:gives {((2 4 7 3) "=<") list:sort (2 3 4 7)}] + [ a r:Fact; r:gives {((2 4 7 3) ">=") list:sort (7 4 3 2)}] + skolem:lemma4636 + skolem:lemma4637 + [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2473]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2473 a r:Inference; + r:gives { + 2474 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2474 math:notEqualTo 0}] + skolem:lemma4828 + [ a r:Fact; r:gives {((2 4 7 4) "=<") list:sort (2 4 4 7)}] + [ a r:Fact; r:gives {((2 4 7 4) ">=") list:sort (7 4 4 2)}] + skolem:lemma4778 + skolem:lemma4779 + [ a r:Fact; r:gives {(7442 2447) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2474]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 7 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2447]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2474 a r:Inference; + r:gives { + 2475 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2475 math:notEqualTo 0}] + skolem:lemma4829 + [ a r:Fact; r:gives {((2 4 7 5) "=<") list:sort (2 4 5 7)}] + [ a r:Fact; r:gives {((2 4 7 5) ">=") list:sort (7 5 4 2)}] + skolem:lemma4798 + skolem:lemma4799 + [ a r:Fact; r:gives {(7542 2457) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2475]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 7 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2457]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2475 a r:Inference; + r:gives { + 2476 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2476 math:notEqualTo 0}] + skolem:lemma4830 + [ a r:Fact; r:gives {((2 4 7 6) "=<") list:sort (2 4 6 7)}] + [ a r:Fact; r:gives {((2 4 7 6) ">=") list:sort (7 6 4 2)}] + skolem:lemma4816 + skolem:lemma4817 + [ a r:Fact; r:gives {(7642 2467) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2476]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 7 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2467]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2476 a r:Inference; + r:gives { + 2477 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2477 math:notEqualTo 0}] + skolem:lemma4831 + [ a r:Fact; r:gives {((2 4 7 7) "=<") list:sort (2 4 7 7)}] + [ a r:Fact; r:gives {((2 4 7 7) ">=") list:sort (7 7 4 2)}] + skolem:lemma4832 + skolem:lemma4833 + [ a r:Fact; r:gives {(7742 2477) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2477]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2477]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2477 a r:Inference; + r:gives { + 2478 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2478 math:notEqualTo 0}] + skolem:lemma4834 + [ a r:Fact; r:gives {((2 4 7 8) "=<") list:sort (2 4 7 8)}] + [ a r:Fact; r:gives {((2 4 7 8) ">=") list:sort (8 7 4 2)}] + skolem:lemma4835 + skolem:lemma4836 + [ a r:Fact; r:gives {(8742 2478) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2478]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2478]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2478 a r:Inference; + r:gives { + 2479 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2479 math:notEqualTo 0}] + skolem:lemma4837 + [ a r:Fact; r:gives {((2 4 7 9) "=<") list:sort (2 4 7 9)}] + [ a r:Fact; r:gives {((2 4 7 9) ">=") list:sort (9 7 4 2)}] + skolem:lemma4838 + skolem:lemma4839 + [ a r:Fact; r:gives {(9742 2479) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2479]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2479]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2479 a r:Inference; + r:gives { + 2480 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2480 math:notEqualTo 0}] + skolem:lemma4840 + [ a r:Fact; r:gives {((2 4 8 0) "=<") list:sort (0 2 4 8)}] + [ a r:Fact; r:gives {((2 4 8 0) ">=") list:sort (8 4 2 0)}] + skolem:lemma4124 + skolem:lemma4125 + [ a r:Fact; r:gives {(8420 248) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2480]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 8 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2480 a r:Inference; + r:gives { + 2481 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2481 math:notEqualTo 0}] + skolem:lemma4841 + [ a r:Fact; r:gives {((2 4 8 1) "=<") list:sort (1 2 4 8)}] + [ a r:Fact; r:gives {((2 4 8 1) ">=") list:sort (8 4 2 1)}] + skolem:lemma4314 + skolem:lemma4315 + [ a r:Fact; r:gives {(8421 1248) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2481]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 8 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2481 a r:Inference; + r:gives { + 2482 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2482 math:notEqualTo 0}] + skolem:lemma4842 + [ a r:Fact; r:gives {((2 4 8 2) "=<") list:sort (2 2 4 8)}] + [ a r:Fact; r:gives {((2 4 8 2) ">=") list:sort (8 4 2 2)}] + skolem:lemma4483 + skolem:lemma4484 + [ a r:Fact; r:gives {(8422 2248) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2482]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2482 a r:Inference; + r:gives { + 2483 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2483 math:notEqualTo 0}] + skolem:lemma4843 + [ a r:Fact; r:gives {((2 4 8 3) "=<") list:sort (2 3 4 8)}] + [ a r:Fact; r:gives {((2 4 8 3) ">=") list:sort (8 4 3 2)}] + skolem:lemma4639 + skolem:lemma4640 + [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2483]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2483 a r:Inference; + r:gives { + 2484 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2484 math:notEqualTo 0}] + skolem:lemma4844 + [ a r:Fact; r:gives {((2 4 8 4) "=<") list:sort (2 4 4 8)}] + [ a r:Fact; r:gives {((2 4 8 4) ">=") list:sort (8 4 4 2)}] + skolem:lemma4781 + skolem:lemma4782 + [ a r:Fact; r:gives {(8442 2448) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2484]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 8 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2448]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2484 a r:Inference; + r:gives { + 2485 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2485 math:notEqualTo 0}] + skolem:lemma4845 + [ a r:Fact; r:gives {((2 4 8 5) "=<") list:sort (2 4 5 8)}] + [ a r:Fact; r:gives {((2 4 8 5) ">=") list:sort (8 5 4 2)}] + skolem:lemma4801 + skolem:lemma4802 + [ a r:Fact; r:gives {(8542 2458) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2485]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 8 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2458]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2485 a r:Inference; + r:gives { + 2486 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2486 math:notEqualTo 0}] + skolem:lemma4846 + [ a r:Fact; r:gives {((2 4 8 6) "=<") list:sort (2 4 6 8)}] + [ a r:Fact; r:gives {((2 4 8 6) ">=") list:sort (8 6 4 2)}] + skolem:lemma4819 + skolem:lemma4820 + [ a r:Fact; r:gives {(8642 2468) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2486]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 8 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2468]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2486 a r:Inference; + r:gives { + 2487 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2487 math:notEqualTo 0}] + skolem:lemma4847 + [ a r:Fact; r:gives {((2 4 8 7) "=<") list:sort (2 4 7 8)}] + [ a r:Fact; r:gives {((2 4 8 7) ">=") list:sort (8 7 4 2)}] + skolem:lemma4835 + skolem:lemma4836 + [ a r:Fact; r:gives {(8742 2478) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2487]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 8 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2478]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2487 a r:Inference; + r:gives { + 2488 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2488 math:notEqualTo 0}] + skolem:lemma4848 + [ a r:Fact; r:gives {((2 4 8 8) "=<") list:sort (2 4 8 8)}] + [ a r:Fact; r:gives {((2 4 8 8) ">=") list:sort (8 8 4 2)}] + skolem:lemma4849 + skolem:lemma4850 + [ a r:Fact; r:gives {(8842 2488) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2488]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2488]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8842]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2488 a r:Inference; + r:gives { + 2489 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2489 math:notEqualTo 0}] + skolem:lemma4851 + [ a r:Fact; r:gives {((2 4 8 9) "=<") list:sort (2 4 8 9)}] + [ a r:Fact; r:gives {((2 4 8 9) ">=") list:sort (9 8 4 2)}] + skolem:lemma4852 + skolem:lemma4853 + [ a r:Fact; r:gives {(9842 2489) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2489]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2489]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9842]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2489 a r:Inference; + r:gives { + 2490 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2490 math:notEqualTo 0}] + skolem:lemma4854 + [ a r:Fact; r:gives {((2 4 9 0) "=<") list:sort (0 2 4 9)}] + [ a r:Fact; r:gives {((2 4 9 0) ">=") list:sort (9 4 2 0)}] + skolem:lemma4127 + skolem:lemma4128 + [ a r:Fact; r:gives {(9420 249) math:difference 9171}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9171 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9171 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2490]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 9 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2490 a r:Inference; + r:gives { + 2491 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2491 math:notEqualTo 0}] + skolem:lemma4855 + [ a r:Fact; r:gives {((2 4 9 1) "=<") list:sort (1 2 4 9)}] + [ a r:Fact; r:gives {((2 4 9 1) ">=") list:sort (9 4 2 1)}] + skolem:lemma4317 + skolem:lemma4318 + [ a r:Fact; r:gives {(9421 1249) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2491]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 9 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2491 a r:Inference; + r:gives { + 2492 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2492 math:notEqualTo 0}] + skolem:lemma4856 + [ a r:Fact; r:gives {((2 4 9 2) "=<") list:sort (2 2 4 9)}] + [ a r:Fact; r:gives {((2 4 9 2) ">=") list:sort (9 4 2 2)}] + skolem:lemma4486 + skolem:lemma4487 + [ a r:Fact; r:gives {(9422 2249) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2492]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 9 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2492 a r:Inference; + r:gives { + 2493 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2493 math:notEqualTo 0}] + skolem:lemma4857 + [ a r:Fact; r:gives {((2 4 9 3) "=<") list:sort (2 3 4 9)}] + [ a r:Fact; r:gives {((2 4 9 3) ">=") list:sort (9 4 3 2)}] + skolem:lemma4642 + skolem:lemma4643 + [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2493]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 9 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2493 a r:Inference; + r:gives { + 2494 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2494 math:notEqualTo 0}] + skolem:lemma4858 + [ a r:Fact; r:gives {((2 4 9 4) "=<") list:sort (2 4 4 9)}] + [ a r:Fact; r:gives {((2 4 9 4) ">=") list:sort (9 4 4 2)}] + skolem:lemma4784 + skolem:lemma4785 + [ a r:Fact; r:gives {(9442 2449) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2494]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 9 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2449]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2494 a r:Inference; + r:gives { + 2495 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2495 math:notEqualTo 0}] + skolem:lemma4859 + [ a r:Fact; r:gives {((2 4 9 5) "=<") list:sort (2 4 5 9)}] + [ a r:Fact; r:gives {((2 4 9 5) ">=") list:sort (9 5 4 2)}] + skolem:lemma4804 + skolem:lemma4805 + [ a r:Fact; r:gives {(9542 2459) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2495]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 9 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2459]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2495 a r:Inference; + r:gives { + 2496 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2496 math:notEqualTo 0}] + skolem:lemma4860 + [ a r:Fact; r:gives {((2 4 9 6) "=<") list:sort (2 4 6 9)}] + [ a r:Fact; r:gives {((2 4 9 6) ">=") list:sort (9 6 4 2)}] + skolem:lemma4822 + skolem:lemma4823 + [ a r:Fact; r:gives {(9642 2469) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2496]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 9 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2469]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2496 a r:Inference; + r:gives { + 2497 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2497 math:notEqualTo 0}] + skolem:lemma4861 + [ a r:Fact; r:gives {((2 4 9 7) "=<") list:sort (2 4 7 9)}] + [ a r:Fact; r:gives {((2 4 9 7) ">=") list:sort (9 7 4 2)}] + skolem:lemma4838 + skolem:lemma4839 + [ a r:Fact; r:gives {(9742 2479) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2497]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 9 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2479]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2497 a r:Inference; + r:gives { + 2498 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2498 math:notEqualTo 0}] + skolem:lemma4862 + [ a r:Fact; r:gives {((2 4 9 8) "=<") list:sort (2 4 8 9)}] + [ a r:Fact; r:gives {((2 4 9 8) ">=") list:sort (9 8 4 2)}] + skolem:lemma4852 + skolem:lemma4853 + [ a r:Fact; r:gives {(9842 2489) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2498]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 9 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2489]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9842]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2498 a r:Inference; + r:gives { + 2499 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2499 math:notEqualTo 0}] + skolem:lemma4863 + [ a r:Fact; r:gives {((2 4 9 9) "=<") list:sort (2 4 9 9)}] + [ a r:Fact; r:gives {((2 4 9 9) ">=") list:sort (9 9 4 2)}] + skolem:lemma4864 + skolem:lemma4865 + [ a r:Fact; r:gives {(9942 2499) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2499]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 4 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2499]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9942]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2499 a r:Inference; + r:gives { + 2500 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2500 math:notEqualTo 0}] + skolem:lemma4866 + [ a r:Fact; r:gives {((2 5 0 0) "=<") list:sort (0 0 2 5)}] + [ a r:Fact; r:gives {((2 5 0 0) ">=") list:sort (5 2 0 0)}] + skolem:lemma4015 + skolem:lemma4016 + [ a r:Fact; r:gives {(5200 25) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2500 a r:Inference; + r:gives { + 2501 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2501 math:notEqualTo 0}] + skolem:lemma4867 + [ a r:Fact; r:gives {((2 5 0 1) "=<") list:sort (0 1 2 5)}] + [ a r:Fact; r:gives {((2 5 0 1) ">=") list:sort (5 2 1 0)}] + skolem:lemma4043 + skolem:lemma4044 + [ a r:Fact; r:gives {(5210 125) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2501]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 0 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2501 a r:Inference; + r:gives { + 2502 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2502 math:notEqualTo 0}] + skolem:lemma4868 + [ a r:Fact; r:gives {((2 5 0 2) "=<") list:sort (0 2 2 5)}] + [ a r:Fact; r:gives {((2 5 0 2) ">=") list:sort (5 2 2 0)}] + skolem:lemma4069 + skolem:lemma4070 + [ a r:Fact; r:gives {(5220 225) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2502]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 0 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2502 a r:Inference; + r:gives { + 2503 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2503 math:notEqualTo 0}] + skolem:lemma4869 + [ a r:Fact; r:gives {((2 5 0 3) "=<") list:sort (0 2 3 5)}] + [ a r:Fact; r:gives {((2 5 0 3) ">=") list:sort (5 3 2 0)}] + skolem:lemma4093 + skolem:lemma4094 + [ a r:Fact; r:gives {(5320 235) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2503]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 0 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2503 a r:Inference; + r:gives { + 2504 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2504 math:notEqualTo 0}] + skolem:lemma4870 + [ a r:Fact; r:gives {((2 5 0 4) "=<") list:sort (0 2 4 5)}] + [ a r:Fact; r:gives {((2 5 0 4) ">=") list:sort (5 4 2 0)}] + skolem:lemma4115 + skolem:lemma4116 + [ a r:Fact; r:gives {(5420 245) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2504]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 0 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2504 a r:Inference; + r:gives { + 2505 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2505 math:notEqualTo 0}] + skolem:lemma4871 + [ a r:Fact; r:gives {((2 5 0 5) "=<") list:sort (0 2 5 5)}] + [ a r:Fact; r:gives {((2 5 0 5) ">=") list:sort (5 5 2 0)}] + skolem:lemma4135 + skolem:lemma4136 + [ a r:Fact; r:gives {(5520 255) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2505]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 0 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2505 a r:Inference; + r:gives { + 2506 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2506 math:notEqualTo 0}] + skolem:lemma4872 + [ a r:Fact; r:gives {((2 5 0 6) "=<") list:sort (0 2 5 6)}] + [ a r:Fact; r:gives {((2 5 0 6) ">=") list:sort (6 5 2 0)}] + skolem:lemma4138 + skolem:lemma4139 + [ a r:Fact; r:gives {(6520 256) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2506]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 0 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2506 a r:Inference; + r:gives { + 2507 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2507 math:notEqualTo 0}] + skolem:lemma4873 + [ a r:Fact; r:gives {((2 5 0 7) "=<") list:sort (0 2 5 7)}] + [ a r:Fact; r:gives {((2 5 0 7) ">=") list:sort (7 5 2 0)}] + skolem:lemma4141 + skolem:lemma4142 + [ a r:Fact; r:gives {(7520 257) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2507]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 0 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2507 a r:Inference; + r:gives { + 2508 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2508 math:notEqualTo 0}] + skolem:lemma4874 + [ a r:Fact; r:gives {((2 5 0 8) "=<") list:sort (0 2 5 8)}] + [ a r:Fact; r:gives {((2 5 0 8) ">=") list:sort (8 5 2 0)}] + skolem:lemma4144 + skolem:lemma4145 + [ a r:Fact; r:gives {(8520 258) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2508]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 0 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2508 a r:Inference; + r:gives { + 2509 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2509 math:notEqualTo 0}] + skolem:lemma4875 + [ a r:Fact; r:gives {((2 5 0 9) "=<") list:sort (0 2 5 9)}] + [ a r:Fact; r:gives {((2 5 0 9) ">=") list:sort (9 5 2 0)}] + skolem:lemma4147 + skolem:lemma4148 + [ a r:Fact; r:gives {(9520 259) math:difference 9261}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9261 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9261 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2509]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 0 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9261]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2509 a r:Inference; + r:gives { + 2510 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2510 math:notEqualTo 0}] + skolem:lemma4876 + [ a r:Fact; r:gives {((2 5 1 0) "=<") list:sort (0 1 2 5)}] + [ a r:Fact; r:gives {((2 5 1 0) ">=") list:sort (5 2 1 0)}] + skolem:lemma4043 + skolem:lemma4044 + [ a r:Fact; r:gives {(5210 125) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2510]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2510 a r:Inference; + r:gives { + 2511 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2511 math:notEqualTo 0}] + skolem:lemma4877 + [ a r:Fact; r:gives {((2 5 1 1) "=<") list:sort (1 1 2 5)}] + [ a r:Fact; r:gives {((2 5 1 1) ">=") list:sort (5 2 1 1)}] + skolem:lemma4233 + skolem:lemma4234 + [ a r:Fact; r:gives {(5211 1125) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2511]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2511 a r:Inference; + r:gives { + 2512 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2512 math:notEqualTo 0}] + skolem:lemma4878 + [ a r:Fact; r:gives {((2 5 1 2) "=<") list:sort (1 2 2 5)}] + [ a r:Fact; r:gives {((2 5 1 2) ">=") list:sort (5 2 2 1)}] + skolem:lemma4259 + skolem:lemma4260 + [ a r:Fact; r:gives {(5221 1225) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2512]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2512 a r:Inference; + r:gives { + 2513 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2513 math:notEqualTo 0}] + skolem:lemma4879 + [ a r:Fact; r:gives {((2 5 1 3) "=<") list:sort (1 2 3 5)}] + [ a r:Fact; r:gives {((2 5 1 3) ">=") list:sort (5 3 2 1)}] + skolem:lemma4283 + skolem:lemma4284 + [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2513]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2513 a r:Inference; + r:gives { + 2514 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2514 math:notEqualTo 0}] + skolem:lemma4880 + [ a r:Fact; r:gives {((2 5 1 4) "=<") list:sort (1 2 4 5)}] + [ a r:Fact; r:gives {((2 5 1 4) ">=") list:sort (5 4 2 1)}] + skolem:lemma4305 + skolem:lemma4306 + [ a r:Fact; r:gives {(5421 1245) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2514]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 1 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2514 a r:Inference; + r:gives { + 2515 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2515 math:notEqualTo 0}] + skolem:lemma4881 + [ a r:Fact; r:gives {((2 5 1 5) "=<") list:sort (1 2 5 5)}] + [ a r:Fact; r:gives {((2 5 1 5) ">=") list:sort (5 5 2 1)}] + skolem:lemma4325 + skolem:lemma4326 + [ a r:Fact; r:gives {(5521 1255) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2515]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 1 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2515 a r:Inference; + r:gives { + 2516 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2516 math:notEqualTo 0}] + skolem:lemma4882 + [ a r:Fact; r:gives {((2 5 1 6) "=<") list:sort (1 2 5 6)}] + [ a r:Fact; r:gives {((2 5 1 6) ">=") list:sort (6 5 2 1)}] + skolem:lemma4328 + skolem:lemma4329 + [ a r:Fact; r:gives {(6521 1256) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2516]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 1 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2516 a r:Inference; + r:gives { + 2517 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2517 math:notEqualTo 0}] + skolem:lemma4883 + [ a r:Fact; r:gives {((2 5 1 7) "=<") list:sort (1 2 5 7)}] + [ a r:Fact; r:gives {((2 5 1 7) ">=") list:sort (7 5 2 1)}] + skolem:lemma4331 + skolem:lemma4332 + [ a r:Fact; r:gives {(7521 1257) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2517]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 1 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2517 a r:Inference; + r:gives { + 2518 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2518 math:notEqualTo 0}] + skolem:lemma4884 + [ a r:Fact; r:gives {((2 5 1 8) "=<") list:sort (1 2 5 8)}] + [ a r:Fact; r:gives {((2 5 1 8) ">=") list:sort (8 5 2 1)}] + skolem:lemma4334 + skolem:lemma4335 + [ a r:Fact; r:gives {(8521 1258) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2518]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 1 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2518 a r:Inference; + r:gives { + 2519 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2519 math:notEqualTo 0}] + skolem:lemma4885 + [ a r:Fact; r:gives {((2 5 1 9) "=<") list:sort (1 2 5 9)}] + [ a r:Fact; r:gives {((2 5 1 9) ">=") list:sort (9 5 2 1)}] + skolem:lemma4337 + skolem:lemma4338 + [ a r:Fact; r:gives {(9521 1259) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2519]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 1 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2519 a r:Inference; + r:gives { + 2520 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2520 math:notEqualTo 0}] + skolem:lemma4886 + [ a r:Fact; r:gives {((2 5 2 0) "=<") list:sort (0 2 2 5)}] + [ a r:Fact; r:gives {((2 5 2 0) ">=") list:sort (5 2 2 0)}] + skolem:lemma4069 + skolem:lemma4070 + [ a r:Fact; r:gives {(5220 225) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2520 a r:Inference; + r:gives { + 2521 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2521 math:notEqualTo 0}] + skolem:lemma4887 + [ a r:Fact; r:gives {((2 5 2 1) "=<") list:sort (1 2 2 5)}] + [ a r:Fact; r:gives {((2 5 2 1) ">=") list:sort (5 2 2 1)}] + skolem:lemma4259 + skolem:lemma4260 + [ a r:Fact; r:gives {(5221 1225) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2521 a r:Inference; + r:gives { + 2522 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2522 math:notEqualTo 0}] + skolem:lemma4888 + [ a r:Fact; r:gives {((2 5 2 2) "=<") list:sort (2 2 2 5)}] + [ a r:Fact; r:gives {((2 5 2 2) ">=") list:sort (5 2 2 2)}] + skolem:lemma4428 + skolem:lemma4429 + [ a r:Fact; r:gives {(5222 2225) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2522 a r:Inference; + r:gives { + 2523 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2523 math:notEqualTo 0}] + skolem:lemma4889 + [ a r:Fact; r:gives {((2 5 2 3) "=<") list:sort (2 2 3 5)}] + [ a r:Fact; r:gives {((2 5 2 3) ">=") list:sort (5 3 2 2)}] + skolem:lemma4452 + skolem:lemma4453 + [ a r:Fact; r:gives {(5322 2235) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2523]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2523 a r:Inference; + r:gives { + 2524 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2524 math:notEqualTo 0}] + skolem:lemma4890 + [ a r:Fact; r:gives {((2 5 2 4) "=<") list:sort (2 2 4 5)}] + [ a r:Fact; r:gives {((2 5 2 4) ">=") list:sort (5 4 2 2)}] + skolem:lemma4474 + skolem:lemma4475 + [ a r:Fact; r:gives {(5422 2245) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2524]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2524 a r:Inference; + r:gives { + 2525 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2525 math:notEqualTo 0}] + skolem:lemma4891 + [ a r:Fact; r:gives {((2 5 2 5) "=<") list:sort (2 2 5 5)}] + [ a r:Fact; r:gives {((2 5 2 5) ">=") list:sort (5 5 2 2)}] + skolem:lemma4494 + skolem:lemma4495 + [ a r:Fact; r:gives {(5522 2255) math:difference 3267}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3267 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 3267 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2525]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2525 a r:Inference; + r:gives { + 2526 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2526 math:notEqualTo 0}] + skolem:lemma4892 + [ a r:Fact; r:gives {((2 5 2 6) "=<") list:sort (2 2 5 6)}] + [ a r:Fact; r:gives {((2 5 2 6) ">=") list:sort (6 5 2 2)}] + skolem:lemma4497 + skolem:lemma4498 + [ a r:Fact; r:gives {(6522 2256) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2526]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2526 a r:Inference; + r:gives { + 2527 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2527 math:notEqualTo 0}] + skolem:lemma4893 + [ a r:Fact; r:gives {((2 5 2 7) "=<") list:sort (2 2 5 7)}] + [ a r:Fact; r:gives {((2 5 2 7) ">=") list:sort (7 5 2 2)}] + skolem:lemma4500 + skolem:lemma4501 + [ a r:Fact; r:gives {(7522 2257) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2527]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2527 a r:Inference; + r:gives { + 2528 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2528 math:notEqualTo 0}] + skolem:lemma4894 + [ a r:Fact; r:gives {((2 5 2 8) "=<") list:sort (2 2 5 8)}] + [ a r:Fact; r:gives {((2 5 2 8) ">=") list:sort (8 5 2 2)}] + skolem:lemma4503 + skolem:lemma4504 + [ a r:Fact; r:gives {(8522 2258) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2528]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2528 a r:Inference; + r:gives { + 2529 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2529 math:notEqualTo 0}] + skolem:lemma4895 + [ a r:Fact; r:gives {((2 5 2 9) "=<") list:sort (2 2 5 9)}] + [ a r:Fact; r:gives {((2 5 2 9) ">=") list:sort (9 5 2 2)}] + skolem:lemma4506 + skolem:lemma4507 + [ a r:Fact; r:gives {(9522 2259) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2529]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2529 a r:Inference; + r:gives { + 2530 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2530 math:notEqualTo 0}] + skolem:lemma4896 + [ a r:Fact; r:gives {((2 5 3 0) "=<") list:sort (0 2 3 5)}] + [ a r:Fact; r:gives {((2 5 3 0) ">=") list:sort (5 3 2 0)}] + skolem:lemma4093 + skolem:lemma4094 + [ a r:Fact; r:gives {(5320 235) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2530 a r:Inference; + r:gives { + 2531 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2531 math:notEqualTo 0}] + skolem:lemma4897 + [ a r:Fact; r:gives {((2 5 3 1) "=<") list:sort (1 2 3 5)}] + [ a r:Fact; r:gives {((2 5 3 1) ">=") list:sort (5 3 2 1)}] + skolem:lemma4283 + skolem:lemma4284 + [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2531 a r:Inference; + r:gives { + 2532 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2532 math:notEqualTo 0}] + skolem:lemma4898 + [ a r:Fact; r:gives {((2 5 3 2) "=<") list:sort (2 2 3 5)}] + [ a r:Fact; r:gives {((2 5 3 2) ">=") list:sort (5 3 2 2)}] + skolem:lemma4452 + skolem:lemma4453 + [ a r:Fact; r:gives {(5322 2235) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2532 a r:Inference; + r:gives { + 2533 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2533 math:notEqualTo 0}] + skolem:lemma4899 + [ a r:Fact; r:gives {((2 5 3 3) "=<") list:sort (2 3 3 5)}] + [ a r:Fact; r:gives {((2 5 3 3) ">=") list:sort (5 3 3 2)}] + skolem:lemma4608 + skolem:lemma4609 + [ a r:Fact; r:gives {(5332 2335) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2533 a r:Inference; + r:gives { + 2534 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2534 math:notEqualTo 0}] + skolem:lemma4900 + [ a r:Fact; r:gives {((2 5 3 4) "=<") list:sort (2 3 4 5)}] + [ a r:Fact; r:gives {((2 5 3 4) ">=") list:sort (5 4 3 2)}] + skolem:lemma4630 + skolem:lemma4631 + [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2534]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2534 a r:Inference; + r:gives { + 2535 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2535 math:notEqualTo 0}] + skolem:lemma4901 + [ a r:Fact; r:gives {((2 5 3 5) "=<") list:sort (2 3 5 5)}] + [ a r:Fact; r:gives {((2 5 3 5) ">=") list:sort (5 5 3 2)}] + skolem:lemma4650 + skolem:lemma4651 + [ a r:Fact; r:gives {(5532 2355) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2535]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2535 a r:Inference; + r:gives { + 2536 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2536 math:notEqualTo 0}] + skolem:lemma4902 + [ a r:Fact; r:gives {((2 5 3 6) "=<") list:sort (2 3 5 6)}] + [ a r:Fact; r:gives {((2 5 3 6) ">=") list:sort (6 5 3 2)}] + skolem:lemma4653 + skolem:lemma4654 + [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2536]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2536 a r:Inference; + r:gives { + 2537 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2537 math:notEqualTo 0}] + skolem:lemma4903 + [ a r:Fact; r:gives {((2 5 3 7) "=<") list:sort (2 3 5 7)}] + [ a r:Fact; r:gives {((2 5 3 7) ">=") list:sort (7 5 3 2)}] + skolem:lemma4656 + skolem:lemma4657 + [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2537]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2537 a r:Inference; + r:gives { + 2538 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2538 math:notEqualTo 0}] + skolem:lemma4904 + [ a r:Fact; r:gives {((2 5 3 8) "=<") list:sort (2 3 5 8)}] + [ a r:Fact; r:gives {((2 5 3 8) ">=") list:sort (8 5 3 2)}] + skolem:lemma4659 + skolem:lemma4660 + [ a r:Fact; r:gives {(8532 2358) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2538]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2538 a r:Inference; + r:gives { + 2539 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2539 math:notEqualTo 0}] + skolem:lemma4905 + [ a r:Fact; r:gives {((2 5 3 9) "=<") list:sort (2 3 5 9)}] + [ a r:Fact; r:gives {((2 5 3 9) ">=") list:sort (9 5 3 2)}] + skolem:lemma4662 + skolem:lemma4663 + [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2539]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2539 a r:Inference; + r:gives { + 2540 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2540 math:notEqualTo 0}] + skolem:lemma4906 + [ a r:Fact; r:gives {((2 5 4 0) "=<") list:sort (0 2 4 5)}] + [ a r:Fact; r:gives {((2 5 4 0) ">=") list:sort (5 4 2 0)}] + skolem:lemma4115 + skolem:lemma4116 + [ a r:Fact; r:gives {(5420 245) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2540]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 4 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2540 a r:Inference; + r:gives { + 2541 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2541 math:notEqualTo 0}] + skolem:lemma4907 + [ a r:Fact; r:gives {((2 5 4 1) "=<") list:sort (1 2 4 5)}] + [ a r:Fact; r:gives {((2 5 4 1) ">=") list:sort (5 4 2 1)}] + skolem:lemma4305 + skolem:lemma4306 + [ a r:Fact; r:gives {(5421 1245) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2541]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 4 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2541 a r:Inference; + r:gives { + 2542 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2542 math:notEqualTo 0}] + skolem:lemma4908 + [ a r:Fact; r:gives {((2 5 4 2) "=<") list:sort (2 2 4 5)}] + [ a r:Fact; r:gives {((2 5 4 2) ">=") list:sort (5 4 2 2)}] + skolem:lemma4474 + skolem:lemma4475 + [ a r:Fact; r:gives {(5422 2245) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2542 a r:Inference; + r:gives { + 2543 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2543 math:notEqualTo 0}] + skolem:lemma4909 + [ a r:Fact; r:gives {((2 5 4 3) "=<") list:sort (2 3 4 5)}] + [ a r:Fact; r:gives {((2 5 4 3) ">=") list:sort (5 4 3 2)}] + skolem:lemma4630 + skolem:lemma4631 + [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2543 a r:Inference; + r:gives { + 2544 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2544 math:notEqualTo 0}] + skolem:lemma4910 + [ a r:Fact; r:gives {((2 5 4 4) "=<") list:sort (2 4 4 5)}] + [ a r:Fact; r:gives {((2 5 4 4) ">=") list:sort (5 4 4 2)}] + skolem:lemma4772 + skolem:lemma4773 + [ a r:Fact; r:gives {(5442 2445) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2544]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2445]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2544 a r:Inference; + r:gives { + 2545 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2545 math:notEqualTo 0}] + skolem:lemma4911 + [ a r:Fact; r:gives {((2 5 4 5) "=<") list:sort (2 4 5 5)}] + [ a r:Fact; r:gives {((2 5 4 5) ">=") list:sort (5 5 4 2)}] + skolem:lemma4792 + skolem:lemma4793 + [ a r:Fact; r:gives {(5542 2455) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2545]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2455]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2545 a r:Inference; + r:gives { + 2546 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2546 math:notEqualTo 0}] + skolem:lemma4912 + [ a r:Fact; r:gives {((2 5 4 6) "=<") list:sort (2 4 5 6)}] + [ a r:Fact; r:gives {((2 5 4 6) ">=") list:sort (6 5 4 2)}] + skolem:lemma4795 + skolem:lemma4796 + [ a r:Fact; r:gives {(6542 2456) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2546]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2546 a r:Inference; + r:gives { + 2547 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2547 math:notEqualTo 0}] + skolem:lemma4913 + [ a r:Fact; r:gives {((2 5 4 7) "=<") list:sort (2 4 5 7)}] + [ a r:Fact; r:gives {((2 5 4 7) ">=") list:sort (7 5 4 2)}] + skolem:lemma4798 + skolem:lemma4799 + [ a r:Fact; r:gives {(7542 2457) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2547]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2457]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2547 a r:Inference; + r:gives { + 2548 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2548 math:notEqualTo 0}] + skolem:lemma4914 + [ a r:Fact; r:gives {((2 5 4 8) "=<") list:sort (2 4 5 8)}] + [ a r:Fact; r:gives {((2 5 4 8) ">=") list:sort (8 5 4 2)}] + skolem:lemma4801 + skolem:lemma4802 + [ a r:Fact; r:gives {(8542 2458) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2548]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2458]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2548 a r:Inference; + r:gives { + 2549 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2549 math:notEqualTo 0}] + skolem:lemma4915 + [ a r:Fact; r:gives {((2 5 4 9) "=<") list:sort (2 4 5 9)}] + [ a r:Fact; r:gives {((2 5 4 9) ">=") list:sort (9 5 4 2)}] + skolem:lemma4804 + skolem:lemma4805 + [ a r:Fact; r:gives {(9542 2459) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2549]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2459]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2549 a r:Inference; + r:gives { + 2550 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2550 math:notEqualTo 0}] + skolem:lemma4916 + [ a r:Fact; r:gives {((2 5 5 0) "=<") list:sort (0 2 5 5)}] + [ a r:Fact; r:gives {((2 5 5 0) ">=") list:sort (5 5 2 0)}] + skolem:lemma4135 + skolem:lemma4136 + [ a r:Fact; r:gives {(5520 255) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2550]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 5 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2550 a r:Inference; + r:gives { + 2551 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2551 math:notEqualTo 0}] + skolem:lemma4917 + [ a r:Fact; r:gives {((2 5 5 1) "=<") list:sort (1 2 5 5)}] + [ a r:Fact; r:gives {((2 5 5 1) ">=") list:sort (5 5 2 1)}] + skolem:lemma4325 + skolem:lemma4326 + [ a r:Fact; r:gives {(5521 1255) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2551]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 5 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2551 a r:Inference; + r:gives { + 2552 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2552 math:notEqualTo 0}] + skolem:lemma4918 + [ a r:Fact; r:gives {((2 5 5 2) "=<") list:sort (2 2 5 5)}] + [ a r:Fact; r:gives {((2 5 5 2) ">=") list:sort (5 5 2 2)}] + skolem:lemma4494 + skolem:lemma4495 + [ a r:Fact; r:gives {(5522 2255) math:difference 3267}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3267 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 3267 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2552 a r:Inference; + r:gives { + 2553 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2553 math:notEqualTo 0}] + skolem:lemma4919 + [ a r:Fact; r:gives {((2 5 5 3) "=<") list:sort (2 3 5 5)}] + [ a r:Fact; r:gives {((2 5 5 3) ">=") list:sort (5 5 3 2)}] + skolem:lemma4650 + skolem:lemma4651 + [ a r:Fact; r:gives {(5532 2355) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2553 a r:Inference; + r:gives { + 2554 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2554 math:notEqualTo 0}] + skolem:lemma4920 + [ a r:Fact; r:gives {((2 5 5 4) "=<") list:sort (2 4 5 5)}] + [ a r:Fact; r:gives {((2 5 5 4) ">=") list:sort (5 5 4 2)}] + skolem:lemma4792 + skolem:lemma4793 + [ a r:Fact; r:gives {(5542 2455) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2554]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 5 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2455]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2554 a r:Inference; + r:gives { + 2555 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2555 math:notEqualTo 0}] + skolem:lemma4921 + [ a r:Fact; r:gives {((2 5 5 5) "=<") list:sort (2 5 5 5)}] + [ a r:Fact; r:gives {((2 5 5 5) ">=") list:sort (5 5 5 2)}] + skolem:lemma4922 + skolem:lemma4923 + [ a r:Fact; r:gives {(5552 2555) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2555]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2555]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2555 a r:Inference; + r:gives { + 2556 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2556 math:notEqualTo 0}] + skolem:lemma4924 + [ a r:Fact; r:gives {((2 5 5 6) "=<") list:sort (2 5 5 6)}] + [ a r:Fact; r:gives {((2 5 5 6) ">=") list:sort (6 5 5 2)}] + skolem:lemma4925 + skolem:lemma4926 + [ a r:Fact; r:gives {(6552 2556) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2556]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2556]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2556 a r:Inference; + r:gives { + 2557 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2557 math:notEqualTo 0}] + skolem:lemma4927 + [ a r:Fact; r:gives {((2 5 5 7) "=<") list:sort (2 5 5 7)}] + [ a r:Fact; r:gives {((2 5 5 7) ">=") list:sort (7 5 5 2)}] + skolem:lemma4928 + skolem:lemma4929 + [ a r:Fact; r:gives {(7552 2557) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2557]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2557]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2557 a r:Inference; + r:gives { + 2558 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2558 math:notEqualTo 0}] + skolem:lemma4930 + [ a r:Fact; r:gives {((2 5 5 8) "=<") list:sort (2 5 5 8)}] + [ a r:Fact; r:gives {((2 5 5 8) ">=") list:sort (8 5 5 2)}] + skolem:lemma4931 + skolem:lemma4932 + [ a r:Fact; r:gives {(8552 2558) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2558]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2558]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2558 a r:Inference; + r:gives { + 2559 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2559 math:notEqualTo 0}] + skolem:lemma4933 + [ a r:Fact; r:gives {((2 5 5 9) "=<") list:sort (2 5 5 9)}] + [ a r:Fact; r:gives {((2 5 5 9) ">=") list:sort (9 5 5 2)}] + skolem:lemma4934 + skolem:lemma4935 + [ a r:Fact; r:gives {(9552 2559) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2559]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2559]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2559 a r:Inference; + r:gives { + 2560 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2560 math:notEqualTo 0}] + skolem:lemma4936 + [ a r:Fact; r:gives {((2 5 6 0) "=<") list:sort (0 2 5 6)}] + [ a r:Fact; r:gives {((2 5 6 0) ">=") list:sort (6 5 2 0)}] + skolem:lemma4138 + skolem:lemma4139 + [ a r:Fact; r:gives {(6520 256) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2560]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 6 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2560 a r:Inference; + r:gives { + 2561 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2561 math:notEqualTo 0}] + skolem:lemma4937 + [ a r:Fact; r:gives {((2 5 6 1) "=<") list:sort (1 2 5 6)}] + [ a r:Fact; r:gives {((2 5 6 1) ">=") list:sort (6 5 2 1)}] + skolem:lemma4328 + skolem:lemma4329 + [ a r:Fact; r:gives {(6521 1256) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2561]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 6 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2561 a r:Inference; + r:gives { + 2562 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2562 math:notEqualTo 0}] + skolem:lemma4938 + [ a r:Fact; r:gives {((2 5 6 2) "=<") list:sort (2 2 5 6)}] + [ a r:Fact; r:gives {((2 5 6 2) ">=") list:sort (6 5 2 2)}] + skolem:lemma4497 + skolem:lemma4498 + [ a r:Fact; r:gives {(6522 2256) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2562]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2562 a r:Inference; + r:gives { + 2563 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2563 math:notEqualTo 0}] + skolem:lemma4939 + [ a r:Fact; r:gives {((2 5 6 3) "=<") list:sort (2 3 5 6)}] + [ a r:Fact; r:gives {((2 5 6 3) ">=") list:sort (6 5 3 2)}] + skolem:lemma4653 + skolem:lemma4654 + [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2563]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2563 a r:Inference; + r:gives { + 2564 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2564 math:notEqualTo 0}] + skolem:lemma4940 + [ a r:Fact; r:gives {((2 5 6 4) "=<") list:sort (2 4 5 6)}] + [ a r:Fact; r:gives {((2 5 6 4) ">=") list:sort (6 5 4 2)}] + skolem:lemma4795 + skolem:lemma4796 + [ a r:Fact; r:gives {(6542 2456) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2564]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 6 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2564 a r:Inference; + r:gives { + 2565 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2565 math:notEqualTo 0}] + skolem:lemma4941 + [ a r:Fact; r:gives {((2 5 6 5) "=<") list:sort (2 5 5 6)}] + [ a r:Fact; r:gives {((2 5 6 5) ">=") list:sort (6 5 5 2)}] + skolem:lemma4925 + skolem:lemma4926 + [ a r:Fact; r:gives {(6552 2556) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2565]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 6 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2556]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2565 a r:Inference; + r:gives { + 2566 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2566 math:notEqualTo 0}] + skolem:lemma4942 + [ a r:Fact; r:gives {((2 5 6 6) "=<") list:sort (2 5 6 6)}] + [ a r:Fact; r:gives {((2 5 6 6) ">=") list:sort (6 6 5 2)}] + skolem:lemma4943 + skolem:lemma4944 + [ a r:Fact; r:gives {(6652 2566) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2566]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2566]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2566 a r:Inference; + r:gives { + 2567 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2567 math:notEqualTo 0}] + skolem:lemma4945 + [ a r:Fact; r:gives {((2 5 6 7) "=<") list:sort (2 5 6 7)}] + [ a r:Fact; r:gives {((2 5 6 7) ">=") list:sort (7 6 5 2)}] + skolem:lemma4946 + skolem:lemma4947 + [ a r:Fact; r:gives {(7652 2567) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2567]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2567]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2567 a r:Inference; + r:gives { + 2568 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2568 math:notEqualTo 0}] + skolem:lemma4948 + [ a r:Fact; r:gives {((2 5 6 8) "=<") list:sort (2 5 6 8)}] + [ a r:Fact; r:gives {((2 5 6 8) ">=") list:sort (8 6 5 2)}] + skolem:lemma4949 + skolem:lemma4950 + [ a r:Fact; r:gives {(8652 2568) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2568]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2568]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2568 a r:Inference; + r:gives { + 2569 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2569 math:notEqualTo 0}] + skolem:lemma4951 + [ a r:Fact; r:gives {((2 5 6 9) "=<") list:sort (2 5 6 9)}] + [ a r:Fact; r:gives {((2 5 6 9) ">=") list:sort (9 6 5 2)}] + skolem:lemma4952 + skolem:lemma4953 + [ a r:Fact; r:gives {(9652 2569) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2569]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2569]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2569 a r:Inference; + r:gives { + 2570 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2570 math:notEqualTo 0}] + skolem:lemma4954 + [ a r:Fact; r:gives {((2 5 7 0) "=<") list:sort (0 2 5 7)}] + [ a r:Fact; r:gives {((2 5 7 0) ">=") list:sort (7 5 2 0)}] + skolem:lemma4141 + skolem:lemma4142 + [ a r:Fact; r:gives {(7520 257) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2570]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 7 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2570 a r:Inference; + r:gives { + 2571 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2571 math:notEqualTo 0}] + skolem:lemma4955 + [ a r:Fact; r:gives {((2 5 7 1) "=<") list:sort (1 2 5 7)}] + [ a r:Fact; r:gives {((2 5 7 1) ">=") list:sort (7 5 2 1)}] + skolem:lemma4331 + skolem:lemma4332 + [ a r:Fact; r:gives {(7521 1257) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2571]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 7 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2571 a r:Inference; + r:gives { + 2572 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2572 math:notEqualTo 0}] + skolem:lemma4956 + [ a r:Fact; r:gives {((2 5 7 2) "=<") list:sort (2 2 5 7)}] + [ a r:Fact; r:gives {((2 5 7 2) ">=") list:sort (7 5 2 2)}] + skolem:lemma4500 + skolem:lemma4501 + [ a r:Fact; r:gives {(7522 2257) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2572]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2572 a r:Inference; + r:gives { + 2573 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2573 math:notEqualTo 0}] + skolem:lemma4957 + [ a r:Fact; r:gives {((2 5 7 3) "=<") list:sort (2 3 5 7)}] + [ a r:Fact; r:gives {((2 5 7 3) ">=") list:sort (7 5 3 2)}] + skolem:lemma4656 + skolem:lemma4657 + [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2573]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2573 a r:Inference; + r:gives { + 2574 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2574 math:notEqualTo 0}] + skolem:lemma4958 + [ a r:Fact; r:gives {((2 5 7 4) "=<") list:sort (2 4 5 7)}] + [ a r:Fact; r:gives {((2 5 7 4) ">=") list:sort (7 5 4 2)}] + skolem:lemma4798 + skolem:lemma4799 + [ a r:Fact; r:gives {(7542 2457) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2574]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 7 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2457]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2574 a r:Inference; + r:gives { + 2575 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2575 math:notEqualTo 0}] + skolem:lemma4959 + [ a r:Fact; r:gives {((2 5 7 5) "=<") list:sort (2 5 5 7)}] + [ a r:Fact; r:gives {((2 5 7 5) ">=") list:sort (7 5 5 2)}] + skolem:lemma4928 + skolem:lemma4929 + [ a r:Fact; r:gives {(7552 2557) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2575]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 7 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2557]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2575 a r:Inference; + r:gives { + 2576 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2576 math:notEqualTo 0}] + skolem:lemma4960 + [ a r:Fact; r:gives {((2 5 7 6) "=<") list:sort (2 5 6 7)}] + [ a r:Fact; r:gives {((2 5 7 6) ">=") list:sort (7 6 5 2)}] + skolem:lemma4946 + skolem:lemma4947 + [ a r:Fact; r:gives {(7652 2567) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2576]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 7 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2567]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2576 a r:Inference; + r:gives { + 2577 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2577 math:notEqualTo 0}] + skolem:lemma4961 + [ a r:Fact; r:gives {((2 5 7 7) "=<") list:sort (2 5 7 7)}] + [ a r:Fact; r:gives {((2 5 7 7) ">=") list:sort (7 7 5 2)}] + skolem:lemma4962 + skolem:lemma4963 + [ a r:Fact; r:gives {(7752 2577) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2577]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2577]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2577 a r:Inference; + r:gives { + 2578 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2578 math:notEqualTo 0}] + skolem:lemma4964 + [ a r:Fact; r:gives {((2 5 7 8) "=<") list:sort (2 5 7 8)}] + [ a r:Fact; r:gives {((2 5 7 8) ">=") list:sort (8 7 5 2)}] + skolem:lemma4965 + skolem:lemma4966 + [ a r:Fact; r:gives {(8752 2578) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2578]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2578]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2578 a r:Inference; + r:gives { + 2579 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2579 math:notEqualTo 0}] + skolem:lemma4967 + [ a r:Fact; r:gives {((2 5 7 9) "=<") list:sort (2 5 7 9)}] + [ a r:Fact; r:gives {((2 5 7 9) ">=") list:sort (9 7 5 2)}] + skolem:lemma4968 + skolem:lemma4969 + [ a r:Fact; r:gives {(9752 2579) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2579]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2579]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2579 a r:Inference; + r:gives { + 2580 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2580 math:notEqualTo 0}] + skolem:lemma4970 + [ a r:Fact; r:gives {((2 5 8 0) "=<") list:sort (0 2 5 8)}] + [ a r:Fact; r:gives {((2 5 8 0) ">=") list:sort (8 5 2 0)}] + skolem:lemma4144 + skolem:lemma4145 + [ a r:Fact; r:gives {(8520 258) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2580]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 8 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2580 a r:Inference; + r:gives { + 2581 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2581 math:notEqualTo 0}] + skolem:lemma4971 + [ a r:Fact; r:gives {((2 5 8 1) "=<") list:sort (1 2 5 8)}] + [ a r:Fact; r:gives {((2 5 8 1) ">=") list:sort (8 5 2 1)}] + skolem:lemma4334 + skolem:lemma4335 + [ a r:Fact; r:gives {(8521 1258) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2581]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 8 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2581 a r:Inference; + r:gives { + 2582 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2582 math:notEqualTo 0}] + skolem:lemma4972 + [ a r:Fact; r:gives {((2 5 8 2) "=<") list:sort (2 2 5 8)}] + [ a r:Fact; r:gives {((2 5 8 2) ">=") list:sort (8 5 2 2)}] + skolem:lemma4503 + skolem:lemma4504 + [ a r:Fact; r:gives {(8522 2258) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2582]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2582 a r:Inference; + r:gives { + 2583 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2583 math:notEqualTo 0}] + skolem:lemma4973 + [ a r:Fact; r:gives {((2 5 8 3) "=<") list:sort (2 3 5 8)}] + [ a r:Fact; r:gives {((2 5 8 3) ">=") list:sort (8 5 3 2)}] + skolem:lemma4659 + skolem:lemma4660 + [ a r:Fact; r:gives {(8532 2358) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2583]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2583 a r:Inference; + r:gives { + 2584 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2584 math:notEqualTo 0}] + skolem:lemma4974 + [ a r:Fact; r:gives {((2 5 8 4) "=<") list:sort (2 4 5 8)}] + [ a r:Fact; r:gives {((2 5 8 4) ">=") list:sort (8 5 4 2)}] + skolem:lemma4801 + skolem:lemma4802 + [ a r:Fact; r:gives {(8542 2458) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2584]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 8 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2458]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2584 a r:Inference; + r:gives { + 2585 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2585 math:notEqualTo 0}] + skolem:lemma4975 + [ a r:Fact; r:gives {((2 5 8 5) "=<") list:sort (2 5 5 8)}] + [ a r:Fact; r:gives {((2 5 8 5) ">=") list:sort (8 5 5 2)}] + skolem:lemma4931 + skolem:lemma4932 + [ a r:Fact; r:gives {(8552 2558) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2585]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 8 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2558]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2585 a r:Inference; + r:gives { + 2586 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2586 math:notEqualTo 0}] + skolem:lemma4976 + [ a r:Fact; r:gives {((2 5 8 6) "=<") list:sort (2 5 6 8)}] + [ a r:Fact; r:gives {((2 5 8 6) ">=") list:sort (8 6 5 2)}] + skolem:lemma4949 + skolem:lemma4950 + [ a r:Fact; r:gives {(8652 2568) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2586]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 8 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2568]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2586 a r:Inference; + r:gives { + 2587 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2587 math:notEqualTo 0}] + skolem:lemma4977 + [ a r:Fact; r:gives {((2 5 8 7) "=<") list:sort (2 5 7 8)}] + [ a r:Fact; r:gives {((2 5 8 7) ">=") list:sort (8 7 5 2)}] + skolem:lemma4965 + skolem:lemma4966 + [ a r:Fact; r:gives {(8752 2578) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2587]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 8 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2578]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2587 a r:Inference; + r:gives { + 2588 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2588 math:notEqualTo 0}] + skolem:lemma4978 + [ a r:Fact; r:gives {((2 5 8 8) "=<") list:sort (2 5 8 8)}] + [ a r:Fact; r:gives {((2 5 8 8) ">=") list:sort (8 8 5 2)}] + skolem:lemma4979 + skolem:lemma4980 + [ a r:Fact; r:gives {(8852 2588) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2588]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2588]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8852]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2588 a r:Inference; + r:gives { + 2589 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2589 math:notEqualTo 0}] + skolem:lemma4981 + [ a r:Fact; r:gives {((2 5 8 9) "=<") list:sort (2 5 8 9)}] + [ a r:Fact; r:gives {((2 5 8 9) ">=") list:sort (9 8 5 2)}] + skolem:lemma4982 + skolem:lemma4983 + [ a r:Fact; r:gives {(9852 2589) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2589]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2589]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9852]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2589 a r:Inference; + r:gives { + 2590 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2590 math:notEqualTo 0}] + skolem:lemma4984 + [ a r:Fact; r:gives {((2 5 9 0) "=<") list:sort (0 2 5 9)}] + [ a r:Fact; r:gives {((2 5 9 0) ">=") list:sort (9 5 2 0)}] + skolem:lemma4147 + skolem:lemma4148 + [ a r:Fact; r:gives {(9520 259) math:difference 9261}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9261 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9261 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2590]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 9 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9261]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2590 a r:Inference; + r:gives { + 2591 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2591 math:notEqualTo 0}] + skolem:lemma4985 + [ a r:Fact; r:gives {((2 5 9 1) "=<") list:sort (1 2 5 9)}] + [ a r:Fact; r:gives {((2 5 9 1) ">=") list:sort (9 5 2 1)}] + skolem:lemma4337 + skolem:lemma4338 + [ a r:Fact; r:gives {(9521 1259) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2591]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 9 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2591 a r:Inference; + r:gives { + 2592 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2592 math:notEqualTo 0}] + skolem:lemma4986 + [ a r:Fact; r:gives {((2 5 9 2) "=<") list:sort (2 2 5 9)}] + [ a r:Fact; r:gives {((2 5 9 2) ">=") list:sort (9 5 2 2)}] + skolem:lemma4506 + skolem:lemma4507 + [ a r:Fact; r:gives {(9522 2259) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2592]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 9 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2592 a r:Inference; + r:gives { + 2593 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2593 math:notEqualTo 0}] + skolem:lemma4987 + [ a r:Fact; r:gives {((2 5 9 3) "=<") list:sort (2 3 5 9)}] + [ a r:Fact; r:gives {((2 5 9 3) ">=") list:sort (9 5 3 2)}] + skolem:lemma4662 + skolem:lemma4663 + [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2593]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 9 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2593 a r:Inference; + r:gives { + 2594 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2594 math:notEqualTo 0}] + skolem:lemma4988 + [ a r:Fact; r:gives {((2 5 9 4) "=<") list:sort (2 4 5 9)}] + [ a r:Fact; r:gives {((2 5 9 4) ">=") list:sort (9 5 4 2)}] + skolem:lemma4804 + skolem:lemma4805 + [ a r:Fact; r:gives {(9542 2459) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2594]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 9 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2459]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2594 a r:Inference; + r:gives { + 2595 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2595 math:notEqualTo 0}] + skolem:lemma4989 + [ a r:Fact; r:gives {((2 5 9 5) "=<") list:sort (2 5 5 9)}] + [ a r:Fact; r:gives {((2 5 9 5) ">=") list:sort (9 5 5 2)}] + skolem:lemma4934 + skolem:lemma4935 + [ a r:Fact; r:gives {(9552 2559) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2595]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 9 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2559]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2595 a r:Inference; + r:gives { + 2596 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2596 math:notEqualTo 0}] + skolem:lemma4990 + [ a r:Fact; r:gives {((2 5 9 6) "=<") list:sort (2 5 6 9)}] + [ a r:Fact; r:gives {((2 5 9 6) ">=") list:sort (9 6 5 2)}] + skolem:lemma4952 + skolem:lemma4953 + [ a r:Fact; r:gives {(9652 2569) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2596]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 9 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2569]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2596 a r:Inference; + r:gives { + 2597 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2597 math:notEqualTo 0}] + skolem:lemma4991 + [ a r:Fact; r:gives {((2 5 9 7) "=<") list:sort (2 5 7 9)}] + [ a r:Fact; r:gives {((2 5 9 7) ">=") list:sort (9 7 5 2)}] + skolem:lemma4968 + skolem:lemma4969 + [ a r:Fact; r:gives {(9752 2579) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2597]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 9 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2579]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2597 a r:Inference; + r:gives { + 2598 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2598 math:notEqualTo 0}] + skolem:lemma4992 + [ a r:Fact; r:gives {((2 5 9 8) "=<") list:sort (2 5 8 9)}] + [ a r:Fact; r:gives {((2 5 9 8) ">=") list:sort (9 8 5 2)}] + skolem:lemma4982 + skolem:lemma4983 + [ a r:Fact; r:gives {(9852 2589) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2598]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 9 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2589]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9852]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2598 a r:Inference; + r:gives { + 2599 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2599 math:notEqualTo 0}] + skolem:lemma4993 + [ a r:Fact; r:gives {((2 5 9 9) "=<") list:sort (2 5 9 9)}] + [ a r:Fact; r:gives {((2 5 9 9) ">=") list:sort (9 9 5 2)}] + skolem:lemma4994 + skolem:lemma4995 + [ a r:Fact; r:gives {(9952 2599) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2599]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 5 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2599]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9952]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2599 a r:Inference; + r:gives { + 2600 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2600 math:notEqualTo 0}] + skolem:lemma4996 + [ a r:Fact; r:gives {((2 6 0 0) "=<") list:sort (0 0 2 6)}] + [ a r:Fact; r:gives {((2 6 0 0) ">=") list:sort (6 2 0 0)}] + skolem:lemma4018 + skolem:lemma4019 + [ a r:Fact; r:gives {(6200 26) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2600 a r:Inference; + r:gives { + 2601 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2601 math:notEqualTo 0}] + skolem:lemma4997 + [ a r:Fact; r:gives {((2 6 0 1) "=<") list:sort (0 1 2 6)}] + [ a r:Fact; r:gives {((2 6 0 1) ">=") list:sort (6 2 1 0)}] + skolem:lemma4046 + skolem:lemma4047 + [ a r:Fact; r:gives {(6210 126) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2601]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 0 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2601 a r:Inference; + r:gives { + 2602 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2602 math:notEqualTo 0}] + skolem:lemma4998 + [ a r:Fact; r:gives {((2 6 0 2) "=<") list:sort (0 2 2 6)}] + [ a r:Fact; r:gives {((2 6 0 2) ">=") list:sort (6 2 2 0)}] + skolem:lemma4072 + skolem:lemma4073 + [ a r:Fact; r:gives {(6220 226) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2602]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 0 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2602 a r:Inference; + r:gives { + 2603 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2603 math:notEqualTo 0}] + skolem:lemma4999 + [ a r:Fact; r:gives {((2 6 0 3) "=<") list:sort (0 2 3 6)}] + [ a r:Fact; r:gives {((2 6 0 3) ">=") list:sort (6 3 2 0)}] + skolem:lemma4096 + skolem:lemma4097 + [ a r:Fact; r:gives {(6320 236) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2603]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 0 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2603 a r:Inference; + r:gives { + 2604 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2604 math:notEqualTo 0}] + skolem:lemma5000 + [ a r:Fact; r:gives {((2 6 0 4) "=<") list:sort (0 2 4 6)}] + [ a r:Fact; r:gives {((2 6 0 4) ">=") list:sort (6 4 2 0)}] + skolem:lemma4118 + skolem:lemma4119 + [ a r:Fact; r:gives {(6420 246) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2604]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 0 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2604 a r:Inference; + r:gives { + 2605 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2605 math:notEqualTo 0}] + skolem:lemma5001 + [ a r:Fact; r:gives {((2 6 0 5) "=<") list:sort (0 2 5 6)}] + [ a r:Fact; r:gives {((2 6 0 5) ">=") list:sort (6 5 2 0)}] + skolem:lemma4138 + skolem:lemma4139 + [ a r:Fact; r:gives {(6520 256) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2605]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 0 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2605 a r:Inference; + r:gives { + 2606 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2606 math:notEqualTo 0}] + skolem:lemma5002 + [ a r:Fact; r:gives {((2 6 0 6) "=<") list:sort (0 2 6 6)}] + [ a r:Fact; r:gives {((2 6 0 6) ">=") list:sort (6 6 2 0)}] + skolem:lemma4156 + skolem:lemma4157 + [ a r:Fact; r:gives {(6620 266) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2606]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 0 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2606 a r:Inference; + r:gives { + 2607 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2607 math:notEqualTo 0}] + skolem:lemma5003 + [ a r:Fact; r:gives {((2 6 0 7) "=<") list:sort (0 2 6 7)}] + [ a r:Fact; r:gives {((2 6 0 7) ">=") list:sort (7 6 2 0)}] + skolem:lemma4159 + skolem:lemma4160 + [ a r:Fact; r:gives {(7620 267) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2607]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 0 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2607 a r:Inference; + r:gives { + 2608 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2608 math:notEqualTo 0}] + skolem:lemma5004 + [ a r:Fact; r:gives {((2 6 0 8) "=<") list:sort (0 2 6 8)}] + [ a r:Fact; r:gives {((2 6 0 8) ">=") list:sort (8 6 2 0)}] + skolem:lemma4162 + skolem:lemma4163 + [ a r:Fact; r:gives {(8620 268) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2608]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 0 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2608 a r:Inference; + r:gives { + 2609 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2609 math:notEqualTo 0}] + skolem:lemma5005 + [ a r:Fact; r:gives {((2 6 0 9) "=<") list:sort (0 2 6 9)}] + [ a r:Fact; r:gives {((2 6 0 9) ">=") list:sort (9 6 2 0)}] + skolem:lemma4165 + skolem:lemma4166 + [ a r:Fact; r:gives {(9620 269) math:difference 9351}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9351 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9351 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2609]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 0 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9351]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2609 a r:Inference; + r:gives { + 2610 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2610 math:notEqualTo 0}] + skolem:lemma5006 + [ a r:Fact; r:gives {((2 6 1 0) "=<") list:sort (0 1 2 6)}] + [ a r:Fact; r:gives {((2 6 1 0) ">=") list:sort (6 2 1 0)}] + skolem:lemma4046 + skolem:lemma4047 + [ a r:Fact; r:gives {(6210 126) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2610]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2610 a r:Inference; + r:gives { + 2611 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2611 math:notEqualTo 0}] + skolem:lemma5007 + [ a r:Fact; r:gives {((2 6 1 1) "=<") list:sort (1 1 2 6)}] + [ a r:Fact; r:gives {((2 6 1 1) ">=") list:sort (6 2 1 1)}] + skolem:lemma4236 + skolem:lemma4237 + [ a r:Fact; r:gives {(6211 1126) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2611]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2611 a r:Inference; + r:gives { + 2612 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2612 math:notEqualTo 0}] + skolem:lemma5008 + [ a r:Fact; r:gives {((2 6 1 2) "=<") list:sort (1 2 2 6)}] + [ a r:Fact; r:gives {((2 6 1 2) ">=") list:sort (6 2 2 1)}] + skolem:lemma4262 + skolem:lemma4263 + [ a r:Fact; r:gives {(6221 1226) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2612]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2612 a r:Inference; + r:gives { + 2613 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2613 math:notEqualTo 0}] + skolem:lemma5009 + [ a r:Fact; r:gives {((2 6 1 3) "=<") list:sort (1 2 3 6)}] + [ a r:Fact; r:gives {((2 6 1 3) ">=") list:sort (6 3 2 1)}] + skolem:lemma4286 + skolem:lemma4287 + [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2613]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2613 a r:Inference; + r:gives { + 2614 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2614 math:notEqualTo 0}] + skolem:lemma5010 + [ a r:Fact; r:gives {((2 6 1 4) "=<") list:sort (1 2 4 6)}] + [ a r:Fact; r:gives {((2 6 1 4) ">=") list:sort (6 4 2 1)}] + skolem:lemma4308 + skolem:lemma4309 + [ a r:Fact; r:gives {(6421 1246) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2614]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 1 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2614 a r:Inference; + r:gives { + 2615 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2615 math:notEqualTo 0}] + skolem:lemma5011 + [ a r:Fact; r:gives {((2 6 1 5) "=<") list:sort (1 2 5 6)}] + [ a r:Fact; r:gives {((2 6 1 5) ">=") list:sort (6 5 2 1)}] + skolem:lemma4328 + skolem:lemma4329 + [ a r:Fact; r:gives {(6521 1256) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2615]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 1 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2615 a r:Inference; + r:gives { + 2616 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2616 math:notEqualTo 0}] + skolem:lemma5012 + [ a r:Fact; r:gives {((2 6 1 6) "=<") list:sort (1 2 6 6)}] + [ a r:Fact; r:gives {((2 6 1 6) ">=") list:sort (6 6 2 1)}] + skolem:lemma4346 + skolem:lemma4347 + [ a r:Fact; r:gives {(6621 1266) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2616]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 1 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2616 a r:Inference; + r:gives { + 2617 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2617 math:notEqualTo 0}] + skolem:lemma5013 + [ a r:Fact; r:gives {((2 6 1 7) "=<") list:sort (1 2 6 7)}] + [ a r:Fact; r:gives {((2 6 1 7) ">=") list:sort (7 6 2 1)}] + skolem:lemma4349 + skolem:lemma4350 + [ a r:Fact; r:gives {(7621 1267) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2617]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 1 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2617 a r:Inference; + r:gives { + 2618 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2618 math:notEqualTo 0}] + skolem:lemma5014 + [ a r:Fact; r:gives {((2 6 1 8) "=<") list:sort (1 2 6 8)}] + [ a r:Fact; r:gives {((2 6 1 8) ">=") list:sort (8 6 2 1)}] + skolem:lemma4352 + skolem:lemma4353 + [ a r:Fact; r:gives {(8621 1268) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2618]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 1 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2618 a r:Inference; + r:gives { + 2619 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2619 math:notEqualTo 0}] + skolem:lemma5015 + [ a r:Fact; r:gives {((2 6 1 9) "=<") list:sort (1 2 6 9)}] + [ a r:Fact; r:gives {((2 6 1 9) ">=") list:sort (9 6 2 1)}] + skolem:lemma4355 + skolem:lemma4356 + [ a r:Fact; r:gives {(9621 1269) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2619]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 1 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2619 a r:Inference; + r:gives { + 2620 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2620 math:notEqualTo 0}] + skolem:lemma5016 + [ a r:Fact; r:gives {((2 6 2 0) "=<") list:sort (0 2 2 6)}] + [ a r:Fact; r:gives {((2 6 2 0) ">=") list:sort (6 2 2 0)}] + skolem:lemma4072 + skolem:lemma4073 + [ a r:Fact; r:gives {(6220 226) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2620 a r:Inference; + r:gives { + 2621 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2621 math:notEqualTo 0}] + skolem:lemma5017 + [ a r:Fact; r:gives {((2 6 2 1) "=<") list:sort (1 2 2 6)}] + [ a r:Fact; r:gives {((2 6 2 1) ">=") list:sort (6 2 2 1)}] + skolem:lemma4262 + skolem:lemma4263 + [ a r:Fact; r:gives {(6221 1226) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2621 a r:Inference; + r:gives { + 2622 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2622 math:notEqualTo 0}] + skolem:lemma5018 + [ a r:Fact; r:gives {((2 6 2 2) "=<") list:sort (2 2 2 6)}] + [ a r:Fact; r:gives {((2 6 2 2) ">=") list:sort (6 2 2 2)}] + skolem:lemma4431 + skolem:lemma4432 + [ a r:Fact; r:gives {(6222 2226) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2622 a r:Inference; + r:gives { + 2623 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2623 math:notEqualTo 0}] + skolem:lemma5019 + [ a r:Fact; r:gives {((2 6 2 3) "=<") list:sort (2 2 3 6)}] + [ a r:Fact; r:gives {((2 6 2 3) ">=") list:sort (6 3 2 2)}] + skolem:lemma4455 + skolem:lemma4456 + [ a r:Fact; r:gives {(6322 2236) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2623]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2623 a r:Inference; + r:gives { + 2624 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2624 math:notEqualTo 0}] + skolem:lemma5020 + [ a r:Fact; r:gives {((2 6 2 4) "=<") list:sort (2 2 4 6)}] + [ a r:Fact; r:gives {((2 6 2 4) ">=") list:sort (6 4 2 2)}] + skolem:lemma4477 + skolem:lemma4478 + [ a r:Fact; r:gives {(6422 2246) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2624]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2624 a r:Inference; + r:gives { + 2625 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2625 math:notEqualTo 0}] + skolem:lemma5021 + [ a r:Fact; r:gives {((2 6 2 5) "=<") list:sort (2 2 5 6)}] + [ a r:Fact; r:gives {((2 6 2 5) ">=") list:sort (6 5 2 2)}] + skolem:lemma4497 + skolem:lemma4498 + [ a r:Fact; r:gives {(6522 2256) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2625]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2625 a r:Inference; + r:gives { + 2626 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2626 math:notEqualTo 0}] + skolem:lemma5022 + [ a r:Fact; r:gives {((2 6 2 6) "=<") list:sort (2 2 6 6)}] + [ a r:Fact; r:gives {((2 6 2 6) ">=") list:sort (6 6 2 2)}] + skolem:lemma4515 + skolem:lemma4516 + [ a r:Fact; r:gives {(6622 2266) math:difference 4356}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4356 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 4356 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2626]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2626 a r:Inference; + r:gives { + 2627 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2627 math:notEqualTo 0}] + skolem:lemma5023 + [ a r:Fact; r:gives {((2 6 2 7) "=<") list:sort (2 2 6 7)}] + [ a r:Fact; r:gives {((2 6 2 7) ">=") list:sort (7 6 2 2)}] + skolem:lemma4518 + skolem:lemma4519 + [ a r:Fact; r:gives {(7622 2267) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2627]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2627 a r:Inference; + r:gives { + 2628 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2628 math:notEqualTo 0}] + skolem:lemma5024 + [ a r:Fact; r:gives {((2 6 2 8) "=<") list:sort (2 2 6 8)}] + [ a r:Fact; r:gives {((2 6 2 8) ">=") list:sort (8 6 2 2)}] + skolem:lemma4521 + skolem:lemma4522 + [ a r:Fact; r:gives {(8622 2268) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2628]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2628 a r:Inference; + r:gives { + 2629 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2629 math:notEqualTo 0}] + skolem:lemma5025 + [ a r:Fact; r:gives {((2 6 2 9) "=<") list:sort (2 2 6 9)}] + [ a r:Fact; r:gives {((2 6 2 9) ">=") list:sort (9 6 2 2)}] + skolem:lemma4524 + skolem:lemma4525 + [ a r:Fact; r:gives {(9622 2269) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2629]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2629 a r:Inference; + r:gives { + 2630 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2630 math:notEqualTo 0}] + skolem:lemma5026 + [ a r:Fact; r:gives {((2 6 3 0) "=<") list:sort (0 2 3 6)}] + [ a r:Fact; r:gives {((2 6 3 0) ">=") list:sort (6 3 2 0)}] + skolem:lemma4096 + skolem:lemma4097 + [ a r:Fact; r:gives {(6320 236) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2630 a r:Inference; + r:gives { + 2631 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2631 math:notEqualTo 0}] + skolem:lemma5027 + [ a r:Fact; r:gives {((2 6 3 1) "=<") list:sort (1 2 3 6)}] + [ a r:Fact; r:gives {((2 6 3 1) ">=") list:sort (6 3 2 1)}] + skolem:lemma4286 + skolem:lemma4287 + [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2631 a r:Inference; + r:gives { + 2632 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2632 math:notEqualTo 0}] + skolem:lemma5028 + [ a r:Fact; r:gives {((2 6 3 2) "=<") list:sort (2 2 3 6)}] + [ a r:Fact; r:gives {((2 6 3 2) ">=") list:sort (6 3 2 2)}] + skolem:lemma4455 + skolem:lemma4456 + [ a r:Fact; r:gives {(6322 2236) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2632 a r:Inference; + r:gives { + 2633 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2633 math:notEqualTo 0}] + skolem:lemma5029 + [ a r:Fact; r:gives {((2 6 3 3) "=<") list:sort (2 3 3 6)}] + [ a r:Fact; r:gives {((2 6 3 3) ">=") list:sort (6 3 3 2)}] + skolem:lemma4611 + skolem:lemma4612 + [ a r:Fact; r:gives {(6332 2336) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2633 a r:Inference; + r:gives { + 2634 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2634 math:notEqualTo 0}] + skolem:lemma5030 + [ a r:Fact; r:gives {((2 6 3 4) "=<") list:sort (2 3 4 6)}] + [ a r:Fact; r:gives {((2 6 3 4) ">=") list:sort (6 4 3 2)}] + skolem:lemma4633 + skolem:lemma4634 + [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2634]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2634 a r:Inference; + r:gives { + 2635 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2635 math:notEqualTo 0}] + skolem:lemma5031 + [ a r:Fact; r:gives {((2 6 3 5) "=<") list:sort (2 3 5 6)}] + [ a r:Fact; r:gives {((2 6 3 5) ">=") list:sort (6 5 3 2)}] + skolem:lemma4653 + skolem:lemma4654 + [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2635]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2635 a r:Inference; + r:gives { + 2636 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2636 math:notEqualTo 0}] + skolem:lemma5032 + [ a r:Fact; r:gives {((2 6 3 6) "=<") list:sort (2 3 6 6)}] + [ a r:Fact; r:gives {((2 6 3 6) ">=") list:sort (6 6 3 2)}] + skolem:lemma4671 + skolem:lemma4672 + [ a r:Fact; r:gives {(6632 2366) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2636]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2636 a r:Inference; + r:gives { + 2637 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2637 math:notEqualTo 0}] + skolem:lemma5033 + [ a r:Fact; r:gives {((2 6 3 7) "=<") list:sort (2 3 6 7)}] + [ a r:Fact; r:gives {((2 6 3 7) ">=") list:sort (7 6 3 2)}] + skolem:lemma4674 + skolem:lemma4675 + [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2637]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2637 a r:Inference; + r:gives { + 2638 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2638 math:notEqualTo 0}] + skolem:lemma5034 + [ a r:Fact; r:gives {((2 6 3 8) "=<") list:sort (2 3 6 8)}] + [ a r:Fact; r:gives {((2 6 3 8) ">=") list:sort (8 6 3 2)}] + skolem:lemma4677 + skolem:lemma4678 + [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2638]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2638 a r:Inference; + r:gives { + 2639 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2639 math:notEqualTo 0}] + skolem:lemma5035 + [ a r:Fact; r:gives {((2 6 3 9) "=<") list:sort (2 3 6 9)}] + [ a r:Fact; r:gives {((2 6 3 9) ">=") list:sort (9 6 3 2)}] + skolem:lemma4680 + skolem:lemma4681 + [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2639]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2639 a r:Inference; + r:gives { + 2640 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2640 math:notEqualTo 0}] + skolem:lemma5036 + [ a r:Fact; r:gives {((2 6 4 0) "=<") list:sort (0 2 4 6)}] + [ a r:Fact; r:gives {((2 6 4 0) ">=") list:sort (6 4 2 0)}] + skolem:lemma4118 + skolem:lemma4119 + [ a r:Fact; r:gives {(6420 246) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2640]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 4 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2640 a r:Inference; + r:gives { + 2641 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2641 math:notEqualTo 0}] + skolem:lemma5037 + [ a r:Fact; r:gives {((2 6 4 1) "=<") list:sort (1 2 4 6)}] + [ a r:Fact; r:gives {((2 6 4 1) ">=") list:sort (6 4 2 1)}] + skolem:lemma4308 + skolem:lemma4309 + [ a r:Fact; r:gives {(6421 1246) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2641]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 4 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2641 a r:Inference; + r:gives { + 2642 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2642 math:notEqualTo 0}] + skolem:lemma5038 + [ a r:Fact; r:gives {((2 6 4 2) "=<") list:sort (2 2 4 6)}] + [ a r:Fact; r:gives {((2 6 4 2) ">=") list:sort (6 4 2 2)}] + skolem:lemma4477 + skolem:lemma4478 + [ a r:Fact; r:gives {(6422 2246) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2642 a r:Inference; + r:gives { + 2643 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2643 math:notEqualTo 0}] + skolem:lemma5039 + [ a r:Fact; r:gives {((2 6 4 3) "=<") list:sort (2 3 4 6)}] + [ a r:Fact; r:gives {((2 6 4 3) ">=") list:sort (6 4 3 2)}] + skolem:lemma4633 + skolem:lemma4634 + [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2643 a r:Inference; + r:gives { + 2644 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2644 math:notEqualTo 0}] + skolem:lemma5040 + [ a r:Fact; r:gives {((2 6 4 4) "=<") list:sort (2 4 4 6)}] + [ a r:Fact; r:gives {((2 6 4 4) ">=") list:sort (6 4 4 2)}] + skolem:lemma4775 + skolem:lemma4776 + [ a r:Fact; r:gives {(6442 2446) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2644]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2446]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2644 a r:Inference; + r:gives { + 2645 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2645 math:notEqualTo 0}] + skolem:lemma5041 + [ a r:Fact; r:gives {((2 6 4 5) "=<") list:sort (2 4 5 6)}] + [ a r:Fact; r:gives {((2 6 4 5) ">=") list:sort (6 5 4 2)}] + skolem:lemma4795 + skolem:lemma4796 + [ a r:Fact; r:gives {(6542 2456) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2645]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2645 a r:Inference; + r:gives { + 2646 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2646 math:notEqualTo 0}] + skolem:lemma5042 + [ a r:Fact; r:gives {((2 6 4 6) "=<") list:sort (2 4 6 6)}] + [ a r:Fact; r:gives {((2 6 4 6) ">=") list:sort (6 6 4 2)}] + skolem:lemma4813 + skolem:lemma4814 + [ a r:Fact; r:gives {(6642 2466) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2646]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2466]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2646 a r:Inference; + r:gives { + 2647 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2647 math:notEqualTo 0}] + skolem:lemma5043 + [ a r:Fact; r:gives {((2 6 4 7) "=<") list:sort (2 4 6 7)}] + [ a r:Fact; r:gives {((2 6 4 7) ">=") list:sort (7 6 4 2)}] + skolem:lemma4816 + skolem:lemma4817 + [ a r:Fact; r:gives {(7642 2467) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2647]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2467]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2647 a r:Inference; + r:gives { + 2648 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2648 math:notEqualTo 0}] + skolem:lemma5044 + [ a r:Fact; r:gives {((2 6 4 8) "=<") list:sort (2 4 6 8)}] + [ a r:Fact; r:gives {((2 6 4 8) ">=") list:sort (8 6 4 2)}] + skolem:lemma4819 + skolem:lemma4820 + [ a r:Fact; r:gives {(8642 2468) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2648]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2468]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2648 a r:Inference; + r:gives { + 2649 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2649 math:notEqualTo 0}] + skolem:lemma5045 + [ a r:Fact; r:gives {((2 6 4 9) "=<") list:sort (2 4 6 9)}] + [ a r:Fact; r:gives {((2 6 4 9) ">=") list:sort (9 6 4 2)}] + skolem:lemma4822 + skolem:lemma4823 + [ a r:Fact; r:gives {(9642 2469) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2649]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2469]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2649 a r:Inference; + r:gives { + 2650 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2650 math:notEqualTo 0}] + skolem:lemma5046 + [ a r:Fact; r:gives {((2 6 5 0) "=<") list:sort (0 2 5 6)}] + [ a r:Fact; r:gives {((2 6 5 0) ">=") list:sort (6 5 2 0)}] + skolem:lemma4138 + skolem:lemma4139 + [ a r:Fact; r:gives {(6520 256) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2650]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 5 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2650 a r:Inference; + r:gives { + 2651 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2651 math:notEqualTo 0}] + skolem:lemma5047 + [ a r:Fact; r:gives {((2 6 5 1) "=<") list:sort (1 2 5 6)}] + [ a r:Fact; r:gives {((2 6 5 1) ">=") list:sort (6 5 2 1)}] + skolem:lemma4328 + skolem:lemma4329 + [ a r:Fact; r:gives {(6521 1256) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2651]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 5 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2651 a r:Inference; + r:gives { + 2652 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2652 math:notEqualTo 0}] + skolem:lemma5048 + [ a r:Fact; r:gives {((2 6 5 2) "=<") list:sort (2 2 5 6)}] + [ a r:Fact; r:gives {((2 6 5 2) ">=") list:sort (6 5 2 2)}] + skolem:lemma4497 + skolem:lemma4498 + [ a r:Fact; r:gives {(6522 2256) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2652 a r:Inference; + r:gives { + 2653 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2653 math:notEqualTo 0}] + skolem:lemma5049 + [ a r:Fact; r:gives {((2 6 5 3) "=<") list:sort (2 3 5 6)}] + [ a r:Fact; r:gives {((2 6 5 3) ">=") list:sort (6 5 3 2)}] + skolem:lemma4653 + skolem:lemma4654 + [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2653 a r:Inference; + r:gives { + 2654 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2654 math:notEqualTo 0}] + skolem:lemma5050 + [ a r:Fact; r:gives {((2 6 5 4) "=<") list:sort (2 4 5 6)}] + [ a r:Fact; r:gives {((2 6 5 4) ">=") list:sort (6 5 4 2)}] + skolem:lemma4795 + skolem:lemma4796 + [ a r:Fact; r:gives {(6542 2456) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2654]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 5 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2654 a r:Inference; + r:gives { + 2655 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2655 math:notEqualTo 0}] + skolem:lemma5051 + [ a r:Fact; r:gives {((2 6 5 5) "=<") list:sort (2 5 5 6)}] + [ a r:Fact; r:gives {((2 6 5 5) ">=") list:sort (6 5 5 2)}] + skolem:lemma4925 + skolem:lemma4926 + [ a r:Fact; r:gives {(6552 2556) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2655]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2556]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2655 a r:Inference; + r:gives { + 2656 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2656 math:notEqualTo 0}] + skolem:lemma5052 + [ a r:Fact; r:gives {((2 6 5 6) "=<") list:sort (2 5 6 6)}] + [ a r:Fact; r:gives {((2 6 5 6) ">=") list:sort (6 6 5 2)}] + skolem:lemma4943 + skolem:lemma4944 + [ a r:Fact; r:gives {(6652 2566) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2656]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2566]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2656 a r:Inference; + r:gives { + 2657 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2657 math:notEqualTo 0}] + skolem:lemma5053 + [ a r:Fact; r:gives {((2 6 5 7) "=<") list:sort (2 5 6 7)}] + [ a r:Fact; r:gives {((2 6 5 7) ">=") list:sort (7 6 5 2)}] + skolem:lemma4946 + skolem:lemma4947 + [ a r:Fact; r:gives {(7652 2567) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2657]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2567]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2657 a r:Inference; + r:gives { + 2658 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2658 math:notEqualTo 0}] + skolem:lemma5054 + [ a r:Fact; r:gives {((2 6 5 8) "=<") list:sort (2 5 6 8)}] + [ a r:Fact; r:gives {((2 6 5 8) ">=") list:sort (8 6 5 2)}] + skolem:lemma4949 + skolem:lemma4950 + [ a r:Fact; r:gives {(8652 2568) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2658]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2568]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2658 a r:Inference; + r:gives { + 2659 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2659 math:notEqualTo 0}] + skolem:lemma5055 + [ a r:Fact; r:gives {((2 6 5 9) "=<") list:sort (2 5 6 9)}] + [ a r:Fact; r:gives {((2 6 5 9) ">=") list:sort (9 6 5 2)}] + skolem:lemma4952 + skolem:lemma4953 + [ a r:Fact; r:gives {(9652 2569) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2659]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2569]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2659 a r:Inference; + r:gives { + 2660 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2660 math:notEqualTo 0}] + skolem:lemma5056 + [ a r:Fact; r:gives {((2 6 6 0) "=<") list:sort (0 2 6 6)}] + [ a r:Fact; r:gives {((2 6 6 0) ">=") list:sort (6 6 2 0)}] + skolem:lemma4156 + skolem:lemma4157 + [ a r:Fact; r:gives {(6620 266) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2660]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 6 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2660 a r:Inference; + r:gives { + 2661 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2661 math:notEqualTo 0}] + skolem:lemma5057 + [ a r:Fact; r:gives {((2 6 6 1) "=<") list:sort (1 2 6 6)}] + [ a r:Fact; r:gives {((2 6 6 1) ">=") list:sort (6 6 2 1)}] + skolem:lemma4346 + skolem:lemma4347 + [ a r:Fact; r:gives {(6621 1266) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2661]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 6 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2661 a r:Inference; + r:gives { + 2662 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2662 math:notEqualTo 0}] + skolem:lemma5058 + [ a r:Fact; r:gives {((2 6 6 2) "=<") list:sort (2 2 6 6)}] + [ a r:Fact; r:gives {((2 6 6 2) ">=") list:sort (6 6 2 2)}] + skolem:lemma4515 + skolem:lemma4516 + [ a r:Fact; r:gives {(6622 2266) math:difference 4356}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4356 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 4356 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2662]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2662 a r:Inference; + r:gives { + 2663 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2663 math:notEqualTo 0}] + skolem:lemma5059 + [ a r:Fact; r:gives {((2 6 6 3) "=<") list:sort (2 3 6 6)}] + [ a r:Fact; r:gives {((2 6 6 3) ">=") list:sort (6 6 3 2)}] + skolem:lemma4671 + skolem:lemma4672 + [ a r:Fact; r:gives {(6632 2366) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2663]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2663 a r:Inference; + r:gives { + 2664 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2664 math:notEqualTo 0}] + skolem:lemma5060 + [ a r:Fact; r:gives {((2 6 6 4) "=<") list:sort (2 4 6 6)}] + [ a r:Fact; r:gives {((2 6 6 4) ">=") list:sort (6 6 4 2)}] + skolem:lemma4813 + skolem:lemma4814 + [ a r:Fact; r:gives {(6642 2466) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2664]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 6 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2466]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2664 a r:Inference; + r:gives { + 2665 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2665 math:notEqualTo 0}] + skolem:lemma5061 + [ a r:Fact; r:gives {((2 6 6 5) "=<") list:sort (2 5 6 6)}] + [ a r:Fact; r:gives {((2 6 6 5) ">=") list:sort (6 6 5 2)}] + skolem:lemma4943 + skolem:lemma4944 + [ a r:Fact; r:gives {(6652 2566) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2665]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 6 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2566]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2665 a r:Inference; + r:gives { + 2666 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2666 math:notEqualTo 0}] + skolem:lemma5062 + [ a r:Fact; r:gives {((2 6 6 6) "=<") list:sort (2 6 6 6)}] + [ a r:Fact; r:gives {((2 6 6 6) ">=") list:sort (6 6 6 2)}] + skolem:lemma5063 + skolem:lemma5064 + [ a r:Fact; r:gives {(6662 2666) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2666]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2666]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6662]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2666 a r:Inference; + r:gives { + 2667 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2667 math:notEqualTo 0}] + skolem:lemma5065 + [ a r:Fact; r:gives {((2 6 6 7) "=<") list:sort (2 6 6 7)}] + [ a r:Fact; r:gives {((2 6 6 7) ">=") list:sort (7 6 6 2)}] + skolem:lemma5066 + skolem:lemma5067 + [ a r:Fact; r:gives {(7662 2667) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2667]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2667]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7662]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2667 a r:Inference; + r:gives { + 2668 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2668 math:notEqualTo 0}] + skolem:lemma5068 + [ a r:Fact; r:gives {((2 6 6 8) "=<") list:sort (2 6 6 8)}] + [ a r:Fact; r:gives {((2 6 6 8) ">=") list:sort (8 6 6 2)}] + skolem:lemma5069 + skolem:lemma5070 + [ a r:Fact; r:gives {(8662 2668) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2668]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2668]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8662]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2668 a r:Inference; + r:gives { + 2669 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2669 math:notEqualTo 0}] + skolem:lemma5071 + [ a r:Fact; r:gives {((2 6 6 9) "=<") list:sort (2 6 6 9)}] + [ a r:Fact; r:gives {((2 6 6 9) ">=") list:sort (9 6 6 2)}] + skolem:lemma5072 + skolem:lemma5073 + [ a r:Fact; r:gives {(9662 2669) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2669]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2669]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9662]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2669 a r:Inference; + r:gives { + 2670 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2670 math:notEqualTo 0}] + skolem:lemma5074 + [ a r:Fact; r:gives {((2 6 7 0) "=<") list:sort (0 2 6 7)}] + [ a r:Fact; r:gives {((2 6 7 0) ">=") list:sort (7 6 2 0)}] + skolem:lemma4159 + skolem:lemma4160 + [ a r:Fact; r:gives {(7620 267) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2670]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 7 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2670 a r:Inference; + r:gives { + 2671 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2671 math:notEqualTo 0}] + skolem:lemma5075 + [ a r:Fact; r:gives {((2 6 7 1) "=<") list:sort (1 2 6 7)}] + [ a r:Fact; r:gives {((2 6 7 1) ">=") list:sort (7 6 2 1)}] + skolem:lemma4349 + skolem:lemma4350 + [ a r:Fact; r:gives {(7621 1267) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2671]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 7 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2671 a r:Inference; + r:gives { + 2672 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2672 math:notEqualTo 0}] + skolem:lemma5076 + [ a r:Fact; r:gives {((2 6 7 2) "=<") list:sort (2 2 6 7)}] + [ a r:Fact; r:gives {((2 6 7 2) ">=") list:sort (7 6 2 2)}] + skolem:lemma4518 + skolem:lemma4519 + [ a r:Fact; r:gives {(7622 2267) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2672]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2672 a r:Inference; + r:gives { + 2673 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2673 math:notEqualTo 0}] + skolem:lemma5077 + [ a r:Fact; r:gives {((2 6 7 3) "=<") list:sort (2 3 6 7)}] + [ a r:Fact; r:gives {((2 6 7 3) ">=") list:sort (7 6 3 2)}] + skolem:lemma4674 + skolem:lemma4675 + [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2673]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2673 a r:Inference; + r:gives { + 2674 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2674 math:notEqualTo 0}] + skolem:lemma5078 + [ a r:Fact; r:gives {((2 6 7 4) "=<") list:sort (2 4 6 7)}] + [ a r:Fact; r:gives {((2 6 7 4) ">=") list:sort (7 6 4 2)}] + skolem:lemma4816 + skolem:lemma4817 + [ a r:Fact; r:gives {(7642 2467) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2674]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 7 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2467]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2674 a r:Inference; + r:gives { + 2675 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2675 math:notEqualTo 0}] + skolem:lemma5079 + [ a r:Fact; r:gives {((2 6 7 5) "=<") list:sort (2 5 6 7)}] + [ a r:Fact; r:gives {((2 6 7 5) ">=") list:sort (7 6 5 2)}] + skolem:lemma4946 + skolem:lemma4947 + [ a r:Fact; r:gives {(7652 2567) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2675]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 7 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2567]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2675 a r:Inference; + r:gives { + 2676 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2676 math:notEqualTo 0}] + skolem:lemma5080 + [ a r:Fact; r:gives {((2 6 7 6) "=<") list:sort (2 6 6 7)}] + [ a r:Fact; r:gives {((2 6 7 6) ">=") list:sort (7 6 6 2)}] + skolem:lemma5066 + skolem:lemma5067 + [ a r:Fact; r:gives {(7662 2667) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2676]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 7 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2667]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7662]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2676 a r:Inference; + r:gives { + 2677 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2677 math:notEqualTo 0}] + skolem:lemma5081 + [ a r:Fact; r:gives {((2 6 7 7) "=<") list:sort (2 6 7 7)}] + [ a r:Fact; r:gives {((2 6 7 7) ">=") list:sort (7 7 6 2)}] + skolem:lemma5082 + skolem:lemma5083 + [ a r:Fact; r:gives {(7762 2677) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2677]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2677]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2677 a r:Inference; + r:gives { + 2678 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2678 math:notEqualTo 0}] + skolem:lemma5084 + [ a r:Fact; r:gives {((2 6 7 8) "=<") list:sort (2 6 7 8)}] + [ a r:Fact; r:gives {((2 6 7 8) ">=") list:sort (8 7 6 2)}] + skolem:lemma5085 + skolem:lemma5086 + [ a r:Fact; r:gives {(8762 2678) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2678]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2678]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2678 a r:Inference; + r:gives { + 2679 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2679 math:notEqualTo 0}] + skolem:lemma5087 + [ a r:Fact; r:gives {((2 6 7 9) "=<") list:sort (2 6 7 9)}] + [ a r:Fact; r:gives {((2 6 7 9) ">=") list:sort (9 7 6 2)}] + skolem:lemma5088 + skolem:lemma5089 + [ a r:Fact; r:gives {(9762 2679) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2679]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2679]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2679 a r:Inference; + r:gives { + 2680 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2680 math:notEqualTo 0}] + skolem:lemma5090 + [ a r:Fact; r:gives {((2 6 8 0) "=<") list:sort (0 2 6 8)}] + [ a r:Fact; r:gives {((2 6 8 0) ">=") list:sort (8 6 2 0)}] + skolem:lemma4162 + skolem:lemma4163 + [ a r:Fact; r:gives {(8620 268) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2680]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 8 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2680 a r:Inference; + r:gives { + 2681 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2681 math:notEqualTo 0}] + skolem:lemma5091 + [ a r:Fact; r:gives {((2 6 8 1) "=<") list:sort (1 2 6 8)}] + [ a r:Fact; r:gives {((2 6 8 1) ">=") list:sort (8 6 2 1)}] + skolem:lemma4352 + skolem:lemma4353 + [ a r:Fact; r:gives {(8621 1268) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2681]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 8 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2681 a r:Inference; + r:gives { + 2682 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2682 math:notEqualTo 0}] + skolem:lemma5092 + [ a r:Fact; r:gives {((2 6 8 2) "=<") list:sort (2 2 6 8)}] + [ a r:Fact; r:gives {((2 6 8 2) ">=") list:sort (8 6 2 2)}] + skolem:lemma4521 + skolem:lemma4522 + [ a r:Fact; r:gives {(8622 2268) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2682]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2682 a r:Inference; + r:gives { + 2683 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2683 math:notEqualTo 0}] + skolem:lemma5093 + [ a r:Fact; r:gives {((2 6 8 3) "=<") list:sort (2 3 6 8)}] + [ a r:Fact; r:gives {((2 6 8 3) ">=") list:sort (8 6 3 2)}] + skolem:lemma4677 + skolem:lemma4678 + [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2683]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2683 a r:Inference; + r:gives { + 2684 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2684 math:notEqualTo 0}] + skolem:lemma5094 + [ a r:Fact; r:gives {((2 6 8 4) "=<") list:sort (2 4 6 8)}] + [ a r:Fact; r:gives {((2 6 8 4) ">=") list:sort (8 6 4 2)}] + skolem:lemma4819 + skolem:lemma4820 + [ a r:Fact; r:gives {(8642 2468) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2684]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 8 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2468]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2684 a r:Inference; + r:gives { + 2685 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2685 math:notEqualTo 0}] + skolem:lemma5095 + [ a r:Fact; r:gives {((2 6 8 5) "=<") list:sort (2 5 6 8)}] + [ a r:Fact; r:gives {((2 6 8 5) ">=") list:sort (8 6 5 2)}] + skolem:lemma4949 + skolem:lemma4950 + [ a r:Fact; r:gives {(8652 2568) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2685]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 8 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2568]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2685 a r:Inference; + r:gives { + 2686 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2686 math:notEqualTo 0}] + skolem:lemma5096 + [ a r:Fact; r:gives {((2 6 8 6) "=<") list:sort (2 6 6 8)}] + [ a r:Fact; r:gives {((2 6 8 6) ">=") list:sort (8 6 6 2)}] + skolem:lemma5069 + skolem:lemma5070 + [ a r:Fact; r:gives {(8662 2668) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2686]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 8 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2668]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8662]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2686 a r:Inference; + r:gives { + 2687 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2687 math:notEqualTo 0}] + skolem:lemma5097 + [ a r:Fact; r:gives {((2 6 8 7) "=<") list:sort (2 6 7 8)}] + [ a r:Fact; r:gives {((2 6 8 7) ">=") list:sort (8 7 6 2)}] + skolem:lemma5085 + skolem:lemma5086 + [ a r:Fact; r:gives {(8762 2678) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2687]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 8 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2678]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2687 a r:Inference; + r:gives { + 2688 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2688 math:notEqualTo 0}] + skolem:lemma5098 + [ a r:Fact; r:gives {((2 6 8 8) "=<") list:sort (2 6 8 8)}] + [ a r:Fact; r:gives {((2 6 8 8) ">=") list:sort (8 8 6 2)}] + skolem:lemma5099 + skolem:lemma5100 + [ a r:Fact; r:gives {(8862 2688) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2688]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2688]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8862]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2688 a r:Inference; + r:gives { + 2689 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2689 math:notEqualTo 0}] + skolem:lemma5101 + [ a r:Fact; r:gives {((2 6 8 9) "=<") list:sort (2 6 8 9)}] + [ a r:Fact; r:gives {((2 6 8 9) ">=") list:sort (9 8 6 2)}] + skolem:lemma5102 + skolem:lemma5103 + [ a r:Fact; r:gives {(9862 2689) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2689]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2689]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9862]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2689 a r:Inference; + r:gives { + 2690 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2690 math:notEqualTo 0}] + skolem:lemma5104 + [ a r:Fact; r:gives {((2 6 9 0) "=<") list:sort (0 2 6 9)}] + [ a r:Fact; r:gives {((2 6 9 0) ">=") list:sort (9 6 2 0)}] + skolem:lemma4165 + skolem:lemma4166 + [ a r:Fact; r:gives {(9620 269) math:difference 9351}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9351 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9351 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2690]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 9 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9351]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2690 a r:Inference; + r:gives { + 2691 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2691 math:notEqualTo 0}] + skolem:lemma5105 + [ a r:Fact; r:gives {((2 6 9 1) "=<") list:sort (1 2 6 9)}] + [ a r:Fact; r:gives {((2 6 9 1) ">=") list:sort (9 6 2 1)}] + skolem:lemma4355 + skolem:lemma4356 + [ a r:Fact; r:gives {(9621 1269) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2691]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 9 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2691 a r:Inference; + r:gives { + 2692 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2692 math:notEqualTo 0}] + skolem:lemma5106 + [ a r:Fact; r:gives {((2 6 9 2) "=<") list:sort (2 2 6 9)}] + [ a r:Fact; r:gives {((2 6 9 2) ">=") list:sort (9 6 2 2)}] + skolem:lemma4524 + skolem:lemma4525 + [ a r:Fact; r:gives {(9622 2269) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2692]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 9 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2692 a r:Inference; + r:gives { + 2693 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2693 math:notEqualTo 0}] + skolem:lemma5107 + [ a r:Fact; r:gives {((2 6 9 3) "=<") list:sort (2 3 6 9)}] + [ a r:Fact; r:gives {((2 6 9 3) ">=") list:sort (9 6 3 2)}] + skolem:lemma4680 + skolem:lemma4681 + [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2693]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 9 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2693 a r:Inference; + r:gives { + 2694 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2694 math:notEqualTo 0}] + skolem:lemma5108 + [ a r:Fact; r:gives {((2 6 9 4) "=<") list:sort (2 4 6 9)}] + [ a r:Fact; r:gives {((2 6 9 4) ">=") list:sort (9 6 4 2)}] + skolem:lemma4822 + skolem:lemma4823 + [ a r:Fact; r:gives {(9642 2469) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2694]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 9 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2469]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2694 a r:Inference; + r:gives { + 2695 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2695 math:notEqualTo 0}] + skolem:lemma5109 + [ a r:Fact; r:gives {((2 6 9 5) "=<") list:sort (2 5 6 9)}] + [ a r:Fact; r:gives {((2 6 9 5) ">=") list:sort (9 6 5 2)}] + skolem:lemma4952 + skolem:lemma4953 + [ a r:Fact; r:gives {(9652 2569) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2695]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 9 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2569]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2695 a r:Inference; + r:gives { + 2696 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2696 math:notEqualTo 0}] + skolem:lemma5110 + [ a r:Fact; r:gives {((2 6 9 6) "=<") list:sort (2 6 6 9)}] + [ a r:Fact; r:gives {((2 6 9 6) ">=") list:sort (9 6 6 2)}] + skolem:lemma5072 + skolem:lemma5073 + [ a r:Fact; r:gives {(9662 2669) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2696]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 9 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2669]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9662]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2696 a r:Inference; + r:gives { + 2697 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2697 math:notEqualTo 0}] + skolem:lemma5111 + [ a r:Fact; r:gives {((2 6 9 7) "=<") list:sort (2 6 7 9)}] + [ a r:Fact; r:gives {((2 6 9 7) ">=") list:sort (9 7 6 2)}] + skolem:lemma5088 + skolem:lemma5089 + [ a r:Fact; r:gives {(9762 2679) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2697]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 9 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2679]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2697 a r:Inference; + r:gives { + 2698 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2698 math:notEqualTo 0}] + skolem:lemma5112 + [ a r:Fact; r:gives {((2 6 9 8) "=<") list:sort (2 6 8 9)}] + [ a r:Fact; r:gives {((2 6 9 8) ">=") list:sort (9 8 6 2)}] + skolem:lemma5102 + skolem:lemma5103 + [ a r:Fact; r:gives {(9862 2689) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2698]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 9 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2689]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9862]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2698 a r:Inference; + r:gives { + 2699 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2699 math:notEqualTo 0}] + skolem:lemma5113 + [ a r:Fact; r:gives {((2 6 9 9) "=<") list:sort (2 6 9 9)}] + [ a r:Fact; r:gives {((2 6 9 9) ">=") list:sort (9 9 6 2)}] + skolem:lemma5114 + skolem:lemma5115 + [ a r:Fact; r:gives {(9962 2699) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2699]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 6 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2699]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9962]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2699 a r:Inference; + r:gives { + 2700 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2700 math:notEqualTo 0}] + skolem:lemma5116 + [ a r:Fact; r:gives {((2 7 0 0) "=<") list:sort (0 0 2 7)}] + [ a r:Fact; r:gives {((2 7 0 0) ">=") list:sort (7 2 0 0)}] + skolem:lemma4021 + skolem:lemma4022 + [ a r:Fact; r:gives {(7200 27) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2700 a r:Inference; + r:gives { + 2701 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2701 math:notEqualTo 0}] + skolem:lemma5117 + [ a r:Fact; r:gives {((2 7 0 1) "=<") list:sort (0 1 2 7)}] + [ a r:Fact; r:gives {((2 7 0 1) ">=") list:sort (7 2 1 0)}] + skolem:lemma4049 + skolem:lemma4050 + [ a r:Fact; r:gives {(7210 127) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2701]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 0 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2701 a r:Inference; + r:gives { + 2702 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2702 math:notEqualTo 0}] + skolem:lemma5118 + [ a r:Fact; r:gives {((2 7 0 2) "=<") list:sort (0 2 2 7)}] + [ a r:Fact; r:gives {((2 7 0 2) ">=") list:sort (7 2 2 0)}] + skolem:lemma4075 + skolem:lemma4076 + [ a r:Fact; r:gives {(7220 227) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2702]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 0 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2702 a r:Inference; + r:gives { + 2703 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2703 math:notEqualTo 0}] + skolem:lemma5119 + [ a r:Fact; r:gives {((2 7 0 3) "=<") list:sort (0 2 3 7)}] + [ a r:Fact; r:gives {((2 7 0 3) ">=") list:sort (7 3 2 0)}] + skolem:lemma4099 + skolem:lemma4100 + [ a r:Fact; r:gives {(7320 237) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2703]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 0 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2703 a r:Inference; + r:gives { + 2704 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2704 math:notEqualTo 0}] + skolem:lemma5120 + [ a r:Fact; r:gives {((2 7 0 4) "=<") list:sort (0 2 4 7)}] + [ a r:Fact; r:gives {((2 7 0 4) ">=") list:sort (7 4 2 0)}] + skolem:lemma4121 + skolem:lemma4122 + [ a r:Fact; r:gives {(7420 247) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2704]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 0 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2704 a r:Inference; + r:gives { + 2705 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2705 math:notEqualTo 0}] + skolem:lemma5121 + [ a r:Fact; r:gives {((2 7 0 5) "=<") list:sort (0 2 5 7)}] + [ a r:Fact; r:gives {((2 7 0 5) ">=") list:sort (7 5 2 0)}] + skolem:lemma4141 + skolem:lemma4142 + [ a r:Fact; r:gives {(7520 257) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2705]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 0 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2705 a r:Inference; + r:gives { + 2706 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2706 math:notEqualTo 0}] + skolem:lemma5122 + [ a r:Fact; r:gives {((2 7 0 6) "=<") list:sort (0 2 6 7)}] + [ a r:Fact; r:gives {((2 7 0 6) ">=") list:sort (7 6 2 0)}] + skolem:lemma4159 + skolem:lemma4160 + [ a r:Fact; r:gives {(7620 267) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2706]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 0 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2706 a r:Inference; + r:gives { + 2707 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2707 math:notEqualTo 0}] + skolem:lemma5123 + [ a r:Fact; r:gives {((2 7 0 7) "=<") list:sort (0 2 7 7)}] + [ a r:Fact; r:gives {((2 7 0 7) ">=") list:sort (7 7 2 0)}] + skolem:lemma4175 + skolem:lemma4176 + [ a r:Fact; r:gives {(7720 277) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2707]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 0 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 277]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2707 a r:Inference; + r:gives { + 2708 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2708 math:notEqualTo 0}] + skolem:lemma5124 + [ a r:Fact; r:gives {((2 7 0 8) "=<") list:sort (0 2 7 8)}] + [ a r:Fact; r:gives {((2 7 0 8) ">=") list:sort (8 7 2 0)}] + skolem:lemma4178 + skolem:lemma4179 + [ a r:Fact; r:gives {(8720 278) math:difference 8442}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8442 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 8442 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2708]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 0 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2708 a r:Inference; + r:gives { + 2709 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2709 math:notEqualTo 0}] + skolem:lemma5125 + [ a r:Fact; r:gives {((2 7 0 9) "=<") list:sort (0 2 7 9)}] + [ a r:Fact; r:gives {((2 7 0 9) ">=") list:sort (9 7 2 0)}] + skolem:lemma4181 + skolem:lemma4182 + [ a r:Fact; r:gives {(9720 279) math:difference 9441}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9441 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9441 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2709]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 0 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9441]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2709 a r:Inference; + r:gives { + 2710 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2710 math:notEqualTo 0}] + skolem:lemma5126 + [ a r:Fact; r:gives {((2 7 1 0) "=<") list:sort (0 1 2 7)}] + [ a r:Fact; r:gives {((2 7 1 0) ">=") list:sort (7 2 1 0)}] + skolem:lemma4049 + skolem:lemma4050 + [ a r:Fact; r:gives {(7210 127) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2710]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2710 a r:Inference; + r:gives { + 2711 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2711 math:notEqualTo 0}] + skolem:lemma5127 + [ a r:Fact; r:gives {((2 7 1 1) "=<") list:sort (1 1 2 7)}] + [ a r:Fact; r:gives {((2 7 1 1) ">=") list:sort (7 2 1 1)}] + skolem:lemma4239 + skolem:lemma4240 + [ a r:Fact; r:gives {(7211 1127) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2711]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2711 a r:Inference; + r:gives { + 2712 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2712 math:notEqualTo 0}] + skolem:lemma5128 + [ a r:Fact; r:gives {((2 7 1 2) "=<") list:sort (1 2 2 7)}] + [ a r:Fact; r:gives {((2 7 1 2) ">=") list:sort (7 2 2 1)}] + skolem:lemma4265 + skolem:lemma4266 + [ a r:Fact; r:gives {(7221 1227) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2712]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2712 a r:Inference; + r:gives { + 2713 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2713 math:notEqualTo 0}] + skolem:lemma5129 + [ a r:Fact; r:gives {((2 7 1 3) "=<") list:sort (1 2 3 7)}] + [ a r:Fact; r:gives {((2 7 1 3) ">=") list:sort (7 3 2 1)}] + skolem:lemma4289 + skolem:lemma4290 + [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2713]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2713 a r:Inference; + r:gives { + 2714 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2714 math:notEqualTo 0}] + skolem:lemma5130 + [ a r:Fact; r:gives {((2 7 1 4) "=<") list:sort (1 2 4 7)}] + [ a r:Fact; r:gives {((2 7 1 4) ">=") list:sort (7 4 2 1)}] + skolem:lemma4311 + skolem:lemma4312 + [ a r:Fact; r:gives {(7421 1247) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2714]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 1 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2714 a r:Inference; + r:gives { + 2715 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2715 math:notEqualTo 0}] + skolem:lemma5131 + [ a r:Fact; r:gives {((2 7 1 5) "=<") list:sort (1 2 5 7)}] + [ a r:Fact; r:gives {((2 7 1 5) ">=") list:sort (7 5 2 1)}] + skolem:lemma4331 + skolem:lemma4332 + [ a r:Fact; r:gives {(7521 1257) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2715]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 1 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2715 a r:Inference; + r:gives { + 2716 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2716 math:notEqualTo 0}] + skolem:lemma5132 + [ a r:Fact; r:gives {((2 7 1 6) "=<") list:sort (1 2 6 7)}] + [ a r:Fact; r:gives {((2 7 1 6) ">=") list:sort (7 6 2 1)}] + skolem:lemma4349 + skolem:lemma4350 + [ a r:Fact; r:gives {(7621 1267) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2716]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 1 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2716 a r:Inference; + r:gives { + 2717 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2717 math:notEqualTo 0}] + skolem:lemma5133 + [ a r:Fact; r:gives {((2 7 1 7) "=<") list:sort (1 2 7 7)}] + [ a r:Fact; r:gives {((2 7 1 7) ">=") list:sort (7 7 2 1)}] + skolem:lemma4365 + skolem:lemma4366 + [ a r:Fact; r:gives {(7721 1277) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2717]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 1 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1277]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2717 a r:Inference; + r:gives { + 2718 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2718 math:notEqualTo 0}] + skolem:lemma5134 + [ a r:Fact; r:gives {((2 7 1 8) "=<") list:sort (1 2 7 8)}] + [ a r:Fact; r:gives {((2 7 1 8) ">=") list:sort (8 7 2 1)}] + skolem:lemma4368 + skolem:lemma4369 + [ a r:Fact; r:gives {(8721 1278) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2718]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 1 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2718 a r:Inference; + r:gives { + 2719 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2719 math:notEqualTo 0}] + skolem:lemma5135 + [ a r:Fact; r:gives {((2 7 1 9) "=<") list:sort (1 2 7 9)}] + [ a r:Fact; r:gives {((2 7 1 9) ">=") list:sort (9 7 2 1)}] + skolem:lemma4371 + skolem:lemma4372 + [ a r:Fact; r:gives {(9721 1279) math:difference 8442}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8442 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 8442 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2719]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 1 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2719 a r:Inference; + r:gives { + 2720 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2720 math:notEqualTo 0}] + skolem:lemma5136 + [ a r:Fact; r:gives {((2 7 2 0) "=<") list:sort (0 2 2 7)}] + [ a r:Fact; r:gives {((2 7 2 0) ">=") list:sort (7 2 2 0)}] + skolem:lemma4075 + skolem:lemma4076 + [ a r:Fact; r:gives {(7220 227) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2720 a r:Inference; + r:gives { + 2721 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2721 math:notEqualTo 0}] + skolem:lemma5137 + [ a r:Fact; r:gives {((2 7 2 1) "=<") list:sort (1 2 2 7)}] + [ a r:Fact; r:gives {((2 7 2 1) ">=") list:sort (7 2 2 1)}] + skolem:lemma4265 + skolem:lemma4266 + [ a r:Fact; r:gives {(7221 1227) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2721 a r:Inference; + r:gives { + 2722 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2722 math:notEqualTo 0}] + skolem:lemma5138 + [ a r:Fact; r:gives {((2 7 2 2) "=<") list:sort (2 2 2 7)}] + [ a r:Fact; r:gives {((2 7 2 2) ">=") list:sort (7 2 2 2)}] + skolem:lemma4434 + skolem:lemma4435 + [ a r:Fact; r:gives {(7222 2227) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2722 a r:Inference; + r:gives { + 2723 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2723 math:notEqualTo 0}] + skolem:lemma5139 + [ a r:Fact; r:gives {((2 7 2 3) "=<") list:sort (2 2 3 7)}] + [ a r:Fact; r:gives {((2 7 2 3) ">=") list:sort (7 3 2 2)}] + skolem:lemma4458 + skolem:lemma4459 + [ a r:Fact; r:gives {(7322 2237) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2723]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2723 a r:Inference; + r:gives { + 2724 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2724 math:notEqualTo 0}] + skolem:lemma5140 + [ a r:Fact; r:gives {((2 7 2 4) "=<") list:sort (2 2 4 7)}] + [ a r:Fact; r:gives {((2 7 2 4) ">=") list:sort (7 4 2 2)}] + skolem:lemma4480 + skolem:lemma4481 + [ a r:Fact; r:gives {(7422 2247) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2724]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2724 a r:Inference; + r:gives { + 2725 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2725 math:notEqualTo 0}] + skolem:lemma5141 + [ a r:Fact; r:gives {((2 7 2 5) "=<") list:sort (2 2 5 7)}] + [ a r:Fact; r:gives {((2 7 2 5) ">=") list:sort (7 5 2 2)}] + skolem:lemma4500 + skolem:lemma4501 + [ a r:Fact; r:gives {(7522 2257) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2725]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2725 a r:Inference; + r:gives { + 2726 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2726 math:notEqualTo 0}] + skolem:lemma5142 + [ a r:Fact; r:gives {((2 7 2 6) "=<") list:sort (2 2 6 7)}] + [ a r:Fact; r:gives {((2 7 2 6) ">=") list:sort (7 6 2 2)}] + skolem:lemma4518 + skolem:lemma4519 + [ a r:Fact; r:gives {(7622 2267) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2726]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2726 a r:Inference; + r:gives { + 2727 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2727 math:notEqualTo 0}] + skolem:lemma5143 + [ a r:Fact; r:gives {((2 7 2 7) "=<") list:sort (2 2 7 7)}] + [ a r:Fact; r:gives {((2 7 2 7) ">=") list:sort (7 7 2 2)}] + skolem:lemma4534 + skolem:lemma4535 + [ a r:Fact; r:gives {(7722 2277) math:difference 5445}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5445 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5445 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2727]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2277]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5445]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2727 a r:Inference; + r:gives { + 2728 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2728 math:notEqualTo 0}] + skolem:lemma5144 + [ a r:Fact; r:gives {((2 7 2 8) "=<") list:sort (2 2 7 8)}] + [ a r:Fact; r:gives {((2 7 2 8) ">=") list:sort (8 7 2 2)}] + skolem:lemma4537 + skolem:lemma4538 + [ a r:Fact; r:gives {(8722 2278) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2728]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2728 a r:Inference; + r:gives { + 2729 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2729 math:notEqualTo 0}] + skolem:lemma5145 + [ a r:Fact; r:gives {((2 7 2 9) "=<") list:sort (2 2 7 9)}] + [ a r:Fact; r:gives {((2 7 2 9) ">=") list:sort (9 7 2 2)}] + skolem:lemma4540 + skolem:lemma4541 + [ a r:Fact; r:gives {(9722 2279) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2729]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2729 a r:Inference; + r:gives { + 2730 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2730 math:notEqualTo 0}] + skolem:lemma5146 + [ a r:Fact; r:gives {((2 7 3 0) "=<") list:sort (0 2 3 7)}] + [ a r:Fact; r:gives {((2 7 3 0) ">=") list:sort (7 3 2 0)}] + skolem:lemma4099 + skolem:lemma4100 + [ a r:Fact; r:gives {(7320 237) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2730 a r:Inference; + r:gives { + 2731 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2731 math:notEqualTo 0}] + skolem:lemma5147 + [ a r:Fact; r:gives {((2 7 3 1) "=<") list:sort (1 2 3 7)}] + [ a r:Fact; r:gives {((2 7 3 1) ">=") list:sort (7 3 2 1)}] + skolem:lemma4289 + skolem:lemma4290 + [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2731]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2731 a r:Inference; + r:gives { + 2732 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2732 math:notEqualTo 0}] + skolem:lemma5148 + [ a r:Fact; r:gives {((2 7 3 2) "=<") list:sort (2 2 3 7)}] + [ a r:Fact; r:gives {((2 7 3 2) ">=") list:sort (7 3 2 2)}] + skolem:lemma4458 + skolem:lemma4459 + [ a r:Fact; r:gives {(7322 2237) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2732 a r:Inference; + r:gives { + 2733 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2733 math:notEqualTo 0}] + skolem:lemma5149 + [ a r:Fact; r:gives {((2 7 3 3) "=<") list:sort (2 3 3 7)}] + [ a r:Fact; r:gives {((2 7 3 3) ">=") list:sort (7 3 3 2)}] + skolem:lemma4614 + skolem:lemma4615 + [ a r:Fact; r:gives {(7332 2337) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2733 a r:Inference; + r:gives { + 2734 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2734 math:notEqualTo 0}] + skolem:lemma5150 + [ a r:Fact; r:gives {((2 7 3 4) "=<") list:sort (2 3 4 7)}] + [ a r:Fact; r:gives {((2 7 3 4) ">=") list:sort (7 4 3 2)}] + skolem:lemma4636 + skolem:lemma4637 + [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2734]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2734 a r:Inference; + r:gives { + 2735 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2735 math:notEqualTo 0}] + skolem:lemma5151 + [ a r:Fact; r:gives {((2 7 3 5) "=<") list:sort (2 3 5 7)}] + [ a r:Fact; r:gives {((2 7 3 5) ">=") list:sort (7 5 3 2)}] + skolem:lemma4656 + skolem:lemma4657 + [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2735]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2735 a r:Inference; + r:gives { + 2736 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2736 math:notEqualTo 0}] + skolem:lemma5152 + [ a r:Fact; r:gives {((2 7 3 6) "=<") list:sort (2 3 6 7)}] + [ a r:Fact; r:gives {((2 7 3 6) ">=") list:sort (7 6 3 2)}] + skolem:lemma4674 + skolem:lemma4675 + [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2736]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2736 a r:Inference; + r:gives { + 2737 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2737 math:notEqualTo 0}] + skolem:lemma5153 + [ a r:Fact; r:gives {((2 7 3 7) "=<") list:sort (2 3 7 7)}] + [ a r:Fact; r:gives {((2 7 3 7) ">=") list:sort (7 7 3 2)}] + skolem:lemma4690 + skolem:lemma4691 + [ a r:Fact; r:gives {(7732 2377) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2737]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2737 a r:Inference; + r:gives { + 2738 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2738 math:notEqualTo 0}] + skolem:lemma5154 + [ a r:Fact; r:gives {((2 7 3 8) "=<") list:sort (2 3 7 8)}] + [ a r:Fact; r:gives {((2 7 3 8) ">=") list:sort (8 7 3 2)}] + skolem:lemma4693 + skolem:lemma4694 + [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2738]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2738 a r:Inference; + r:gives { + 2739 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2739 math:notEqualTo 0}] + skolem:lemma5155 + [ a r:Fact; r:gives {((2 7 3 9) "=<") list:sort (2 3 7 9)}] + [ a r:Fact; r:gives {((2 7 3 9) ">=") list:sort (9 7 3 2)}] + skolem:lemma4696 + skolem:lemma4697 + [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2739]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2739 a r:Inference; + r:gives { + 2740 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2740 math:notEqualTo 0}] + skolem:lemma5156 + [ a r:Fact; r:gives {((2 7 4 0) "=<") list:sort (0 2 4 7)}] + [ a r:Fact; r:gives {((2 7 4 0) ">=") list:sort (7 4 2 0)}] + skolem:lemma4121 + skolem:lemma4122 + [ a r:Fact; r:gives {(7420 247) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2740]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 4 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2740 a r:Inference; + r:gives { + 2741 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2741 math:notEqualTo 0}] + skolem:lemma5157 + [ a r:Fact; r:gives {((2 7 4 1) "=<") list:sort (1 2 4 7)}] + [ a r:Fact; r:gives {((2 7 4 1) ">=") list:sort (7 4 2 1)}] + skolem:lemma4311 + skolem:lemma4312 + [ a r:Fact; r:gives {(7421 1247) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2741]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 4 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2741 a r:Inference; + r:gives { + 2742 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2742 math:notEqualTo 0}] + skolem:lemma5158 + [ a r:Fact; r:gives {((2 7 4 2) "=<") list:sort (2 2 4 7)}] + [ a r:Fact; r:gives {((2 7 4 2) ">=") list:sort (7 4 2 2)}] + skolem:lemma4480 + skolem:lemma4481 + [ a r:Fact; r:gives {(7422 2247) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2742 a r:Inference; + r:gives { + 2743 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2743 math:notEqualTo 0}] + skolem:lemma5159 + [ a r:Fact; r:gives {((2 7 4 3) "=<") list:sort (2 3 4 7)}] + [ a r:Fact; r:gives {((2 7 4 3) ">=") list:sort (7 4 3 2)}] + skolem:lemma4636 + skolem:lemma4637 + [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2743 a r:Inference; + r:gives { + 2744 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2744 math:notEqualTo 0}] + skolem:lemma5160 + [ a r:Fact; r:gives {((2 7 4 4) "=<") list:sort (2 4 4 7)}] + [ a r:Fact; r:gives {((2 7 4 4) ">=") list:sort (7 4 4 2)}] + skolem:lemma4778 + skolem:lemma4779 + [ a r:Fact; r:gives {(7442 2447) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2744]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2447]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2744 a r:Inference; + r:gives { + 2745 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2745 math:notEqualTo 0}] + skolem:lemma5161 + [ a r:Fact; r:gives {((2 7 4 5) "=<") list:sort (2 4 5 7)}] + [ a r:Fact; r:gives {((2 7 4 5) ">=") list:sort (7 5 4 2)}] + skolem:lemma4798 + skolem:lemma4799 + [ a r:Fact; r:gives {(7542 2457) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2745]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2457]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2745 a r:Inference; + r:gives { + 2746 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2746 math:notEqualTo 0}] + skolem:lemma5162 + [ a r:Fact; r:gives {((2 7 4 6) "=<") list:sort (2 4 6 7)}] + [ a r:Fact; r:gives {((2 7 4 6) ">=") list:sort (7 6 4 2)}] + skolem:lemma4816 + skolem:lemma4817 + [ a r:Fact; r:gives {(7642 2467) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2746]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2467]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2746 a r:Inference; + r:gives { + 2747 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2747 math:notEqualTo 0}] + skolem:lemma5163 + [ a r:Fact; r:gives {((2 7 4 7) "=<") list:sort (2 4 7 7)}] + [ a r:Fact; r:gives {((2 7 4 7) ">=") list:sort (7 7 4 2)}] + skolem:lemma4832 + skolem:lemma4833 + [ a r:Fact; r:gives {(7742 2477) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2747]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2477]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2747 a r:Inference; + r:gives { + 2748 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2748 math:notEqualTo 0}] + skolem:lemma5164 + [ a r:Fact; r:gives {((2 7 4 8) "=<") list:sort (2 4 7 8)}] + [ a r:Fact; r:gives {((2 7 4 8) ">=") list:sort (8 7 4 2)}] + skolem:lemma4835 + skolem:lemma4836 + [ a r:Fact; r:gives {(8742 2478) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2748]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2478]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2748 a r:Inference; + r:gives { + 2749 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2749 math:notEqualTo 0}] + skolem:lemma5165 + [ a r:Fact; r:gives {((2 7 4 9) "=<") list:sort (2 4 7 9)}] + [ a r:Fact; r:gives {((2 7 4 9) ">=") list:sort (9 7 4 2)}] + skolem:lemma4838 + skolem:lemma4839 + [ a r:Fact; r:gives {(9742 2479) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2749]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2479]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2749 a r:Inference; + r:gives { + 2750 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2750 math:notEqualTo 0}] + skolem:lemma5166 + [ a r:Fact; r:gives {((2 7 5 0) "=<") list:sort (0 2 5 7)}] + [ a r:Fact; r:gives {((2 7 5 0) ">=") list:sort (7 5 2 0)}] + skolem:lemma4141 + skolem:lemma4142 + [ a r:Fact; r:gives {(7520 257) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2750]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 5 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2750 a r:Inference; + r:gives { + 2751 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2751 math:notEqualTo 0}] + skolem:lemma5167 + [ a r:Fact; r:gives {((2 7 5 1) "=<") list:sort (1 2 5 7)}] + [ a r:Fact; r:gives {((2 7 5 1) ">=") list:sort (7 5 2 1)}] + skolem:lemma4331 + skolem:lemma4332 + [ a r:Fact; r:gives {(7521 1257) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2751]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 5 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2751 a r:Inference; + r:gives { + 2752 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2752 math:notEqualTo 0}] + skolem:lemma5168 + [ a r:Fact; r:gives {((2 7 5 2) "=<") list:sort (2 2 5 7)}] + [ a r:Fact; r:gives {((2 7 5 2) ">=") list:sort (7 5 2 2)}] + skolem:lemma4500 + skolem:lemma4501 + [ a r:Fact; r:gives {(7522 2257) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2752 a r:Inference; + r:gives { + 2753 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2753 math:notEqualTo 0}] + skolem:lemma5169 + [ a r:Fact; r:gives {((2 7 5 3) "=<") list:sort (2 3 5 7)}] + [ a r:Fact; r:gives {((2 7 5 3) ">=") list:sort (7 5 3 2)}] + skolem:lemma4656 + skolem:lemma4657 + [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2753 a r:Inference; + r:gives { + 2754 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2754 math:notEqualTo 0}] + skolem:lemma5170 + [ a r:Fact; r:gives {((2 7 5 4) "=<") list:sort (2 4 5 7)}] + [ a r:Fact; r:gives {((2 7 5 4) ">=") list:sort (7 5 4 2)}] + skolem:lemma4798 + skolem:lemma4799 + [ a r:Fact; r:gives {(7542 2457) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2754]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 5 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2457]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2754 a r:Inference; + r:gives { + 2755 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2755 math:notEqualTo 0}] + skolem:lemma5171 + [ a r:Fact; r:gives {((2 7 5 5) "=<") list:sort (2 5 5 7)}] + [ a r:Fact; r:gives {((2 7 5 5) ">=") list:sort (7 5 5 2)}] + skolem:lemma4928 + skolem:lemma4929 + [ a r:Fact; r:gives {(7552 2557) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2755]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2557]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2755 a r:Inference; + r:gives { + 2756 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2756 math:notEqualTo 0}] + skolem:lemma5172 + [ a r:Fact; r:gives {((2 7 5 6) "=<") list:sort (2 5 6 7)}] + [ a r:Fact; r:gives {((2 7 5 6) ">=") list:sort (7 6 5 2)}] + skolem:lemma4946 + skolem:lemma4947 + [ a r:Fact; r:gives {(7652 2567) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2756]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2567]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2756 a r:Inference; + r:gives { + 2757 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2757 math:notEqualTo 0}] + skolem:lemma5173 + [ a r:Fact; r:gives {((2 7 5 7) "=<") list:sort (2 5 7 7)}] + [ a r:Fact; r:gives {((2 7 5 7) ">=") list:sort (7 7 5 2)}] + skolem:lemma4962 + skolem:lemma4963 + [ a r:Fact; r:gives {(7752 2577) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2757]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2577]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2757 a r:Inference; + r:gives { + 2758 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2758 math:notEqualTo 0}] + skolem:lemma5174 + [ a r:Fact; r:gives {((2 7 5 8) "=<") list:sort (2 5 7 8)}] + [ a r:Fact; r:gives {((2 7 5 8) ">=") list:sort (8 7 5 2)}] + skolem:lemma4965 + skolem:lemma4966 + [ a r:Fact; r:gives {(8752 2578) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2758]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2578]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2758 a r:Inference; + r:gives { + 2759 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2759 math:notEqualTo 0}] + skolem:lemma5175 + [ a r:Fact; r:gives {((2 7 5 9) "=<") list:sort (2 5 7 9)}] + [ a r:Fact; r:gives {((2 7 5 9) ">=") list:sort (9 7 5 2)}] + skolem:lemma4968 + skolem:lemma4969 + [ a r:Fact; r:gives {(9752 2579) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2759]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2579]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2759 a r:Inference; + r:gives { + 2760 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2760 math:notEqualTo 0}] + skolem:lemma5176 + [ a r:Fact; r:gives {((2 7 6 0) "=<") list:sort (0 2 6 7)}] + [ a r:Fact; r:gives {((2 7 6 0) ">=") list:sort (7 6 2 0)}] + skolem:lemma4159 + skolem:lemma4160 + [ a r:Fact; r:gives {(7620 267) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2760]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 6 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2760 a r:Inference; + r:gives { + 2761 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2761 math:notEqualTo 0}] + skolem:lemma5177 + [ a r:Fact; r:gives {((2 7 6 1) "=<") list:sort (1 2 6 7)}] + [ a r:Fact; r:gives {((2 7 6 1) ">=") list:sort (7 6 2 1)}] + skolem:lemma4349 + skolem:lemma4350 + [ a r:Fact; r:gives {(7621 1267) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2761]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 6 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2761 a r:Inference; + r:gives { + 2762 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2762 math:notEqualTo 0}] + skolem:lemma5178 + [ a r:Fact; r:gives {((2 7 6 2) "=<") list:sort (2 2 6 7)}] + [ a r:Fact; r:gives {((2 7 6 2) ">=") list:sort (7 6 2 2)}] + skolem:lemma4518 + skolem:lemma4519 + [ a r:Fact; r:gives {(7622 2267) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2762 a r:Inference; + r:gives { + 2763 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2763 math:notEqualTo 0}] + skolem:lemma5179 + [ a r:Fact; r:gives {((2 7 6 3) "=<") list:sort (2 3 6 7)}] + [ a r:Fact; r:gives {((2 7 6 3) ">=") list:sort (7 6 3 2)}] + skolem:lemma4674 + skolem:lemma4675 + [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2763 a r:Inference; + r:gives { + 2764 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2764 math:notEqualTo 0}] + skolem:lemma5180 + [ a r:Fact; r:gives {((2 7 6 4) "=<") list:sort (2 4 6 7)}] + [ a r:Fact; r:gives {((2 7 6 4) ">=") list:sort (7 6 4 2)}] + skolem:lemma4816 + skolem:lemma4817 + [ a r:Fact; r:gives {(7642 2467) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2764]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 6 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2467]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2764 a r:Inference; + r:gives { + 2765 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2765 math:notEqualTo 0}] + skolem:lemma5181 + [ a r:Fact; r:gives {((2 7 6 5) "=<") list:sort (2 5 6 7)}] + [ a r:Fact; r:gives {((2 7 6 5) ">=") list:sort (7 6 5 2)}] + skolem:lemma4946 + skolem:lemma4947 + [ a r:Fact; r:gives {(7652 2567) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2765]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 6 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2567]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2765 a r:Inference; + r:gives { + 2766 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2766 math:notEqualTo 0}] + skolem:lemma5182 + [ a r:Fact; r:gives {((2 7 6 6) "=<") list:sort (2 6 6 7)}] + [ a r:Fact; r:gives {((2 7 6 6) ">=") list:sort (7 6 6 2)}] + skolem:lemma5066 + skolem:lemma5067 + [ a r:Fact; r:gives {(7662 2667) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2766]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2667]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7662]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2766 a r:Inference; + r:gives { + 2767 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2767 math:notEqualTo 0}] + skolem:lemma5183 + [ a r:Fact; r:gives {((2 7 6 7) "=<") list:sort (2 6 7 7)}] + [ a r:Fact; r:gives {((2 7 6 7) ">=") list:sort (7 7 6 2)}] + skolem:lemma5082 + skolem:lemma5083 + [ a r:Fact; r:gives {(7762 2677) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2767]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2677]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2767 a r:Inference; + r:gives { + 2768 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2768 math:notEqualTo 0}] + skolem:lemma5184 + [ a r:Fact; r:gives {((2 7 6 8) "=<") list:sort (2 6 7 8)}] + [ a r:Fact; r:gives {((2 7 6 8) ">=") list:sort (8 7 6 2)}] + skolem:lemma5085 + skolem:lemma5086 + [ a r:Fact; r:gives {(8762 2678) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2768]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2678]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2768 a r:Inference; + r:gives { + 2769 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2769 math:notEqualTo 0}] + skolem:lemma5185 + [ a r:Fact; r:gives {((2 7 6 9) "=<") list:sort (2 6 7 9)}] + [ a r:Fact; r:gives {((2 7 6 9) ">=") list:sort (9 7 6 2)}] + skolem:lemma5088 + skolem:lemma5089 + [ a r:Fact; r:gives {(9762 2679) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2769]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2679]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2769 a r:Inference; + r:gives { + 2770 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2770 math:notEqualTo 0}] + skolem:lemma5186 + [ a r:Fact; r:gives {((2 7 7 0) "=<") list:sort (0 2 7 7)}] + [ a r:Fact; r:gives {((2 7 7 0) ">=") list:sort (7 7 2 0)}] + skolem:lemma4175 + skolem:lemma4176 + [ a r:Fact; r:gives {(7720 277) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2770]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 7 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 277]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2770 a r:Inference; + r:gives { + 2771 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2771 math:notEqualTo 0}] + skolem:lemma5187 + [ a r:Fact; r:gives {((2 7 7 1) "=<") list:sort (1 2 7 7)}] + [ a r:Fact; r:gives {((2 7 7 1) ">=") list:sort (7 7 2 1)}] + skolem:lemma4365 + skolem:lemma4366 + [ a r:Fact; r:gives {(7721 1277) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2771]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 7 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1277]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2771 a r:Inference; + r:gives { + 2772 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2772 math:notEqualTo 0}] + skolem:lemma5188 + [ a r:Fact; r:gives {((2 7 7 2) "=<") list:sort (2 2 7 7)}] + [ a r:Fact; r:gives {((2 7 7 2) ">=") list:sort (7 7 2 2)}] + skolem:lemma4534 + skolem:lemma4535 + [ a r:Fact; r:gives {(7722 2277) math:difference 5445}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5445 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5445 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2772]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2277]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5445]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2772 a r:Inference; + r:gives { + 2773 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2773 math:notEqualTo 0}] + skolem:lemma5189 + [ a r:Fact; r:gives {((2 7 7 3) "=<") list:sort (2 3 7 7)}] + [ a r:Fact; r:gives {((2 7 7 3) ">=") list:sort (7 7 3 2)}] + skolem:lemma4690 + skolem:lemma4691 + [ a r:Fact; r:gives {(7732 2377) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2773]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2773 a r:Inference; + r:gives { + 2774 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2774 math:notEqualTo 0}] + skolem:lemma5190 + [ a r:Fact; r:gives {((2 7 7 4) "=<") list:sort (2 4 7 7)}] + [ a r:Fact; r:gives {((2 7 7 4) ">=") list:sort (7 7 4 2)}] + skolem:lemma4832 + skolem:lemma4833 + [ a r:Fact; r:gives {(7742 2477) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2774]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 7 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2477]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2774 a r:Inference; + r:gives { + 2775 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2775 math:notEqualTo 0}] + skolem:lemma5191 + [ a r:Fact; r:gives {((2 7 7 5) "=<") list:sort (2 5 7 7)}] + [ a r:Fact; r:gives {((2 7 7 5) ">=") list:sort (7 7 5 2)}] + skolem:lemma4962 + skolem:lemma4963 + [ a r:Fact; r:gives {(7752 2577) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2775]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 7 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2577]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2775 a r:Inference; + r:gives { + 2776 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2776 math:notEqualTo 0}] + skolem:lemma5192 + [ a r:Fact; r:gives {((2 7 7 6) "=<") list:sort (2 6 7 7)}] + [ a r:Fact; r:gives {((2 7 7 6) ">=") list:sort (7 7 6 2)}] + skolem:lemma5082 + skolem:lemma5083 + [ a r:Fact; r:gives {(7762 2677) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2776]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 7 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2677]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2776 a r:Inference; + r:gives { + 2777 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2777 math:notEqualTo 0}] + skolem:lemma5193 + [ a r:Fact; r:gives {((2 7 7 7) "=<") list:sort (2 7 7 7)}] + [ a r:Fact; r:gives {((2 7 7 7) ">=") list:sort (7 7 7 2)}] + skolem:lemma5194 + skolem:lemma5195 + [ a r:Fact; r:gives {(7772 2777) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2777]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2777]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7772]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2777 a r:Inference; + r:gives { + 2778 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2778 math:notEqualTo 0}] + skolem:lemma5196 + [ a r:Fact; r:gives {((2 7 7 8) "=<") list:sort (2 7 7 8)}] + [ a r:Fact; r:gives {((2 7 7 8) ">=") list:sort (8 7 7 2)}] + skolem:lemma5197 + skolem:lemma5198 + [ a r:Fact; r:gives {(8772 2778) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2778]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2778]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8772]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2778 a r:Inference; + r:gives { + 2779 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2779 math:notEqualTo 0}] + skolem:lemma5199 + [ a r:Fact; r:gives {((2 7 7 9) "=<") list:sort (2 7 7 9)}] + [ a r:Fact; r:gives {((2 7 7 9) ">=") list:sort (9 7 7 2)}] + skolem:lemma5200 + skolem:lemma5201 + [ a r:Fact; r:gives {(9772 2779) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2779]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2779]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9772]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2779 a r:Inference; + r:gives { + 2780 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2780 math:notEqualTo 0}] + skolem:lemma5202 + [ a r:Fact; r:gives {((2 7 8 0) "=<") list:sort (0 2 7 8)}] + [ a r:Fact; r:gives {((2 7 8 0) ">=") list:sort (8 7 2 0)}] + skolem:lemma4178 + skolem:lemma4179 + [ a r:Fact; r:gives {(8720 278) math:difference 8442}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8442 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 8442 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2780]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 8 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2780 a r:Inference; + r:gives { + 2781 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2781 math:notEqualTo 0}] + skolem:lemma5203 + [ a r:Fact; r:gives {((2 7 8 1) "=<") list:sort (1 2 7 8)}] + [ a r:Fact; r:gives {((2 7 8 1) ">=") list:sort (8 7 2 1)}] + skolem:lemma4368 + skolem:lemma4369 + [ a r:Fact; r:gives {(8721 1278) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2781]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 8 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2781 a r:Inference; + r:gives { + 2782 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2782 math:notEqualTo 0}] + skolem:lemma5204 + [ a r:Fact; r:gives {((2 7 8 2) "=<") list:sort (2 2 7 8)}] + [ a r:Fact; r:gives {((2 7 8 2) ">=") list:sort (8 7 2 2)}] + skolem:lemma4537 + skolem:lemma4538 + [ a r:Fact; r:gives {(8722 2278) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2782]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2782 a r:Inference; + r:gives { + 2783 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2783 math:notEqualTo 0}] + skolem:lemma5205 + [ a r:Fact; r:gives {((2 7 8 3) "=<") list:sort (2 3 7 8)}] + [ a r:Fact; r:gives {((2 7 8 3) ">=") list:sort (8 7 3 2)}] + skolem:lemma4693 + skolem:lemma4694 + [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2783]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2783 a r:Inference; + r:gives { + 2784 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2784 math:notEqualTo 0}] + skolem:lemma5206 + [ a r:Fact; r:gives {((2 7 8 4) "=<") list:sort (2 4 7 8)}] + [ a r:Fact; r:gives {((2 7 8 4) ">=") list:sort (8 7 4 2)}] + skolem:lemma4835 + skolem:lemma4836 + [ a r:Fact; r:gives {(8742 2478) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2784]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 8 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2478]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2784 a r:Inference; + r:gives { + 2785 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2785 math:notEqualTo 0}] + skolem:lemma5207 + [ a r:Fact; r:gives {((2 7 8 5) "=<") list:sort (2 5 7 8)}] + [ a r:Fact; r:gives {((2 7 8 5) ">=") list:sort (8 7 5 2)}] + skolem:lemma4965 + skolem:lemma4966 + [ a r:Fact; r:gives {(8752 2578) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2785]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 8 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2578]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2785 a r:Inference; + r:gives { + 2786 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2786 math:notEqualTo 0}] + skolem:lemma5208 + [ a r:Fact; r:gives {((2 7 8 6) "=<") list:sort (2 6 7 8)}] + [ a r:Fact; r:gives {((2 7 8 6) ">=") list:sort (8 7 6 2)}] + skolem:lemma5085 + skolem:lemma5086 + [ a r:Fact; r:gives {(8762 2678) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2786]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 8 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2678]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2786 a r:Inference; + r:gives { + 2787 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2787 math:notEqualTo 0}] + skolem:lemma5209 + [ a r:Fact; r:gives {((2 7 8 7) "=<") list:sort (2 7 7 8)}] + [ a r:Fact; r:gives {((2 7 8 7) ">=") list:sort (8 7 7 2)}] + skolem:lemma5197 + skolem:lemma5198 + [ a r:Fact; r:gives {(8772 2778) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2787]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 8 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2778]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8772]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2787 a r:Inference; + r:gives { + 2788 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2788 math:notEqualTo 0}] + skolem:lemma5210 + [ a r:Fact; r:gives {((2 7 8 8) "=<") list:sort (2 7 8 8)}] + [ a r:Fact; r:gives {((2 7 8 8) ">=") list:sort (8 8 7 2)}] + skolem:lemma5211 + skolem:lemma5212 + [ a r:Fact; r:gives {(8872 2788) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2788]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2788]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8872]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2788 a r:Inference; + r:gives { + 2789 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2789 math:notEqualTo 0}] + skolem:lemma5213 + [ a r:Fact; r:gives {((2 7 8 9) "=<") list:sort (2 7 8 9)}] + [ a r:Fact; r:gives {((2 7 8 9) ">=") list:sort (9 8 7 2)}] + skolem:lemma5214 + skolem:lemma5215 + [ a r:Fact; r:gives {(9872 2789) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2789]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2789]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9872]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2789 a r:Inference; + r:gives { + 2790 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2790 math:notEqualTo 0}] + skolem:lemma5216 + [ a r:Fact; r:gives {((2 7 9 0) "=<") list:sort (0 2 7 9)}] + [ a r:Fact; r:gives {((2 7 9 0) ">=") list:sort (9 7 2 0)}] + skolem:lemma4181 + skolem:lemma4182 + [ a r:Fact; r:gives {(9720 279) math:difference 9441}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9441 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9441 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2790]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 9 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9441]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2790 a r:Inference; + r:gives { + 2791 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2791 math:notEqualTo 0}] + skolem:lemma5217 + [ a r:Fact; r:gives {((2 7 9 1) "=<") list:sort (1 2 7 9)}] + [ a r:Fact; r:gives {((2 7 9 1) ">=") list:sort (9 7 2 1)}] + skolem:lemma4371 + skolem:lemma4372 + [ a r:Fact; r:gives {(9721 1279) math:difference 8442}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8442 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 8442 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2791]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 9 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2791 a r:Inference; + r:gives { + 2792 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2792 math:notEqualTo 0}] + skolem:lemma5218 + [ a r:Fact; r:gives {((2 7 9 2) "=<") list:sort (2 2 7 9)}] + [ a r:Fact; r:gives {((2 7 9 2) ">=") list:sort (9 7 2 2)}] + skolem:lemma4540 + skolem:lemma4541 + [ a r:Fact; r:gives {(9722 2279) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2792]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 9 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2792 a r:Inference; + r:gives { + 2793 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2793 math:notEqualTo 0}] + skolem:lemma5219 + [ a r:Fact; r:gives {((2 7 9 3) "=<") list:sort (2 3 7 9)}] + [ a r:Fact; r:gives {((2 7 9 3) ">=") list:sort (9 7 3 2)}] + skolem:lemma4696 + skolem:lemma4697 + [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2793]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 9 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2793 a r:Inference; + r:gives { + 2794 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2794 math:notEqualTo 0}] + skolem:lemma5220 + [ a r:Fact; r:gives {((2 7 9 4) "=<") list:sort (2 4 7 9)}] + [ a r:Fact; r:gives {((2 7 9 4) ">=") list:sort (9 7 4 2)}] + skolem:lemma4838 + skolem:lemma4839 + [ a r:Fact; r:gives {(9742 2479) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2794]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 9 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2479]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2794 a r:Inference; + r:gives { + 2795 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2795 math:notEqualTo 0}] + skolem:lemma5221 + [ a r:Fact; r:gives {((2 7 9 5) "=<") list:sort (2 5 7 9)}] + [ a r:Fact; r:gives {((2 7 9 5) ">=") list:sort (9 7 5 2)}] + skolem:lemma4968 + skolem:lemma4969 + [ a r:Fact; r:gives {(9752 2579) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2795]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 9 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2579]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2795 a r:Inference; + r:gives { + 2796 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2796 math:notEqualTo 0}] + skolem:lemma5222 + [ a r:Fact; r:gives {((2 7 9 6) "=<") list:sort (2 6 7 9)}] + [ a r:Fact; r:gives {((2 7 9 6) ">=") list:sort (9 7 6 2)}] + skolem:lemma5088 + skolem:lemma5089 + [ a r:Fact; r:gives {(9762 2679) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2796]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 9 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2679]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2796 a r:Inference; + r:gives { + 2797 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2797 math:notEqualTo 0}] + skolem:lemma5223 + [ a r:Fact; r:gives {((2 7 9 7) "=<") list:sort (2 7 7 9)}] + [ a r:Fact; r:gives {((2 7 9 7) ">=") list:sort (9 7 7 2)}] + skolem:lemma5200 + skolem:lemma5201 + [ a r:Fact; r:gives {(9772 2779) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2797]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 9 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2779]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9772]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2797 a r:Inference; + r:gives { + 2798 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2798 math:notEqualTo 0}] + skolem:lemma5224 + [ a r:Fact; r:gives {((2 7 9 8) "=<") list:sort (2 7 8 9)}] + [ a r:Fact; r:gives {((2 7 9 8) ">=") list:sort (9 8 7 2)}] + skolem:lemma5214 + skolem:lemma5215 + [ a r:Fact; r:gives {(9872 2789) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2798]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 9 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2789]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9872]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2798 a r:Inference; + r:gives { + 2799 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2799 math:notEqualTo 0}] + skolem:lemma5225 + [ a r:Fact; r:gives {((2 7 9 9) "=<") list:sort (2 7 9 9)}] + [ a r:Fact; r:gives {((2 7 9 9) ">=") list:sort (9 9 7 2)}] + skolem:lemma5226 + skolem:lemma5227 + [ a r:Fact; r:gives {(9972 2799) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2799]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 7 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2799]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9972]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2799 a r:Inference; + r:gives { + 2800 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2800 math:notEqualTo 0}] + skolem:lemma5228 + [ a r:Fact; r:gives {((2 8 0 0) "=<") list:sort (0 0 2 8)}] + [ a r:Fact; r:gives {((2 8 0 0) ">=") list:sort (8 2 0 0)}] + skolem:lemma4024 + skolem:lemma4025 + [ a r:Fact; r:gives {(8200 28) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2800 a r:Inference; + r:gives { + 2801 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2801 math:notEqualTo 0}] + skolem:lemma5229 + [ a r:Fact; r:gives {((2 8 0 1) "=<") list:sort (0 1 2 8)}] + [ a r:Fact; r:gives {((2 8 0 1) ">=") list:sort (8 2 1 0)}] + skolem:lemma4052 + skolem:lemma4053 + [ a r:Fact; r:gives {(8210 128) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2801]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 0 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2801 a r:Inference; + r:gives { + 2802 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2802 math:notEqualTo 0}] + skolem:lemma5230 + [ a r:Fact; r:gives {((2 8 0 2) "=<") list:sort (0 2 2 8)}] + [ a r:Fact; r:gives {((2 8 0 2) ">=") list:sort (8 2 2 0)}] + skolem:lemma4078 + skolem:lemma4079 + [ a r:Fact; r:gives {(8220 228) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2802]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 0 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2802 a r:Inference; + r:gives { + 2803 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2803 math:notEqualTo 0}] + skolem:lemma5231 + [ a r:Fact; r:gives {((2 8 0 3) "=<") list:sort (0 2 3 8)}] + [ a r:Fact; r:gives {((2 8 0 3) ">=") list:sort (8 3 2 0)}] + skolem:lemma4102 + skolem:lemma4103 + [ a r:Fact; r:gives {(8320 238) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2803]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 0 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2803 a r:Inference; + r:gives { + 2804 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2804 math:notEqualTo 0}] + skolem:lemma5232 + [ a r:Fact; r:gives {((2 8 0 4) "=<") list:sort (0 2 4 8)}] + [ a r:Fact; r:gives {((2 8 0 4) ">=") list:sort (8 4 2 0)}] + skolem:lemma4124 + skolem:lemma4125 + [ a r:Fact; r:gives {(8420 248) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2804]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 0 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2804 a r:Inference; + r:gives { + 2805 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2805 math:notEqualTo 0}] + skolem:lemma5233 + [ a r:Fact; r:gives {((2 8 0 5) "=<") list:sort (0 2 5 8)}] + [ a r:Fact; r:gives {((2 8 0 5) ">=") list:sort (8 5 2 0)}] + skolem:lemma4144 + skolem:lemma4145 + [ a r:Fact; r:gives {(8520 258) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2805]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 0 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2805 a r:Inference; + r:gives { + 2806 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2806 math:notEqualTo 0}] + skolem:lemma5234 + [ a r:Fact; r:gives {((2 8 0 6) "=<") list:sort (0 2 6 8)}] + [ a r:Fact; r:gives {((2 8 0 6) ">=") list:sort (8 6 2 0)}] + skolem:lemma4162 + skolem:lemma4163 + [ a r:Fact; r:gives {(8620 268) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2806]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 0 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2806 a r:Inference; + r:gives { + 2807 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2807 math:notEqualTo 0}] + skolem:lemma5235 + [ a r:Fact; r:gives {((2 8 0 7) "=<") list:sort (0 2 7 8)}] + [ a r:Fact; r:gives {((2 8 0 7) ">=") list:sort (8 7 2 0)}] + skolem:lemma4178 + skolem:lemma4179 + [ a r:Fact; r:gives {(8720 278) math:difference 8442}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8442 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 8442 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2807]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 0 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2807 a r:Inference; + r:gives { + 2808 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2808 math:notEqualTo 0}] + skolem:lemma5236 + [ a r:Fact; r:gives {((2 8 0 8) "=<") list:sort (0 2 8 8)}] + [ a r:Fact; r:gives {((2 8 0 8) ">=") list:sort (8 8 2 0)}] + skolem:lemma4192 + skolem:lemma4193 + [ a r:Fact; r:gives {(8820 288) math:difference 8532}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8532 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8532 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2808]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 0 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 288]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8820]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2808 a r:Inference; + r:gives { + 2809 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2809 math:notEqualTo 0}] + skolem:lemma5237 + [ a r:Fact; r:gives {((2 8 0 9) "=<") list:sort (0 2 8 9)}] + [ a r:Fact; r:gives {((2 8 0 9) ">=") list:sort (9 8 2 0)}] + skolem:lemma4195 + skolem:lemma4196 + [ a r:Fact; r:gives {(9820 289) math:difference 9531}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9531 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9531 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2809]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 0 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9820]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2809 a r:Inference; + r:gives { + 2810 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2810 math:notEqualTo 0}] + skolem:lemma5238 + [ a r:Fact; r:gives {((2 8 1 0) "=<") list:sort (0 1 2 8)}] + [ a r:Fact; r:gives {((2 8 1 0) ">=") list:sort (8 2 1 0)}] + skolem:lemma4052 + skolem:lemma4053 + [ a r:Fact; r:gives {(8210 128) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2810]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2810 a r:Inference; + r:gives { + 2811 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2811 math:notEqualTo 0}] + skolem:lemma5239 + [ a r:Fact; r:gives {((2 8 1 1) "=<") list:sort (1 1 2 8)}] + [ a r:Fact; r:gives {((2 8 1 1) ">=") list:sort (8 2 1 1)}] + skolem:lemma4242 + skolem:lemma4243 + [ a r:Fact; r:gives {(8211 1128) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2811]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2811 a r:Inference; + r:gives { + 2812 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2812 math:notEqualTo 0}] + skolem:lemma5240 + [ a r:Fact; r:gives {((2 8 1 2) "=<") list:sort (1 2 2 8)}] + [ a r:Fact; r:gives {((2 8 1 2) ">=") list:sort (8 2 2 1)}] + skolem:lemma4268 + skolem:lemma4269 + [ a r:Fact; r:gives {(8221 1228) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2812]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2812 a r:Inference; + r:gives { + 2813 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2813 math:notEqualTo 0}] + skolem:lemma5241 + [ a r:Fact; r:gives {((2 8 1 3) "=<") list:sort (1 2 3 8)}] + [ a r:Fact; r:gives {((2 8 1 3) ">=") list:sort (8 3 2 1)}] + skolem:lemma4292 + skolem:lemma4293 + [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2813]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2813 a r:Inference; + r:gives { + 2814 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2814 math:notEqualTo 0}] + skolem:lemma5242 + [ a r:Fact; r:gives {((2 8 1 4) "=<") list:sort (1 2 4 8)}] + [ a r:Fact; r:gives {((2 8 1 4) ">=") list:sort (8 4 2 1)}] + skolem:lemma4314 + skolem:lemma4315 + [ a r:Fact; r:gives {(8421 1248) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2814]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 1 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2814 a r:Inference; + r:gives { + 2815 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2815 math:notEqualTo 0}] + skolem:lemma5243 + [ a r:Fact; r:gives {((2 8 1 5) "=<") list:sort (1 2 5 8)}] + [ a r:Fact; r:gives {((2 8 1 5) ">=") list:sort (8 5 2 1)}] + skolem:lemma4334 + skolem:lemma4335 + [ a r:Fact; r:gives {(8521 1258) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2815]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 1 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2815 a r:Inference; + r:gives { + 2816 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2816 math:notEqualTo 0}] + skolem:lemma5244 + [ a r:Fact; r:gives {((2 8 1 6) "=<") list:sort (1 2 6 8)}] + [ a r:Fact; r:gives {((2 8 1 6) ">=") list:sort (8 6 2 1)}] + skolem:lemma4352 + skolem:lemma4353 + [ a r:Fact; r:gives {(8621 1268) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2816]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 1 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2816 a r:Inference; + r:gives { + 2817 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2817 math:notEqualTo 0}] + skolem:lemma5245 + [ a r:Fact; r:gives {((2 8 1 7) "=<") list:sort (1 2 7 8)}] + [ a r:Fact; r:gives {((2 8 1 7) ">=") list:sort (8 7 2 1)}] + skolem:lemma4368 + skolem:lemma4369 + [ a r:Fact; r:gives {(8721 1278) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2817]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 1 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2817 a r:Inference; + r:gives { + 2818 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2818 math:notEqualTo 0}] + skolem:lemma5246 + [ a r:Fact; r:gives {((2 8 1 8) "=<") list:sort (1 2 8 8)}] + [ a r:Fact; r:gives {((2 8 1 8) ">=") list:sort (8 8 2 1)}] + skolem:lemma4382 + skolem:lemma4383 + [ a r:Fact; r:gives {(8821 1288) math:difference 7533}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7533 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7533 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2818]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 1 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1288]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8821]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2818 a r:Inference; + r:gives { + 2819 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2819 math:notEqualTo 0}] + skolem:lemma5247 + [ a r:Fact; r:gives {((2 8 1 9) "=<") list:sort (1 2 8 9)}] + [ a r:Fact; r:gives {((2 8 1 9) ">=") list:sort (9 8 2 1)}] + skolem:lemma4385 + skolem:lemma4386 + [ a r:Fact; r:gives {(9821 1289) math:difference 8532}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8532 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8532 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2819]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 1 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9821]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2819 a r:Inference; + r:gives { + 2820 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2820 math:notEqualTo 0}] + skolem:lemma5248 + [ a r:Fact; r:gives {((2 8 2 0) "=<") list:sort (0 2 2 8)}] + [ a r:Fact; r:gives {((2 8 2 0) ">=") list:sort (8 2 2 0)}] + skolem:lemma4078 + skolem:lemma4079 + [ a r:Fact; r:gives {(8220 228) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2820]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2820 a r:Inference; + r:gives { + 2821 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2821 math:notEqualTo 0}] + skolem:lemma5249 + [ a r:Fact; r:gives {((2 8 2 1) "=<") list:sort (1 2 2 8)}] + [ a r:Fact; r:gives {((2 8 2 1) ">=") list:sort (8 2 2 1)}] + skolem:lemma4268 + skolem:lemma4269 + [ a r:Fact; r:gives {(8221 1228) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2821]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2821 a r:Inference; + r:gives { + 2822 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2822 math:notEqualTo 0}] + skolem:lemma5250 + [ a r:Fact; r:gives {((2 8 2 2) "=<") list:sort (2 2 2 8)}] + [ a r:Fact; r:gives {((2 8 2 2) ">=") list:sort (8 2 2 2)}] + skolem:lemma4437 + skolem:lemma4438 + [ a r:Fact; r:gives {(8222 2228) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2822]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2822 a r:Inference; + r:gives { + 2823 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2823 math:notEqualTo 0}] + skolem:lemma5251 + [ a r:Fact; r:gives {((2 8 2 3) "=<") list:sort (2 2 3 8)}] + [ a r:Fact; r:gives {((2 8 2 3) ">=") list:sort (8 3 2 2)}] + skolem:lemma4461 + skolem:lemma4462 + [ a r:Fact; r:gives {(8322 2238) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2823]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2823 a r:Inference; + r:gives { + 2824 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2824 math:notEqualTo 0}] + skolem:lemma5252 + [ a r:Fact; r:gives {((2 8 2 4) "=<") list:sort (2 2 4 8)}] + [ a r:Fact; r:gives {((2 8 2 4) ">=") list:sort (8 4 2 2)}] + skolem:lemma4483 + skolem:lemma4484 + [ a r:Fact; r:gives {(8422 2248) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2824]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2824 a r:Inference; + r:gives { + 2825 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2825 math:notEqualTo 0}] + skolem:lemma5253 + [ a r:Fact; r:gives {((2 8 2 5) "=<") list:sort (2 2 5 8)}] + [ a r:Fact; r:gives {((2 8 2 5) ">=") list:sort (8 5 2 2)}] + skolem:lemma4503 + skolem:lemma4504 + [ a r:Fact; r:gives {(8522 2258) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2825]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2825 a r:Inference; + r:gives { + 2826 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2826 math:notEqualTo 0}] + skolem:lemma5254 + [ a r:Fact; r:gives {((2 8 2 6) "=<") list:sort (2 2 6 8)}] + [ a r:Fact; r:gives {((2 8 2 6) ">=") list:sort (8 6 2 2)}] + skolem:lemma4521 + skolem:lemma4522 + [ a r:Fact; r:gives {(8622 2268) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2826]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2826 a r:Inference; + r:gives { + 2827 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2827 math:notEqualTo 0}] + skolem:lemma5255 + [ a r:Fact; r:gives {((2 8 2 7) "=<") list:sort (2 2 7 8)}] + [ a r:Fact; r:gives {((2 8 2 7) ">=") list:sort (8 7 2 2)}] + skolem:lemma4537 + skolem:lemma4538 + [ a r:Fact; r:gives {(8722 2278) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2827]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2827 a r:Inference; + r:gives { + 2828 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2828 math:notEqualTo 0}] + skolem:lemma5256 + [ a r:Fact; r:gives {((2 8 2 8) "=<") list:sort (2 2 8 8)}] + [ a r:Fact; r:gives {((2 8 2 8) ">=") list:sort (8 8 2 2)}] + skolem:lemma4551 + skolem:lemma4552 + [ a r:Fact; r:gives {(8822 2288) math:difference 6534}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6534 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6534 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2828]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2288]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8822]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6534]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2828 a r:Inference; + r:gives { + 2829 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2829 math:notEqualTo 0}] + skolem:lemma5257 + [ a r:Fact; r:gives {((2 8 2 9) "=<") list:sort (2 2 8 9)}] + [ a r:Fact; r:gives {((2 8 2 9) ">=") list:sort (9 8 2 2)}] + skolem:lemma4554 + skolem:lemma4555 + [ a r:Fact; r:gives {(9822 2289) math:difference 7533}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7533 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7533 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2829]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9822]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2829 a r:Inference; + r:gives { + 2830 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2830 math:notEqualTo 0}] + skolem:lemma5258 + [ a r:Fact; r:gives {((2 8 3 0) "=<") list:sort (0 2 3 8)}] + [ a r:Fact; r:gives {((2 8 3 0) ">=") list:sort (8 3 2 0)}] + skolem:lemma4102 + skolem:lemma4103 + [ a r:Fact; r:gives {(8320 238) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2830]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2830 a r:Inference; + r:gives { + 2831 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2831 math:notEqualTo 0}] + skolem:lemma5259 + [ a r:Fact; r:gives {((2 8 3 1) "=<") list:sort (1 2 3 8)}] + [ a r:Fact; r:gives {((2 8 3 1) ">=") list:sort (8 3 2 1)}] + skolem:lemma4292 + skolem:lemma4293 + [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2831]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2831 a r:Inference; + r:gives { + 2832 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2832 math:notEqualTo 0}] + skolem:lemma5260 + [ a r:Fact; r:gives {((2 8 3 2) "=<") list:sort (2 2 3 8)}] + [ a r:Fact; r:gives {((2 8 3 2) ">=") list:sort (8 3 2 2)}] + skolem:lemma4461 + skolem:lemma4462 + [ a r:Fact; r:gives {(8322 2238) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2832 a r:Inference; + r:gives { + 2833 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2833 math:notEqualTo 0}] + skolem:lemma5261 + [ a r:Fact; r:gives {((2 8 3 3) "=<") list:sort (2 3 3 8)}] + [ a r:Fact; r:gives {((2 8 3 3) ">=") list:sort (8 3 3 2)}] + skolem:lemma4617 + skolem:lemma4618 + [ a r:Fact; r:gives {(8332 2338) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2833]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2833 a r:Inference; + r:gives { + 2834 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2834 math:notEqualTo 0}] + skolem:lemma5262 + [ a r:Fact; r:gives {((2 8 3 4) "=<") list:sort (2 3 4 8)}] + [ a r:Fact; r:gives {((2 8 3 4) ">=") list:sort (8 4 3 2)}] + skolem:lemma4639 + skolem:lemma4640 + [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2834]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2834 a r:Inference; + r:gives { + 2835 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2835 math:notEqualTo 0}] + skolem:lemma5263 + [ a r:Fact; r:gives {((2 8 3 5) "=<") list:sort (2 3 5 8)}] + [ a r:Fact; r:gives {((2 8 3 5) ">=") list:sort (8 5 3 2)}] + skolem:lemma4659 + skolem:lemma4660 + [ a r:Fact; r:gives {(8532 2358) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2835]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2835 a r:Inference; + r:gives { + 2836 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2836 math:notEqualTo 0}] + skolem:lemma5264 + [ a r:Fact; r:gives {((2 8 3 6) "=<") list:sort (2 3 6 8)}] + [ a r:Fact; r:gives {((2 8 3 6) ">=") list:sort (8 6 3 2)}] + skolem:lemma4677 + skolem:lemma4678 + [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2836]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2836 a r:Inference; + r:gives { + 2837 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2837 math:notEqualTo 0}] + skolem:lemma5265 + [ a r:Fact; r:gives {((2 8 3 7) "=<") list:sort (2 3 7 8)}] + [ a r:Fact; r:gives {((2 8 3 7) ">=") list:sort (8 7 3 2)}] + skolem:lemma4693 + skolem:lemma4694 + [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2837]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2837 a r:Inference; + r:gives { + 2838 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2838 math:notEqualTo 0}] + skolem:lemma5266 + [ a r:Fact; r:gives {((2 8 3 8) "=<") list:sort (2 3 8 8)}] + [ a r:Fact; r:gives {((2 8 3 8) ">=") list:sort (8 8 3 2)}] + skolem:lemma4707 + skolem:lemma4708 + [ a r:Fact; r:gives {(8832 2388) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2838]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2838 a r:Inference; + r:gives { + 2839 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2839 math:notEqualTo 0}] + skolem:lemma5267 + [ a r:Fact; r:gives {((2 8 3 9) "=<") list:sort (2 3 8 9)}] + [ a r:Fact; r:gives {((2 8 3 9) ">=") list:sort (9 8 3 2)}] + skolem:lemma4710 + skolem:lemma4711 + [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2839]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2839 a r:Inference; + r:gives { + 2840 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2840 math:notEqualTo 0}] + skolem:lemma5268 + [ a r:Fact; r:gives {((2 8 4 0) "=<") list:sort (0 2 4 8)}] + [ a r:Fact; r:gives {((2 8 4 0) ">=") list:sort (8 4 2 0)}] + skolem:lemma4124 + skolem:lemma4125 + [ a r:Fact; r:gives {(8420 248) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2840]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 4 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2840 a r:Inference; + r:gives { + 2841 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2841 math:notEqualTo 0}] + skolem:lemma5269 + [ a r:Fact; r:gives {((2 8 4 1) "=<") list:sort (1 2 4 8)}] + [ a r:Fact; r:gives {((2 8 4 1) ">=") list:sort (8 4 2 1)}] + skolem:lemma4314 + skolem:lemma4315 + [ a r:Fact; r:gives {(8421 1248) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2841]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 4 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2841 a r:Inference; + r:gives { + 2842 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2842 math:notEqualTo 0}] + skolem:lemma5270 + [ a r:Fact; r:gives {((2 8 4 2) "=<") list:sort (2 2 4 8)}] + [ a r:Fact; r:gives {((2 8 4 2) ">=") list:sort (8 4 2 2)}] + skolem:lemma4483 + skolem:lemma4484 + [ a r:Fact; r:gives {(8422 2248) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2842]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2842 a r:Inference; + r:gives { + 2843 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2843 math:notEqualTo 0}] + skolem:lemma5271 + [ a r:Fact; r:gives {((2 8 4 3) "=<") list:sort (2 3 4 8)}] + [ a r:Fact; r:gives {((2 8 4 3) ">=") list:sort (8 4 3 2)}] + skolem:lemma4639 + skolem:lemma4640 + [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2843]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2843 a r:Inference; + r:gives { + 2844 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2844 math:notEqualTo 0}] + skolem:lemma5272 + [ a r:Fact; r:gives {((2 8 4 4) "=<") list:sort (2 4 4 8)}] + [ a r:Fact; r:gives {((2 8 4 4) ">=") list:sort (8 4 4 2)}] + skolem:lemma4781 + skolem:lemma4782 + [ a r:Fact; r:gives {(8442 2448) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2844]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2448]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2844 a r:Inference; + r:gives { + 2845 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2845 math:notEqualTo 0}] + skolem:lemma5273 + [ a r:Fact; r:gives {((2 8 4 5) "=<") list:sort (2 4 5 8)}] + [ a r:Fact; r:gives {((2 8 4 5) ">=") list:sort (8 5 4 2)}] + skolem:lemma4801 + skolem:lemma4802 + [ a r:Fact; r:gives {(8542 2458) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2845]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2458]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2845 a r:Inference; + r:gives { + 2846 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2846 math:notEqualTo 0}] + skolem:lemma5274 + [ a r:Fact; r:gives {((2 8 4 6) "=<") list:sort (2 4 6 8)}] + [ a r:Fact; r:gives {((2 8 4 6) ">=") list:sort (8 6 4 2)}] + skolem:lemma4819 + skolem:lemma4820 + [ a r:Fact; r:gives {(8642 2468) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2846]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2468]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2846 a r:Inference; + r:gives { + 2847 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2847 math:notEqualTo 0}] + skolem:lemma5275 + [ a r:Fact; r:gives {((2 8 4 7) "=<") list:sort (2 4 7 8)}] + [ a r:Fact; r:gives {((2 8 4 7) ">=") list:sort (8 7 4 2)}] + skolem:lemma4835 + skolem:lemma4836 + [ a r:Fact; r:gives {(8742 2478) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2847]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2478]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2847 a r:Inference; + r:gives { + 2848 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2848 math:notEqualTo 0}] + skolem:lemma5276 + [ a r:Fact; r:gives {((2 8 4 8) "=<") list:sort (2 4 8 8)}] + [ a r:Fact; r:gives {((2 8 4 8) ">=") list:sort (8 8 4 2)}] + skolem:lemma4849 + skolem:lemma4850 + [ a r:Fact; r:gives {(8842 2488) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2848]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2488]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8842]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2848 a r:Inference; + r:gives { + 2849 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2849 math:notEqualTo 0}] + skolem:lemma5277 + [ a r:Fact; r:gives {((2 8 4 9) "=<") list:sort (2 4 8 9)}] + [ a r:Fact; r:gives {((2 8 4 9) ">=") list:sort (9 8 4 2)}] + skolem:lemma4852 + skolem:lemma4853 + [ a r:Fact; r:gives {(9842 2489) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2849]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2489]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9842]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2849 a r:Inference; + r:gives { + 2850 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2850 math:notEqualTo 0}] + skolem:lemma5278 + [ a r:Fact; r:gives {((2 8 5 0) "=<") list:sort (0 2 5 8)}] + [ a r:Fact; r:gives {((2 8 5 0) ">=") list:sort (8 5 2 0)}] + skolem:lemma4144 + skolem:lemma4145 + [ a r:Fact; r:gives {(8520 258) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2850]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 5 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2850 a r:Inference; + r:gives { + 2851 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2851 math:notEqualTo 0}] + skolem:lemma5279 + [ a r:Fact; r:gives {((2 8 5 1) "=<") list:sort (1 2 5 8)}] + [ a r:Fact; r:gives {((2 8 5 1) ">=") list:sort (8 5 2 1)}] + skolem:lemma4334 + skolem:lemma4335 + [ a r:Fact; r:gives {(8521 1258) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2851]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 5 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2851 a r:Inference; + r:gives { + 2852 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2852 math:notEqualTo 0}] + skolem:lemma5280 + [ a r:Fact; r:gives {((2 8 5 2) "=<") list:sort (2 2 5 8)}] + [ a r:Fact; r:gives {((2 8 5 2) ">=") list:sort (8 5 2 2)}] + skolem:lemma4503 + skolem:lemma4504 + [ a r:Fact; r:gives {(8522 2258) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2852]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2852 a r:Inference; + r:gives { + 2853 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2853 math:notEqualTo 0}] + skolem:lemma5281 + [ a r:Fact; r:gives {((2 8 5 3) "=<") list:sort (2 3 5 8)}] + [ a r:Fact; r:gives {((2 8 5 3) ">=") list:sort (8 5 3 2)}] + skolem:lemma4659 + skolem:lemma4660 + [ a r:Fact; r:gives {(8532 2358) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2853]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2853 a r:Inference; + r:gives { + 2854 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2854 math:notEqualTo 0}] + skolem:lemma5282 + [ a r:Fact; r:gives {((2 8 5 4) "=<") list:sort (2 4 5 8)}] + [ a r:Fact; r:gives {((2 8 5 4) ">=") list:sort (8 5 4 2)}] + skolem:lemma4801 + skolem:lemma4802 + [ a r:Fact; r:gives {(8542 2458) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2854]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 5 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2458]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2854 a r:Inference; + r:gives { + 2855 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2855 math:notEqualTo 0}] + skolem:lemma5283 + [ a r:Fact; r:gives {((2 8 5 5) "=<") list:sort (2 5 5 8)}] + [ a r:Fact; r:gives {((2 8 5 5) ">=") list:sort (8 5 5 2)}] + skolem:lemma4931 + skolem:lemma4932 + [ a r:Fact; r:gives {(8552 2558) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2855]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2558]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2855 a r:Inference; + r:gives { + 2856 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2856 math:notEqualTo 0}] + skolem:lemma5284 + [ a r:Fact; r:gives {((2 8 5 6) "=<") list:sort (2 5 6 8)}] + [ a r:Fact; r:gives {((2 8 5 6) ">=") list:sort (8 6 5 2)}] + skolem:lemma4949 + skolem:lemma4950 + [ a r:Fact; r:gives {(8652 2568) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2856]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2568]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2856 a r:Inference; + r:gives { + 2857 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2857 math:notEqualTo 0}] + skolem:lemma5285 + [ a r:Fact; r:gives {((2 8 5 7) "=<") list:sort (2 5 7 8)}] + [ a r:Fact; r:gives {((2 8 5 7) ">=") list:sort (8 7 5 2)}] + skolem:lemma4965 + skolem:lemma4966 + [ a r:Fact; r:gives {(8752 2578) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2857]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2578]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2857 a r:Inference; + r:gives { + 2858 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2858 math:notEqualTo 0}] + skolem:lemma5286 + [ a r:Fact; r:gives {((2 8 5 8) "=<") list:sort (2 5 8 8)}] + [ a r:Fact; r:gives {((2 8 5 8) ">=") list:sort (8 8 5 2)}] + skolem:lemma4979 + skolem:lemma4980 + [ a r:Fact; r:gives {(8852 2588) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2858]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2588]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8852]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2858 a r:Inference; + r:gives { + 2859 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2859 math:notEqualTo 0}] + skolem:lemma5287 + [ a r:Fact; r:gives {((2 8 5 9) "=<") list:sort (2 5 8 9)}] + [ a r:Fact; r:gives {((2 8 5 9) ">=") list:sort (9 8 5 2)}] + skolem:lemma4982 + skolem:lemma4983 + [ a r:Fact; r:gives {(9852 2589) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2859]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2589]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9852]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2859 a r:Inference; + r:gives { + 2860 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2860 math:notEqualTo 0}] + skolem:lemma5288 + [ a r:Fact; r:gives {((2 8 6 0) "=<") list:sort (0 2 6 8)}] + [ a r:Fact; r:gives {((2 8 6 0) ">=") list:sort (8 6 2 0)}] + skolem:lemma4162 + skolem:lemma4163 + [ a r:Fact; r:gives {(8620 268) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2860]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 6 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2860 a r:Inference; + r:gives { + 2861 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2861 math:notEqualTo 0}] + skolem:lemma5289 + [ a r:Fact; r:gives {((2 8 6 1) "=<") list:sort (1 2 6 8)}] + [ a r:Fact; r:gives {((2 8 6 1) ">=") list:sort (8 6 2 1)}] + skolem:lemma4352 + skolem:lemma4353 + [ a r:Fact; r:gives {(8621 1268) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2861]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 6 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2861 a r:Inference; + r:gives { + 2862 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2862 math:notEqualTo 0}] + skolem:lemma5290 + [ a r:Fact; r:gives {((2 8 6 2) "=<") list:sort (2 2 6 8)}] + [ a r:Fact; r:gives {((2 8 6 2) ">=") list:sort (8 6 2 2)}] + skolem:lemma4521 + skolem:lemma4522 + [ a r:Fact; r:gives {(8622 2268) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2862]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2862 a r:Inference; + r:gives { + 2863 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2863 math:notEqualTo 0}] + skolem:lemma5291 + [ a r:Fact; r:gives {((2 8 6 3) "=<") list:sort (2 3 6 8)}] + [ a r:Fact; r:gives {((2 8 6 3) ">=") list:sort (8 6 3 2)}] + skolem:lemma4677 + skolem:lemma4678 + [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2863]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2863 a r:Inference; + r:gives { + 2864 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2864 math:notEqualTo 0}] + skolem:lemma5292 + [ a r:Fact; r:gives {((2 8 6 4) "=<") list:sort (2 4 6 8)}] + [ a r:Fact; r:gives {((2 8 6 4) ">=") list:sort (8 6 4 2)}] + skolem:lemma4819 + skolem:lemma4820 + [ a r:Fact; r:gives {(8642 2468) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2864]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 6 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2468]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2864 a r:Inference; + r:gives { + 2865 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2865 math:notEqualTo 0}] + skolem:lemma5293 + [ a r:Fact; r:gives {((2 8 6 5) "=<") list:sort (2 5 6 8)}] + [ a r:Fact; r:gives {((2 8 6 5) ">=") list:sort (8 6 5 2)}] + skolem:lemma4949 + skolem:lemma4950 + [ a r:Fact; r:gives {(8652 2568) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2865]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 6 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2568]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2865 a r:Inference; + r:gives { + 2866 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2866 math:notEqualTo 0}] + skolem:lemma5294 + [ a r:Fact; r:gives {((2 8 6 6) "=<") list:sort (2 6 6 8)}] + [ a r:Fact; r:gives {((2 8 6 6) ">=") list:sort (8 6 6 2)}] + skolem:lemma5069 + skolem:lemma5070 + [ a r:Fact; r:gives {(8662 2668) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2866]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2668]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8662]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2866 a r:Inference; + r:gives { + 2867 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2867 math:notEqualTo 0}] + skolem:lemma5295 + [ a r:Fact; r:gives {((2 8 6 7) "=<") list:sort (2 6 7 8)}] + [ a r:Fact; r:gives {((2 8 6 7) ">=") list:sort (8 7 6 2)}] + skolem:lemma5085 + skolem:lemma5086 + [ a r:Fact; r:gives {(8762 2678) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2867]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2678]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2867 a r:Inference; + r:gives { + 2868 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2868 math:notEqualTo 0}] + skolem:lemma5296 + [ a r:Fact; r:gives {((2 8 6 8) "=<") list:sort (2 6 8 8)}] + [ a r:Fact; r:gives {((2 8 6 8) ">=") list:sort (8 8 6 2)}] + skolem:lemma5099 + skolem:lemma5100 + [ a r:Fact; r:gives {(8862 2688) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2868]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2688]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8862]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2868 a r:Inference; + r:gives { + 2869 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2869 math:notEqualTo 0}] + skolem:lemma5297 + [ a r:Fact; r:gives {((2 8 6 9) "=<") list:sort (2 6 8 9)}] + [ a r:Fact; r:gives {((2 8 6 9) ">=") list:sort (9 8 6 2)}] + skolem:lemma5102 + skolem:lemma5103 + [ a r:Fact; r:gives {(9862 2689) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2869]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2689]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9862]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2869 a r:Inference; + r:gives { + 2870 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2870 math:notEqualTo 0}] + skolem:lemma5298 + [ a r:Fact; r:gives {((2 8 7 0) "=<") list:sort (0 2 7 8)}] + [ a r:Fact; r:gives {((2 8 7 0) ">=") list:sort (8 7 2 0)}] + skolem:lemma4178 + skolem:lemma4179 + [ a r:Fact; r:gives {(8720 278) math:difference 8442}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8442 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 8442 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2870]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 7 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2870 a r:Inference; + r:gives { + 2871 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2871 math:notEqualTo 0}] + skolem:lemma5299 + [ a r:Fact; r:gives {((2 8 7 1) "=<") list:sort (1 2 7 8)}] + [ a r:Fact; r:gives {((2 8 7 1) ">=") list:sort (8 7 2 1)}] + skolem:lemma4368 + skolem:lemma4369 + [ a r:Fact; r:gives {(8721 1278) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2871]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 7 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2871 a r:Inference; + r:gives { + 2872 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2872 math:notEqualTo 0}] + skolem:lemma5300 + [ a r:Fact; r:gives {((2 8 7 2) "=<") list:sort (2 2 7 8)}] + [ a r:Fact; r:gives {((2 8 7 2) ">=") list:sort (8 7 2 2)}] + skolem:lemma4537 + skolem:lemma4538 + [ a r:Fact; r:gives {(8722 2278) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2872]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2872 a r:Inference; + r:gives { + 2873 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2873 math:notEqualTo 0}] + skolem:lemma5301 + [ a r:Fact; r:gives {((2 8 7 3) "=<") list:sort (2 3 7 8)}] + [ a r:Fact; r:gives {((2 8 7 3) ">=") list:sort (8 7 3 2)}] + skolem:lemma4693 + skolem:lemma4694 + [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2873]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2873 a r:Inference; + r:gives { + 2874 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2874 math:notEqualTo 0}] + skolem:lemma5302 + [ a r:Fact; r:gives {((2 8 7 4) "=<") list:sort (2 4 7 8)}] + [ a r:Fact; r:gives {((2 8 7 4) ">=") list:sort (8 7 4 2)}] + skolem:lemma4835 + skolem:lemma4836 + [ a r:Fact; r:gives {(8742 2478) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2874]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 7 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2478]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2874 a r:Inference; + r:gives { + 2875 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2875 math:notEqualTo 0}] + skolem:lemma5303 + [ a r:Fact; r:gives {((2 8 7 5) "=<") list:sort (2 5 7 8)}] + [ a r:Fact; r:gives {((2 8 7 5) ">=") list:sort (8 7 5 2)}] + skolem:lemma4965 + skolem:lemma4966 + [ a r:Fact; r:gives {(8752 2578) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2875]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 7 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2578]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2875 a r:Inference; + r:gives { + 2876 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2876 math:notEqualTo 0}] + skolem:lemma5304 + [ a r:Fact; r:gives {((2 8 7 6) "=<") list:sort (2 6 7 8)}] + [ a r:Fact; r:gives {((2 8 7 6) ">=") list:sort (8 7 6 2)}] + skolem:lemma5085 + skolem:lemma5086 + [ a r:Fact; r:gives {(8762 2678) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2876]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 7 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2678]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2876 a r:Inference; + r:gives { + 2877 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2877 math:notEqualTo 0}] + skolem:lemma5305 + [ a r:Fact; r:gives {((2 8 7 7) "=<") list:sort (2 7 7 8)}] + [ a r:Fact; r:gives {((2 8 7 7) ">=") list:sort (8 7 7 2)}] + skolem:lemma5197 + skolem:lemma5198 + [ a r:Fact; r:gives {(8772 2778) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2877]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2778]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8772]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2877 a r:Inference; + r:gives { + 2878 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2878 math:notEqualTo 0}] + skolem:lemma5306 + [ a r:Fact; r:gives {((2 8 7 8) "=<") list:sort (2 7 8 8)}] + [ a r:Fact; r:gives {((2 8 7 8) ">=") list:sort (8 8 7 2)}] + skolem:lemma5211 + skolem:lemma5212 + [ a r:Fact; r:gives {(8872 2788) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2878]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2788]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8872]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2878 a r:Inference; + r:gives { + 2879 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2879 math:notEqualTo 0}] + skolem:lemma5307 + [ a r:Fact; r:gives {((2 8 7 9) "=<") list:sort (2 7 8 9)}] + [ a r:Fact; r:gives {((2 8 7 9) ">=") list:sort (9 8 7 2)}] + skolem:lemma5214 + skolem:lemma5215 + [ a r:Fact; r:gives {(9872 2789) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2879]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2789]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9872]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2879 a r:Inference; + r:gives { + 2880 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2880 math:notEqualTo 0}] + skolem:lemma5308 + [ a r:Fact; r:gives {((2 8 8 0) "=<") list:sort (0 2 8 8)}] + [ a r:Fact; r:gives {((2 8 8 0) ">=") list:sort (8 8 2 0)}] + skolem:lemma4192 + skolem:lemma4193 + [ a r:Fact; r:gives {(8820 288) math:difference 8532}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8532 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8532 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2880]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 8 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 288]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8820]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2880 a r:Inference; + r:gives { + 2881 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2881 math:notEqualTo 0}] + skolem:lemma5309 + [ a r:Fact; r:gives {((2 8 8 1) "=<") list:sort (1 2 8 8)}] + [ a r:Fact; r:gives {((2 8 8 1) ">=") list:sort (8 8 2 1)}] + skolem:lemma4382 + skolem:lemma4383 + [ a r:Fact; r:gives {(8821 1288) math:difference 7533}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7533 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7533 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2881]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 8 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1288]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8821]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2881 a r:Inference; + r:gives { + 2882 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2882 math:notEqualTo 0}] + skolem:lemma5310 + [ a r:Fact; r:gives {((2 8 8 2) "=<") list:sort (2 2 8 8)}] + [ a r:Fact; r:gives {((2 8 8 2) ">=") list:sort (8 8 2 2)}] + skolem:lemma4551 + skolem:lemma4552 + [ a r:Fact; r:gives {(8822 2288) math:difference 6534}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6534 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6534 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2882]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2288]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8822]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6534]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2882 a r:Inference; + r:gives { + 2883 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2883 math:notEqualTo 0}] + skolem:lemma5311 + [ a r:Fact; r:gives {((2 8 8 3) "=<") list:sort (2 3 8 8)}] + [ a r:Fact; r:gives {((2 8 8 3) ">=") list:sort (8 8 3 2)}] + skolem:lemma4707 + skolem:lemma4708 + [ a r:Fact; r:gives {(8832 2388) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2883]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2883 a r:Inference; + r:gives { + 2884 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2884 math:notEqualTo 0}] + skolem:lemma5312 + [ a r:Fact; r:gives {((2 8 8 4) "=<") list:sort (2 4 8 8)}] + [ a r:Fact; r:gives {((2 8 8 4) ">=") list:sort (8 8 4 2)}] + skolem:lemma4849 + skolem:lemma4850 + [ a r:Fact; r:gives {(8842 2488) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2884]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 8 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2488]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8842]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2884 a r:Inference; + r:gives { + 2885 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2885 math:notEqualTo 0}] + skolem:lemma5313 + [ a r:Fact; r:gives {((2 8 8 5) "=<") list:sort (2 5 8 8)}] + [ a r:Fact; r:gives {((2 8 8 5) ">=") list:sort (8 8 5 2)}] + skolem:lemma4979 + skolem:lemma4980 + [ a r:Fact; r:gives {(8852 2588) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2885]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 8 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2588]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8852]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2885 a r:Inference; + r:gives { + 2886 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {2886 math:notEqualTo 0}] + skolem:lemma5314 + [ a r:Fact; r:gives {((2 8 8 6) "=<") list:sort (2 6 8 8)}] + [ a r:Fact; r:gives {((2 8 8 6) ">=") list:sort (8 8 6 2)}] + skolem:lemma5099 + skolem:lemma5100 + [ a r:Fact; r:gives {(8862 2688) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2886]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 8 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2688]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8862]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma2886 a r:Inference; + r:gives { + 2887 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2887 math:notEqualTo 0}] + skolem:lemma5315 + [ a r:Fact; r:gives {((2 8 8 7) "=<") list:sort (2 7 8 8)}] + [ a r:Fact; r:gives {((2 8 8 7) ">=") list:sort (8 8 7 2)}] + skolem:lemma5211 + skolem:lemma5212 + [ a r:Fact; r:gives {(8872 2788) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2887]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 8 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2788]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8872]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2887 a r:Inference; + r:gives { + 2888 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2888 math:notEqualTo 0}] + skolem:lemma5316 + [ a r:Fact; r:gives {((2 8 8 8) "=<") list:sort (2 8 8 8)}] + [ a r:Fact; r:gives {((2 8 8 8) ">=") list:sort (8 8 8 2)}] + skolem:lemma5317 + skolem:lemma5318 + [ a r:Fact; r:gives {(8882 2888) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2888]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 8 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2888]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8882]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2888 a r:Inference; + r:gives { + 2889 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2889 math:notEqualTo 0}] + skolem:lemma5319 + [ a r:Fact; r:gives {((2 8 8 9) "=<") list:sort (2 8 8 9)}] + [ a r:Fact; r:gives {((2 8 8 9) ">=") list:sort (9 8 8 2)}] + skolem:lemma5320 + skolem:lemma5321 + [ a r:Fact; r:gives {(9882 2889) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2889]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 8 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2889]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9882]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2889 a r:Inference; + r:gives { + 2890 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2890 math:notEqualTo 0}] + skolem:lemma5322 + [ a r:Fact; r:gives {((2 8 9 0) "=<") list:sort (0 2 8 9)}] + [ a r:Fact; r:gives {((2 8 9 0) ">=") list:sort (9 8 2 0)}] + skolem:lemma4195 + skolem:lemma4196 + [ a r:Fact; r:gives {(9820 289) math:difference 9531}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9531 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9531 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2890]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 9 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9820]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2890 a r:Inference; + r:gives { + 2891 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2891 math:notEqualTo 0}] + skolem:lemma5323 + [ a r:Fact; r:gives {((2 8 9 1) "=<") list:sort (1 2 8 9)}] + [ a r:Fact; r:gives {((2 8 9 1) ">=") list:sort (9 8 2 1)}] + skolem:lemma4385 + skolem:lemma4386 + [ a r:Fact; r:gives {(9821 1289) math:difference 8532}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8532 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8532 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2891]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 9 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9821]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2891 a r:Inference; + r:gives { + 2892 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2892 math:notEqualTo 0}] + skolem:lemma5324 + [ a r:Fact; r:gives {((2 8 9 2) "=<") list:sort (2 2 8 9)}] + [ a r:Fact; r:gives {((2 8 9 2) ">=") list:sort (9 8 2 2)}] + skolem:lemma4554 + skolem:lemma4555 + [ a r:Fact; r:gives {(9822 2289) math:difference 7533}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7533 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7533 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2892]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 9 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9822]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2892 a r:Inference; + r:gives { + 2893 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2893 math:notEqualTo 0}] + skolem:lemma5325 + [ a r:Fact; r:gives {((2 8 9 3) "=<") list:sort (2 3 8 9)}] + [ a r:Fact; r:gives {((2 8 9 3) ">=") list:sort (9 8 3 2)}] + skolem:lemma4710 + skolem:lemma4711 + [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2893]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 9 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2893 a r:Inference; + r:gives { + 2894 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2894 math:notEqualTo 0}] + skolem:lemma5326 + [ a r:Fact; r:gives {((2 8 9 4) "=<") list:sort (2 4 8 9)}] + [ a r:Fact; r:gives {((2 8 9 4) ">=") list:sort (9 8 4 2)}] + skolem:lemma4852 + skolem:lemma4853 + [ a r:Fact; r:gives {(9842 2489) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2894]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 9 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2489]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9842]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2894 a r:Inference; + r:gives { + 2895 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2895 math:notEqualTo 0}] + skolem:lemma5327 + [ a r:Fact; r:gives {((2 8 9 5) "=<") list:sort (2 5 8 9)}] + [ a r:Fact; r:gives {((2 8 9 5) ">=") list:sort (9 8 5 2)}] + skolem:lemma4982 + skolem:lemma4983 + [ a r:Fact; r:gives {(9852 2589) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2895]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 9 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2589]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9852]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2895 a r:Inference; + r:gives { + 2896 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2896 math:notEqualTo 0}] + skolem:lemma5328 + [ a r:Fact; r:gives {((2 8 9 6) "=<") list:sort (2 6 8 9)}] + [ a r:Fact; r:gives {((2 8 9 6) ">=") list:sort (9 8 6 2)}] + skolem:lemma5102 + skolem:lemma5103 + [ a r:Fact; r:gives {(9862 2689) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2896]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 9 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2689]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9862]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2896 a r:Inference; + r:gives { + 2897 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2897 math:notEqualTo 0}] + skolem:lemma5329 + [ a r:Fact; r:gives {((2 8 9 7) "=<") list:sort (2 7 8 9)}] + [ a r:Fact; r:gives {((2 8 9 7) ">=") list:sort (9 8 7 2)}] + skolem:lemma5214 + skolem:lemma5215 + [ a r:Fact; r:gives {(9872 2789) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2897]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 9 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2789]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9872]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2897 a r:Inference; + r:gives { + 2898 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2898 math:notEqualTo 0}] + skolem:lemma5330 + [ a r:Fact; r:gives {((2 8 9 8) "=<") list:sort (2 8 8 9)}] + [ a r:Fact; r:gives {((2 8 9 8) ">=") list:sort (9 8 8 2)}] + skolem:lemma5320 + skolem:lemma5321 + [ a r:Fact; r:gives {(9882 2889) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2898]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 9 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 8 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2889]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9882]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2898 a r:Inference; + r:gives { + 2899 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2899 math:notEqualTo 0}] + skolem:lemma5331 + [ a r:Fact; r:gives {((2 8 9 9) "=<") list:sort (2 8 9 9)}] + [ a r:Fact; r:gives {((2 8 9 9) ">=") list:sort (9 9 8 2)}] + skolem:lemma5332 + skolem:lemma5333 + [ a r:Fact; r:gives {(9982 2899) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2899]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 8 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 8 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2899]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9982]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2899 a r:Inference; + r:gives { + 2900 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2900 math:notEqualTo 0}] + skolem:lemma5334 + [ a r:Fact; r:gives {((2 9 0 0) "=<") list:sort (0 0 2 9)}] + [ a r:Fact; r:gives {((2 9 0 0) ">=") list:sort (9 2 0 0)}] + skolem:lemma4027 + skolem:lemma4028 + [ a r:Fact; r:gives {(9200 29) math:difference 9171}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9171 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9171 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2900]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2900 a r:Inference; + r:gives { + 2901 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2901 math:notEqualTo 0}] + skolem:lemma5335 + [ a r:Fact; r:gives {((2 9 0 1) "=<") list:sort (0 1 2 9)}] + [ a r:Fact; r:gives {((2 9 0 1) ">=") list:sort (9 2 1 0)}] + skolem:lemma4055 + skolem:lemma4056 + [ a r:Fact; r:gives {(9210 129) math:difference 9081}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9081 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 9081 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2901]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 0 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2901 a r:Inference; + r:gives { + 2902 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2902 math:notEqualTo 0}] + skolem:lemma5336 + [ a r:Fact; r:gives {((2 9 0 2) "=<") list:sort (0 2 2 9)}] + [ a r:Fact; r:gives {((2 9 0 2) ">=") list:sort (9 2 2 0)}] + skolem:lemma4081 + skolem:lemma4082 + [ a r:Fact; r:gives {(9220 229) math:difference 8991}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8991 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 8991 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2902]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 0 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8991]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2902 a r:Inference; + r:gives { + 2903 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2903 math:notEqualTo 0}] + skolem:lemma5337 + [ a r:Fact; r:gives {((2 9 0 3) "=<") list:sort (0 2 3 9)}] + [ a r:Fact; r:gives {((2 9 0 3) ">=") list:sort (9 3 2 0)}] + skolem:lemma4105 + skolem:lemma4106 + [ a r:Fact; r:gives {(9320 239) math:difference 9081}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9081 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 9081 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2903]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 0 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2903 a r:Inference; + r:gives { + 2904 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2904 math:notEqualTo 0}] + skolem:lemma5338 + [ a r:Fact; r:gives {((2 9 0 4) "=<") list:sort (0 2 4 9)}] + [ a r:Fact; r:gives {((2 9 0 4) ">=") list:sort (9 4 2 0)}] + skolem:lemma4127 + skolem:lemma4128 + [ a r:Fact; r:gives {(9420 249) math:difference 9171}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9171 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9171 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2904]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 0 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2904 a r:Inference; + r:gives { + 2905 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2905 math:notEqualTo 0}] + skolem:lemma5339 + [ a r:Fact; r:gives {((2 9 0 5) "=<") list:sort (0 2 5 9)}] + [ a r:Fact; r:gives {((2 9 0 5) ">=") list:sort (9 5 2 0)}] + skolem:lemma4147 + skolem:lemma4148 + [ a r:Fact; r:gives {(9520 259) math:difference 9261}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9261 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9261 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2905]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 0 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9261]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2905 a r:Inference; + r:gives { + 2906 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2906 math:notEqualTo 0}] + skolem:lemma5340 + [ a r:Fact; r:gives {((2 9 0 6) "=<") list:sort (0 2 6 9)}] + [ a r:Fact; r:gives {((2 9 0 6) ">=") list:sort (9 6 2 0)}] + skolem:lemma4165 + skolem:lemma4166 + [ a r:Fact; r:gives {(9620 269) math:difference 9351}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9351 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9351 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2906]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 0 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9351]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2906 a r:Inference; + r:gives { + 2907 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2907 math:notEqualTo 0}] + skolem:lemma5341 + [ a r:Fact; r:gives {((2 9 0 7) "=<") list:sort (0 2 7 9)}] + [ a r:Fact; r:gives {((2 9 0 7) ">=") list:sort (9 7 2 0)}] + skolem:lemma4181 + skolem:lemma4182 + [ a r:Fact; r:gives {(9720 279) math:difference 9441}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9441 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9441 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2907]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 0 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9441]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2907 a r:Inference; + r:gives { + 2908 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2908 math:notEqualTo 0}] + skolem:lemma5342 + [ a r:Fact; r:gives {((2 9 0 8) "=<") list:sort (0 2 8 9)}] + [ a r:Fact; r:gives {((2 9 0 8) ">=") list:sort (9 8 2 0)}] + skolem:lemma4195 + skolem:lemma4196 + [ a r:Fact; r:gives {(9820 289) math:difference 9531}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9531 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9531 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2908]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 0 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9820]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2908 a r:Inference; + r:gives { + 2909 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2909 math:notEqualTo 0}] + skolem:lemma5343 + [ a r:Fact; r:gives {((2 9 0 9) "=<") list:sort (0 2 9 9)}] + [ a r:Fact; r:gives {((2 9 0 9) ">=") list:sort (9 9 2 0)}] + skolem:lemma4207 + skolem:lemma4208 + [ a r:Fact; r:gives {(9920 299) math:difference 9621}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9621 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9621 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2909]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 0 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9920]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2909 a r:Inference; + r:gives { + 2910 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2910 math:notEqualTo 0}] + skolem:lemma5344 + [ a r:Fact; r:gives {((2 9 1 0) "=<") list:sort (0 1 2 9)}] + [ a r:Fact; r:gives {((2 9 1 0) ">=") list:sort (9 2 1 0)}] + skolem:lemma4055 + skolem:lemma4056 + [ a r:Fact; r:gives {(9210 129) math:difference 9081}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9081 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 9081 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2910]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2910 a r:Inference; + r:gives { + 2911 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2911 math:notEqualTo 0}] + skolem:lemma5345 + [ a r:Fact; r:gives {((2 9 1 1) "=<") list:sort (1 1 2 9)}] + [ a r:Fact; r:gives {((2 9 1 1) ">=") list:sort (9 2 1 1)}] + skolem:lemma4245 + skolem:lemma4246 + [ a r:Fact; r:gives {(9211 1129) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2911]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2911 a r:Inference; + r:gives { + 2912 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2912 math:notEqualTo 0}] + skolem:lemma5346 + [ a r:Fact; r:gives {((2 9 1 2) "=<") list:sort (1 2 2 9)}] + [ a r:Fact; r:gives {((2 9 1 2) ">=") list:sort (9 2 2 1)}] + skolem:lemma4271 + skolem:lemma4272 + [ a r:Fact; r:gives {(9221 1229) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2912]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2912 a r:Inference; + r:gives { + 2913 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2913 math:notEqualTo 0}] + skolem:lemma5347 + [ a r:Fact; r:gives {((2 9 1 3) "=<") list:sort (1 2 3 9)}] + [ a r:Fact; r:gives {((2 9 1 3) ">=") list:sort (9 3 2 1)}] + skolem:lemma4295 + skolem:lemma4296 + [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2913]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2913 a r:Inference; + r:gives { + 2914 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2914 math:notEqualTo 0}] + skolem:lemma5348 + [ a r:Fact; r:gives {((2 9 1 4) "=<") list:sort (1 2 4 9)}] + [ a r:Fact; r:gives {((2 9 1 4) ">=") list:sort (9 4 2 1)}] + skolem:lemma4317 + skolem:lemma4318 + [ a r:Fact; r:gives {(9421 1249) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2914]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 1 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2914 a r:Inference; + r:gives { + 2915 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2915 math:notEqualTo 0}] + skolem:lemma5349 + [ a r:Fact; r:gives {((2 9 1 5) "=<") list:sort (1 2 5 9)}] + [ a r:Fact; r:gives {((2 9 1 5) ">=") list:sort (9 5 2 1)}] + skolem:lemma4337 + skolem:lemma4338 + [ a r:Fact; r:gives {(9521 1259) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2915]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 1 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2915 a r:Inference; + r:gives { + 2916 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2916 math:notEqualTo 0}] + skolem:lemma5350 + [ a r:Fact; r:gives {((2 9 1 6) "=<") list:sort (1 2 6 9)}] + [ a r:Fact; r:gives {((2 9 1 6) ">=") list:sort (9 6 2 1)}] + skolem:lemma4355 + skolem:lemma4356 + [ a r:Fact; r:gives {(9621 1269) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2916]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 1 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2916 a r:Inference; + r:gives { + 2917 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2917 math:notEqualTo 0}] + skolem:lemma5351 + [ a r:Fact; r:gives {((2 9 1 7) "=<") list:sort (1 2 7 9)}] + [ a r:Fact; r:gives {((2 9 1 7) ">=") list:sort (9 7 2 1)}] + skolem:lemma4371 + skolem:lemma4372 + [ a r:Fact; r:gives {(9721 1279) math:difference 8442}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8442 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 8442 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2917]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 1 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2917 a r:Inference; + r:gives { + 2918 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2918 math:notEqualTo 0}] + skolem:lemma5352 + [ a r:Fact; r:gives {((2 9 1 8) "=<") list:sort (1 2 8 9)}] + [ a r:Fact; r:gives {((2 9 1 8) ">=") list:sort (9 8 2 1)}] + skolem:lemma4385 + skolem:lemma4386 + [ a r:Fact; r:gives {(9821 1289) math:difference 8532}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8532 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8532 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2918]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 1 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9821]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2918 a r:Inference; + r:gives { + 2919 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2919 math:notEqualTo 0}] + skolem:lemma5353 + [ a r:Fact; r:gives {((2 9 1 9) "=<") list:sort (1 2 9 9)}] + [ a r:Fact; r:gives {((2 9 1 9) ">=") list:sort (9 9 2 1)}] + skolem:lemma4397 + skolem:lemma4398 + [ a r:Fact; r:gives {(9921 1299) math:difference 8622}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8622 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8622 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2919]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 1 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9921]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2919 a r:Inference; + r:gives { + 2920 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2920 math:notEqualTo 0}] + skolem:lemma5354 + [ a r:Fact; r:gives {((2 9 2 0) "=<") list:sort (0 2 2 9)}] + [ a r:Fact; r:gives {((2 9 2 0) ">=") list:sort (9 2 2 0)}] + skolem:lemma4081 + skolem:lemma4082 + [ a r:Fact; r:gives {(9220 229) math:difference 8991}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8991 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 8991 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2920]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8991]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2920 a r:Inference; + r:gives { + 2921 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2921 math:notEqualTo 0}] + skolem:lemma5355 + [ a r:Fact; r:gives {((2 9 2 1) "=<") list:sort (1 2 2 9)}] + [ a r:Fact; r:gives {((2 9 2 1) ">=") list:sort (9 2 2 1)}] + skolem:lemma4271 + skolem:lemma4272 + [ a r:Fact; r:gives {(9221 1229) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2921]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2921 a r:Inference; + r:gives { + 2922 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2922 math:notEqualTo 0}] + skolem:lemma5356 + [ a r:Fact; r:gives {((2 9 2 2) "=<") list:sort (2 2 2 9)}] + [ a r:Fact; r:gives {((2 9 2 2) ">=") list:sort (9 2 2 2)}] + skolem:lemma4440 + skolem:lemma4441 + [ a r:Fact; r:gives {(9222 2229) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2922]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2922 a r:Inference; + r:gives { + 2923 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2923 math:notEqualTo 0}] + skolem:lemma5357 + [ a r:Fact; r:gives {((2 9 2 3) "=<") list:sort (2 2 3 9)}] + [ a r:Fact; r:gives {((2 9 2 3) ">=") list:sort (9 3 2 2)}] + skolem:lemma4464 + skolem:lemma4465 + [ a r:Fact; r:gives {(9322 2239) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2923]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2923 a r:Inference; + r:gives { + 2924 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2924 math:notEqualTo 0}] + skolem:lemma5358 + [ a r:Fact; r:gives {((2 9 2 4) "=<") list:sort (2 2 4 9)}] + [ a r:Fact; r:gives {((2 9 2 4) ">=") list:sort (9 4 2 2)}] + skolem:lemma4486 + skolem:lemma4487 + [ a r:Fact; r:gives {(9422 2249) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2924]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2924 a r:Inference; + r:gives { + 2925 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2925 math:notEqualTo 0}] + skolem:lemma5359 + [ a r:Fact; r:gives {((2 9 2 5) "=<") list:sort (2 2 5 9)}] + [ a r:Fact; r:gives {((2 9 2 5) ">=") list:sort (9 5 2 2)}] + skolem:lemma4506 + skolem:lemma4507 + [ a r:Fact; r:gives {(9522 2259) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2925]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2925 a r:Inference; + r:gives { + 2926 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2926 math:notEqualTo 0}] + skolem:lemma5360 + [ a r:Fact; r:gives {((2 9 2 6) "=<") list:sort (2 2 6 9)}] + [ a r:Fact; r:gives {((2 9 2 6) ">=") list:sort (9 6 2 2)}] + skolem:lemma4524 + skolem:lemma4525 + [ a r:Fact; r:gives {(9622 2269) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2926]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2926 a r:Inference; + r:gives { + 2927 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2927 math:notEqualTo 0}] + skolem:lemma5361 + [ a r:Fact; r:gives {((2 9 2 7) "=<") list:sort (2 2 7 9)}] + [ a r:Fact; r:gives {((2 9 2 7) ">=") list:sort (9 7 2 2)}] + skolem:lemma4540 + skolem:lemma4541 + [ a r:Fact; r:gives {(9722 2279) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2927]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2927 a r:Inference; + r:gives { + 2928 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2928 math:notEqualTo 0}] + skolem:lemma5362 + [ a r:Fact; r:gives {((2 9 2 8) "=<") list:sort (2 2 8 9)}] + [ a r:Fact; r:gives {((2 9 2 8) ">=") list:sort (9 8 2 2)}] + skolem:lemma4554 + skolem:lemma4555 + [ a r:Fact; r:gives {(9822 2289) math:difference 7533}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7533 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7533 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2928]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9822]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2928 a r:Inference; + r:gives { + 2929 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2929 math:notEqualTo 0}] + skolem:lemma5363 + [ a r:Fact; r:gives {((2 9 2 9) "=<") list:sort (2 2 9 9)}] + [ a r:Fact; r:gives {((2 9 2 9) ">=") list:sort (9 9 2 2)}] + skolem:lemma4566 + skolem:lemma4567 + [ a r:Fact; r:gives {(9922 2299) math:difference 7623}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7623 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7623 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2929]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9922]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7623]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2929 a r:Inference; + r:gives { + 2930 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2930 math:notEqualTo 0}] + skolem:lemma5364 + [ a r:Fact; r:gives {((2 9 3 0) "=<") list:sort (0 2 3 9)}] + [ a r:Fact; r:gives {((2 9 3 0) ">=") list:sort (9 3 2 0)}] + skolem:lemma4105 + skolem:lemma4106 + [ a r:Fact; r:gives {(9320 239) math:difference 9081}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9081 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 9081 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2930]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2930 a r:Inference; + r:gives { + 2931 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2931 math:notEqualTo 0}] + skolem:lemma5365 + [ a r:Fact; r:gives {((2 9 3 1) "=<") list:sort (1 2 3 9)}] + [ a r:Fact; r:gives {((2 9 3 1) ">=") list:sort (9 3 2 1)}] + skolem:lemma4295 + skolem:lemma4296 + [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2931]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2931 a r:Inference; + r:gives { + 2932 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2932 math:notEqualTo 0}] + skolem:lemma5366 + [ a r:Fact; r:gives {((2 9 3 2) "=<") list:sort (2 2 3 9)}] + [ a r:Fact; r:gives {((2 9 3 2) ">=") list:sort (9 3 2 2)}] + skolem:lemma4464 + skolem:lemma4465 + [ a r:Fact; r:gives {(9322 2239) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2932]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2932 a r:Inference; + r:gives { + 2933 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2933 math:notEqualTo 0}] + skolem:lemma5367 + [ a r:Fact; r:gives {((2 9 3 3) "=<") list:sort (2 3 3 9)}] + [ a r:Fact; r:gives {((2 9 3 3) ">=") list:sort (9 3 3 2)}] + skolem:lemma4620 + skolem:lemma4621 + [ a r:Fact; r:gives {(9332 2339) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2933]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2933 a r:Inference; + r:gives { + 2934 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2934 math:notEqualTo 0}] + skolem:lemma5368 + [ a r:Fact; r:gives {((2 9 3 4) "=<") list:sort (2 3 4 9)}] + [ a r:Fact; r:gives {((2 9 3 4) ">=") list:sort (9 4 3 2)}] + skolem:lemma4642 + skolem:lemma4643 + [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2934]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2934 a r:Inference; + r:gives { + 2935 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2935 math:notEqualTo 0}] + skolem:lemma5369 + [ a r:Fact; r:gives {((2 9 3 5) "=<") list:sort (2 3 5 9)}] + [ a r:Fact; r:gives {((2 9 3 5) ">=") list:sort (9 5 3 2)}] + skolem:lemma4662 + skolem:lemma4663 + [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2935]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2935 a r:Inference; + r:gives { + 2936 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2936 math:notEqualTo 0}] + skolem:lemma5370 + [ a r:Fact; r:gives {((2 9 3 6) "=<") list:sort (2 3 6 9)}] + [ a r:Fact; r:gives {((2 9 3 6) ">=") list:sort (9 6 3 2)}] + skolem:lemma4680 + skolem:lemma4681 + [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2936]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2936 a r:Inference; + r:gives { + 2937 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2937 math:notEqualTo 0}] + skolem:lemma5371 + [ a r:Fact; r:gives {((2 9 3 7) "=<") list:sort (2 3 7 9)}] + [ a r:Fact; r:gives {((2 9 3 7) ">=") list:sort (9 7 3 2)}] + skolem:lemma4696 + skolem:lemma4697 + [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2937]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2937 a r:Inference; + r:gives { + 2938 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2938 math:notEqualTo 0}] + skolem:lemma5372 + [ a r:Fact; r:gives {((2 9 3 8) "=<") list:sort (2 3 8 9)}] + [ a r:Fact; r:gives {((2 9 3 8) ">=") list:sort (9 8 3 2)}] + skolem:lemma4710 + skolem:lemma4711 + [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2938]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2938 a r:Inference; + r:gives { + 2939 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2939 math:notEqualTo 0}] + skolem:lemma5373 + [ a r:Fact; r:gives {((2 9 3 9) "=<") list:sort (2 3 9 9)}] + [ a r:Fact; r:gives {((2 9 3 9) ">=") list:sort (9 9 3 2)}] + skolem:lemma4722 + skolem:lemma4723 + [ a r:Fact; r:gives {(9932 2399) math:difference 7533}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7533 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7533 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2939]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9932]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2939 a r:Inference; + r:gives { + 2940 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2940 math:notEqualTo 0}] + skolem:lemma5374 + [ a r:Fact; r:gives {((2 9 4 0) "=<") list:sort (0 2 4 9)}] + [ a r:Fact; r:gives {((2 9 4 0) ">=") list:sort (9 4 2 0)}] + skolem:lemma4127 + skolem:lemma4128 + [ a r:Fact; r:gives {(9420 249) math:difference 9171}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9171 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9171 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2940]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 4 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2940 a r:Inference; + r:gives { + 2941 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2941 math:notEqualTo 0}] + skolem:lemma5375 + [ a r:Fact; r:gives {((2 9 4 1) "=<") list:sort (1 2 4 9)}] + [ a r:Fact; r:gives {((2 9 4 1) ">=") list:sort (9 4 2 1)}] + skolem:lemma4317 + skolem:lemma4318 + [ a r:Fact; r:gives {(9421 1249) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2941]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 4 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2941 a r:Inference; + r:gives { + 2942 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2942 math:notEqualTo 0}] + skolem:lemma5376 + [ a r:Fact; r:gives {((2 9 4 2) "=<") list:sort (2 2 4 9)}] + [ a r:Fact; r:gives {((2 9 4 2) ">=") list:sort (9 4 2 2)}] + skolem:lemma4486 + skolem:lemma4487 + [ a r:Fact; r:gives {(9422 2249) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2942]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2942 a r:Inference; + r:gives { + 2943 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2943 math:notEqualTo 0}] + skolem:lemma5377 + [ a r:Fact; r:gives {((2 9 4 3) "=<") list:sort (2 3 4 9)}] + [ a r:Fact; r:gives {((2 9 4 3) ">=") list:sort (9 4 3 2)}] + skolem:lemma4642 + skolem:lemma4643 + [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2943]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2943 a r:Inference; + r:gives { + 2944 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2944 math:notEqualTo 0}] + skolem:lemma5378 + [ a r:Fact; r:gives {((2 9 4 4) "=<") list:sort (2 4 4 9)}] + [ a r:Fact; r:gives {((2 9 4 4) ">=") list:sort (9 4 4 2)}] + skolem:lemma4784 + skolem:lemma4785 + [ a r:Fact; r:gives {(9442 2449) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2944]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2449]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2944 a r:Inference; + r:gives { + 2945 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2945 math:notEqualTo 0}] + skolem:lemma5379 + [ a r:Fact; r:gives {((2 9 4 5) "=<") list:sort (2 4 5 9)}] + [ a r:Fact; r:gives {((2 9 4 5) ">=") list:sort (9 5 4 2)}] + skolem:lemma4804 + skolem:lemma4805 + [ a r:Fact; r:gives {(9542 2459) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2945]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2459]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2945 a r:Inference; + r:gives { + 2946 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2946 math:notEqualTo 0}] + skolem:lemma5380 + [ a r:Fact; r:gives {((2 9 4 6) "=<") list:sort (2 4 6 9)}] + [ a r:Fact; r:gives {((2 9 4 6) ">=") list:sort (9 6 4 2)}] + skolem:lemma4822 + skolem:lemma4823 + [ a r:Fact; r:gives {(9642 2469) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2946]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2469]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2946 a r:Inference; + r:gives { + 2947 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2947 math:notEqualTo 0}] + skolem:lemma5381 + [ a r:Fact; r:gives {((2 9 4 7) "=<") list:sort (2 4 7 9)}] + [ a r:Fact; r:gives {((2 9 4 7) ">=") list:sort (9 7 4 2)}] + skolem:lemma4838 + skolem:lemma4839 + [ a r:Fact; r:gives {(9742 2479) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2947]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2479]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2947 a r:Inference; + r:gives { + 2948 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2948 math:notEqualTo 0}] + skolem:lemma5382 + [ a r:Fact; r:gives {((2 9 4 8) "=<") list:sort (2 4 8 9)}] + [ a r:Fact; r:gives {((2 9 4 8) ">=") list:sort (9 8 4 2)}] + skolem:lemma4852 + skolem:lemma4853 + [ a r:Fact; r:gives {(9842 2489) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2948]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2489]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9842]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2948 a r:Inference; + r:gives { + 2949 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2949 math:notEqualTo 0}] + skolem:lemma5383 + [ a r:Fact; r:gives {((2 9 4 9) "=<") list:sort (2 4 9 9)}] + [ a r:Fact; r:gives {((2 9 4 9) ">=") list:sort (9 9 4 2)}] + skolem:lemma4864 + skolem:lemma4865 + [ a r:Fact; r:gives {(9942 2499) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2949]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2499]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9942]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2949 a r:Inference; + r:gives { + 2950 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2950 math:notEqualTo 0}] + skolem:lemma5384 + [ a r:Fact; r:gives {((2 9 5 0) "=<") list:sort (0 2 5 9)}] + [ a r:Fact; r:gives {((2 9 5 0) ">=") list:sort (9 5 2 0)}] + skolem:lemma4147 + skolem:lemma4148 + [ a r:Fact; r:gives {(9520 259) math:difference 9261}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9261 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9261 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2950]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 5 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9261]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2950 a r:Inference; + r:gives { + 2951 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2951 math:notEqualTo 0}] + skolem:lemma5385 + [ a r:Fact; r:gives {((2 9 5 1) "=<") list:sort (1 2 5 9)}] + [ a r:Fact; r:gives {((2 9 5 1) ">=") list:sort (9 5 2 1)}] + skolem:lemma4337 + skolem:lemma4338 + [ a r:Fact; r:gives {(9521 1259) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2951]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 5 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2951 a r:Inference; + r:gives { + 2952 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2952 math:notEqualTo 0}] + skolem:lemma5386 + [ a r:Fact; r:gives {((2 9 5 2) "=<") list:sort (2 2 5 9)}] + [ a r:Fact; r:gives {((2 9 5 2) ">=") list:sort (9 5 2 2)}] + skolem:lemma4506 + skolem:lemma4507 + [ a r:Fact; r:gives {(9522 2259) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2952]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2952 a r:Inference; + r:gives { + 2953 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2953 math:notEqualTo 0}] + skolem:lemma5387 + [ a r:Fact; r:gives {((2 9 5 3) "=<") list:sort (2 3 5 9)}] + [ a r:Fact; r:gives {((2 9 5 3) ">=") list:sort (9 5 3 2)}] + skolem:lemma4662 + skolem:lemma4663 + [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2953]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2953 a r:Inference; + r:gives { + 2954 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2954 math:notEqualTo 0}] + skolem:lemma5388 + [ a r:Fact; r:gives {((2 9 5 4) "=<") list:sort (2 4 5 9)}] + [ a r:Fact; r:gives {((2 9 5 4) ">=") list:sort (9 5 4 2)}] + skolem:lemma4804 + skolem:lemma4805 + [ a r:Fact; r:gives {(9542 2459) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2954]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 5 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2459]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2954 a r:Inference; + r:gives { + 2955 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2955 math:notEqualTo 0}] + skolem:lemma5389 + [ a r:Fact; r:gives {((2 9 5 5) "=<") list:sort (2 5 5 9)}] + [ a r:Fact; r:gives {((2 9 5 5) ">=") list:sort (9 5 5 2)}] + skolem:lemma4934 + skolem:lemma4935 + [ a r:Fact; r:gives {(9552 2559) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2955]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2559]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2955 a r:Inference; + r:gives { + 2956 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2956 math:notEqualTo 0}] + skolem:lemma5390 + [ a r:Fact; r:gives {((2 9 5 6) "=<") list:sort (2 5 6 9)}] + [ a r:Fact; r:gives {((2 9 5 6) ">=") list:sort (9 6 5 2)}] + skolem:lemma4952 + skolem:lemma4953 + [ a r:Fact; r:gives {(9652 2569) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2956]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2569]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2956 a r:Inference; + r:gives { + 2957 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2957 math:notEqualTo 0}] + skolem:lemma5391 + [ a r:Fact; r:gives {((2 9 5 7) "=<") list:sort (2 5 7 9)}] + [ a r:Fact; r:gives {((2 9 5 7) ">=") list:sort (9 7 5 2)}] + skolem:lemma4968 + skolem:lemma4969 + [ a r:Fact; r:gives {(9752 2579) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2957]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2579]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2957 a r:Inference; + r:gives { + 2958 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2958 math:notEqualTo 0}] + skolem:lemma5392 + [ a r:Fact; r:gives {((2 9 5 8) "=<") list:sort (2 5 8 9)}] + [ a r:Fact; r:gives {((2 9 5 8) ">=") list:sort (9 8 5 2)}] + skolem:lemma4982 + skolem:lemma4983 + [ a r:Fact; r:gives {(9852 2589) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2958]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2589]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9852]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2958 a r:Inference; + r:gives { + 2959 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2959 math:notEqualTo 0}] + skolem:lemma5393 + [ a r:Fact; r:gives {((2 9 5 9) "=<") list:sort (2 5 9 9)}] + [ a r:Fact; r:gives {((2 9 5 9) ">=") list:sort (9 9 5 2)}] + skolem:lemma4994 + skolem:lemma4995 + [ a r:Fact; r:gives {(9952 2599) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2959]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2599]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9952]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2959 a r:Inference; + r:gives { + 2960 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2960 math:notEqualTo 0}] + skolem:lemma5394 + [ a r:Fact; r:gives {((2 9 6 0) "=<") list:sort (0 2 6 9)}] + [ a r:Fact; r:gives {((2 9 6 0) ">=") list:sort (9 6 2 0)}] + skolem:lemma4165 + skolem:lemma4166 + [ a r:Fact; r:gives {(9620 269) math:difference 9351}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9351 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9351 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2960]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 6 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9351]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2960 a r:Inference; + r:gives { + 2961 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2961 math:notEqualTo 0}] + skolem:lemma5395 + [ a r:Fact; r:gives {((2 9 6 1) "=<") list:sort (1 2 6 9)}] + [ a r:Fact; r:gives {((2 9 6 1) ">=") list:sort (9 6 2 1)}] + skolem:lemma4355 + skolem:lemma4356 + [ a r:Fact; r:gives {(9621 1269) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2961]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 6 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2961 a r:Inference; + r:gives { + 2962 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2962 math:notEqualTo 0}] + skolem:lemma5396 + [ a r:Fact; r:gives {((2 9 6 2) "=<") list:sort (2 2 6 9)}] + [ a r:Fact; r:gives {((2 9 6 2) ">=") list:sort (9 6 2 2)}] + skolem:lemma4524 + skolem:lemma4525 + [ a r:Fact; r:gives {(9622 2269) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2962]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2962 a r:Inference; + r:gives { + 2963 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2963 math:notEqualTo 0}] + skolem:lemma5397 + [ a r:Fact; r:gives {((2 9 6 3) "=<") list:sort (2 3 6 9)}] + [ a r:Fact; r:gives {((2 9 6 3) ">=") list:sort (9 6 3 2)}] + skolem:lemma4680 + skolem:lemma4681 + [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2963]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2963 a r:Inference; + r:gives { + 2964 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2964 math:notEqualTo 0}] + skolem:lemma5398 + [ a r:Fact; r:gives {((2 9 6 4) "=<") list:sort (2 4 6 9)}] + [ a r:Fact; r:gives {((2 9 6 4) ">=") list:sort (9 6 4 2)}] + skolem:lemma4822 + skolem:lemma4823 + [ a r:Fact; r:gives {(9642 2469) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2964]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 6 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2469]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2964 a r:Inference; + r:gives { + 2965 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2965 math:notEqualTo 0}] + skolem:lemma5399 + [ a r:Fact; r:gives {((2 9 6 5) "=<") list:sort (2 5 6 9)}] + [ a r:Fact; r:gives {((2 9 6 5) ">=") list:sort (9 6 5 2)}] + skolem:lemma4952 + skolem:lemma4953 + [ a r:Fact; r:gives {(9652 2569) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2965]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 6 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2569]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2965 a r:Inference; + r:gives { + 2966 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2966 math:notEqualTo 0}] + skolem:lemma5400 + [ a r:Fact; r:gives {((2 9 6 6) "=<") list:sort (2 6 6 9)}] + [ a r:Fact; r:gives {((2 9 6 6) ">=") list:sort (9 6 6 2)}] + skolem:lemma5072 + skolem:lemma5073 + [ a r:Fact; r:gives {(9662 2669) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2966]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2669]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9662]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2966 a r:Inference; + r:gives { + 2967 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2967 math:notEqualTo 0}] + skolem:lemma5401 + [ a r:Fact; r:gives {((2 9 6 7) "=<") list:sort (2 6 7 9)}] + [ a r:Fact; r:gives {((2 9 6 7) ">=") list:sort (9 7 6 2)}] + skolem:lemma5088 + skolem:lemma5089 + [ a r:Fact; r:gives {(9762 2679) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2967]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2679]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2967 a r:Inference; + r:gives { + 2968 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2968 math:notEqualTo 0}] + skolem:lemma5402 + [ a r:Fact; r:gives {((2 9 6 8) "=<") list:sort (2 6 8 9)}] + [ a r:Fact; r:gives {((2 9 6 8) ">=") list:sort (9 8 6 2)}] + skolem:lemma5102 + skolem:lemma5103 + [ a r:Fact; r:gives {(9862 2689) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2968]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2689]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9862]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2968 a r:Inference; + r:gives { + 2969 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2969 math:notEqualTo 0}] + skolem:lemma5403 + [ a r:Fact; r:gives {((2 9 6 9) "=<") list:sort (2 6 9 9)}] + [ a r:Fact; r:gives {((2 9 6 9) ">=") list:sort (9 9 6 2)}] + skolem:lemma5114 + skolem:lemma5115 + [ a r:Fact; r:gives {(9962 2699) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2969]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2699]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9962]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2969 a r:Inference; + r:gives { + 2970 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2970 math:notEqualTo 0}] + skolem:lemma5404 + [ a r:Fact; r:gives {((2 9 7 0) "=<") list:sort (0 2 7 9)}] + [ a r:Fact; r:gives {((2 9 7 0) ">=") list:sort (9 7 2 0)}] + skolem:lemma4181 + skolem:lemma4182 + [ a r:Fact; r:gives {(9720 279) math:difference 9441}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9441 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9441 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2970]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 7 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9441]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2970 a r:Inference; + r:gives { + 2971 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2971 math:notEqualTo 0}] + skolem:lemma5405 + [ a r:Fact; r:gives {((2 9 7 1) "=<") list:sort (1 2 7 9)}] + [ a r:Fact; r:gives {((2 9 7 1) ">=") list:sort (9 7 2 1)}] + skolem:lemma4371 + skolem:lemma4372 + [ a r:Fact; r:gives {(9721 1279) math:difference 8442}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8442 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 8442 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2971]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 7 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2971 a r:Inference; + r:gives { + 2972 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2972 math:notEqualTo 0}] + skolem:lemma5406 + [ a r:Fact; r:gives {((2 9 7 2) "=<") list:sort (2 2 7 9)}] + [ a r:Fact; r:gives {((2 9 7 2) ">=") list:sort (9 7 2 2)}] + skolem:lemma4540 + skolem:lemma4541 + [ a r:Fact; r:gives {(9722 2279) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2972]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2972 a r:Inference; + r:gives { + 2973 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2973 math:notEqualTo 0}] + skolem:lemma5407 + [ a r:Fact; r:gives {((2 9 7 3) "=<") list:sort (2 3 7 9)}] + [ a r:Fact; r:gives {((2 9 7 3) ">=") list:sort (9 7 3 2)}] + skolem:lemma4696 + skolem:lemma4697 + [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2973]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2973 a r:Inference; + r:gives { + 2974 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2974 math:notEqualTo 0}] + skolem:lemma5408 + [ a r:Fact; r:gives {((2 9 7 4) "=<") list:sort (2 4 7 9)}] + [ a r:Fact; r:gives {((2 9 7 4) ">=") list:sort (9 7 4 2)}] + skolem:lemma4838 + skolem:lemma4839 + [ a r:Fact; r:gives {(9742 2479) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2974]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 7 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2479]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2974 a r:Inference; + r:gives { + 2975 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2975 math:notEqualTo 0}] + skolem:lemma5409 + [ a r:Fact; r:gives {((2 9 7 5) "=<") list:sort (2 5 7 9)}] + [ a r:Fact; r:gives {((2 9 7 5) ">=") list:sort (9 7 5 2)}] + skolem:lemma4968 + skolem:lemma4969 + [ a r:Fact; r:gives {(9752 2579) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2975]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 7 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2579]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2975 a r:Inference; + r:gives { + 2976 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2976 math:notEqualTo 0}] + skolem:lemma5410 + [ a r:Fact; r:gives {((2 9 7 6) "=<") list:sort (2 6 7 9)}] + [ a r:Fact; r:gives {((2 9 7 6) ">=") list:sort (9 7 6 2)}] + skolem:lemma5088 + skolem:lemma5089 + [ a r:Fact; r:gives {(9762 2679) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2976]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 7 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2679]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2976 a r:Inference; + r:gives { + 2977 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2977 math:notEqualTo 0}] + skolem:lemma5411 + [ a r:Fact; r:gives {((2 9 7 7) "=<") list:sort (2 7 7 9)}] + [ a r:Fact; r:gives {((2 9 7 7) ">=") list:sort (9 7 7 2)}] + skolem:lemma5200 + skolem:lemma5201 + [ a r:Fact; r:gives {(9772 2779) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2977]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2779]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9772]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2977 a r:Inference; + r:gives { + 2978 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2978 math:notEqualTo 0}] + skolem:lemma5412 + [ a r:Fact; r:gives {((2 9 7 8) "=<") list:sort (2 7 8 9)}] + [ a r:Fact; r:gives {((2 9 7 8) ">=") list:sort (9 8 7 2)}] + skolem:lemma5214 + skolem:lemma5215 + [ a r:Fact; r:gives {(9872 2789) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2978]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2789]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9872]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2978 a r:Inference; + r:gives { + 2979 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2979 math:notEqualTo 0}] + skolem:lemma5413 + [ a r:Fact; r:gives {((2 9 7 9) "=<") list:sort (2 7 9 9)}] + [ a r:Fact; r:gives {((2 9 7 9) ">=") list:sort (9 9 7 2)}] + skolem:lemma5226 + skolem:lemma5227 + [ a r:Fact; r:gives {(9972 2799) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2979]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2799]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9972]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2979 a r:Inference; + r:gives { + 2980 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {2980 math:notEqualTo 0}] + skolem:lemma5414 + [ a r:Fact; r:gives {((2 9 8 0) "=<") list:sort (0 2 8 9)}] + [ a r:Fact; r:gives {((2 9 8 0) ">=") list:sort (9 8 2 0)}] + skolem:lemma4195 + skolem:lemma4196 + [ a r:Fact; r:gives {(9820 289) math:difference 9531}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9531 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9531 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2980]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 8 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9820]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma2980 a r:Inference; + r:gives { + 2981 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {2981 math:notEqualTo 0}] + skolem:lemma5415 + [ a r:Fact; r:gives {((2 9 8 1) "=<") list:sort (1 2 8 9)}] + [ a r:Fact; r:gives {((2 9 8 1) ">=") list:sort (9 8 2 1)}] + skolem:lemma4385 + skolem:lemma4386 + [ a r:Fact; r:gives {(9821 1289) math:difference 8532}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8532 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8532 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2981]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 8 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9821]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma2981 a r:Inference; + r:gives { + 2982 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2982 math:notEqualTo 0}] + skolem:lemma5416 + [ a r:Fact; r:gives {((2 9 8 2) "=<") list:sort (2 2 8 9)}] + [ a r:Fact; r:gives {((2 9 8 2) ">=") list:sort (9 8 2 2)}] + skolem:lemma4554 + skolem:lemma4555 + [ a r:Fact; r:gives {(9822 2289) math:difference 7533}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7533 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7533 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2982]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9822]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2982 a r:Inference; + r:gives { + 2983 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2983 math:notEqualTo 0}] + skolem:lemma5417 + [ a r:Fact; r:gives {((2 9 8 3) "=<") list:sort (2 3 8 9)}] + [ a r:Fact; r:gives {((2 9 8 3) ">=") list:sort (9 8 3 2)}] + skolem:lemma4710 + skolem:lemma4711 + [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2983]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2983 a r:Inference; + r:gives { + 2984 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2984 math:notEqualTo 0}] + skolem:lemma5418 + [ a r:Fact; r:gives {((2 9 8 4) "=<") list:sort (2 4 8 9)}] + [ a r:Fact; r:gives {((2 9 8 4) ">=") list:sort (9 8 4 2)}] + skolem:lemma4852 + skolem:lemma4853 + [ a r:Fact; r:gives {(9842 2489) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2984]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 8 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2489]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9842]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2984 a r:Inference; + r:gives { + 2985 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2985 math:notEqualTo 0}] + skolem:lemma5419 + [ a r:Fact; r:gives {((2 9 8 5) "=<") list:sort (2 5 8 9)}] + [ a r:Fact; r:gives {((2 9 8 5) ">=") list:sort (9 8 5 2)}] + skolem:lemma4982 + skolem:lemma4983 + [ a r:Fact; r:gives {(9852 2589) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2985]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 8 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2589]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9852]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2985 a r:Inference; + r:gives { + 2986 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2986 math:notEqualTo 0}] + skolem:lemma5420 + [ a r:Fact; r:gives {((2 9 8 6) "=<") list:sort (2 6 8 9)}] + [ a r:Fact; r:gives {((2 9 8 6) ">=") list:sort (9 8 6 2)}] + skolem:lemma5102 + skolem:lemma5103 + [ a r:Fact; r:gives {(9862 2689) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2986]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 8 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2689]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9862]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2986 a r:Inference; + r:gives { + 2987 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2987 math:notEqualTo 0}] + skolem:lemma5421 + [ a r:Fact; r:gives {((2 9 8 7) "=<") list:sort (2 7 8 9)}] + [ a r:Fact; r:gives {((2 9 8 7) ">=") list:sort (9 8 7 2)}] + skolem:lemma5214 + skolem:lemma5215 + [ a r:Fact; r:gives {(9872 2789) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2987]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 8 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2789]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9872]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2987 a r:Inference; + r:gives { + 2988 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2988 math:notEqualTo 0}] + skolem:lemma5422 + [ a r:Fact; r:gives {((2 9 8 8) "=<") list:sort (2 8 8 9)}] + [ a r:Fact; r:gives {((2 9 8 8) ">=") list:sort (9 8 8 2)}] + skolem:lemma5320 + skolem:lemma5321 + [ a r:Fact; r:gives {(9882 2889) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2988]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 8 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2889]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9882]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2988 a r:Inference; + r:gives { + 2989 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2989 math:notEqualTo 0}] + skolem:lemma5423 + [ a r:Fact; r:gives {((2 9 8 9) "=<") list:sort (2 8 9 9)}] + [ a r:Fact; r:gives {((2 9 8 9) ">=") list:sort (9 9 8 2)}] + skolem:lemma5332 + skolem:lemma5333 + [ a r:Fact; r:gives {(9982 2899) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2989]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 8 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2899]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9982]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2989 a r:Inference; + r:gives { + 2990 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2990 math:notEqualTo 0}] + skolem:lemma5424 + [ a r:Fact; r:gives {((2 9 9 0) "=<") list:sort (0 2 9 9)}] + [ a r:Fact; r:gives {((2 9 9 0) ">=") list:sort (9 9 2 0)}] + skolem:lemma4207 + skolem:lemma4208 + [ a r:Fact; r:gives {(9920 299) math:difference 9621}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9621 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9621 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2990]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 9 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9920]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2990 a r:Inference; + r:gives { + 2991 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2991 math:notEqualTo 0}] + skolem:lemma5425 + [ a r:Fact; r:gives {((2 9 9 1) "=<") list:sort (1 2 9 9)}] + [ a r:Fact; r:gives {((2 9 9 1) ">=") list:sort (9 9 2 1)}] + skolem:lemma4397 + skolem:lemma4398 + [ a r:Fact; r:gives {(9921 1299) math:difference 8622}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8622 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8622 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2991]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 9 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9921]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2991 a r:Inference; + r:gives { + 2992 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2992 math:notEqualTo 0}] + skolem:lemma5426 + [ a r:Fact; r:gives {((2 9 9 2) "=<") list:sort (2 2 9 9)}] + [ a r:Fact; r:gives {((2 9 9 2) ">=") list:sort (9 9 2 2)}] + skolem:lemma4566 + skolem:lemma4567 + [ a r:Fact; r:gives {(9922 2299) math:difference 7623}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7623 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7623 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 9 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9922]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7623]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2992 a r:Inference; + r:gives { + 2993 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2993 math:notEqualTo 0}] + skolem:lemma5427 + [ a r:Fact; r:gives {((2 9 9 3) "=<") list:sort (2 3 9 9)}] + [ a r:Fact; r:gives {((2 9 9 3) ">=") list:sort (9 9 3 2)}] + skolem:lemma4722 + skolem:lemma4723 + [ a r:Fact; r:gives {(9932 2399) math:difference 7533}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7533 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7533 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 9 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9932]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2993 a r:Inference; + r:gives { + 2994 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2994 math:notEqualTo 0}] + skolem:lemma5428 + [ a r:Fact; r:gives {((2 9 9 4) "=<") list:sort (2 4 9 9)}] + [ a r:Fact; r:gives {((2 9 9 4) ">=") list:sort (9 9 4 2)}] + skolem:lemma4864 + skolem:lemma4865 + [ a r:Fact; r:gives {(9942 2499) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 9 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 4 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2499]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9942]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2994 a r:Inference; + r:gives { + 2995 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2995 math:notEqualTo 0}] + skolem:lemma5429 + [ a r:Fact; r:gives {((2 9 9 5) "=<") list:sort (2 5 9 9)}] + [ a r:Fact; r:gives {((2 9 9 5) ">=") list:sort (9 9 5 2)}] + skolem:lemma4994 + skolem:lemma4995 + [ a r:Fact; r:gives {(9952 2599) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 9 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 5 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2599]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9952]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2995 a r:Inference; + r:gives { + 2996 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {2996 math:notEqualTo 0}] + skolem:lemma5430 + [ a r:Fact; r:gives {((2 9 9 6) "=<") list:sort (2 6 9 9)}] + [ a r:Fact; r:gives {((2 9 9 6) ">=") list:sort (9 9 6 2)}] + skolem:lemma5114 + skolem:lemma5115 + [ a r:Fact; r:gives {(9962 2699) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 9 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 6 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2699]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9962]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma2996 a r:Inference; + r:gives { + 2997 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {2997 math:notEqualTo 0}] + skolem:lemma5431 + [ a r:Fact; r:gives {((2 9 9 7) "=<") list:sort (2 7 9 9)}] + [ a r:Fact; r:gives {((2 9 9 7) ">=") list:sort (9 9 7 2)}] + skolem:lemma5226 + skolem:lemma5227 + [ a r:Fact; r:gives {(9972 2799) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 9 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 7 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2799]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9972]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma2997 a r:Inference; + r:gives { + 2998 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {2998 math:notEqualTo 0}] + skolem:lemma5432 + [ a r:Fact; r:gives {((2 9 9 8) "=<") list:sort (2 8 9 9)}] + [ a r:Fact; r:gives {((2 9 9 8) ">=") list:sort (9 9 8 2)}] + skolem:lemma5332 + skolem:lemma5333 + [ a r:Fact; r:gives {(9982 2899) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 9 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 8 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2899]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9982]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma2998 a r:Inference; + r:gives { + 2999 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {2999 math:notEqualTo 0}] + skolem:lemma5433 + [ a r:Fact; r:gives {((2 9 9 9) "=<") list:sort (2 9 9 9)}] + [ a r:Fact; r:gives {((2 9 9 9) ">=") list:sort (9 9 9 2)}] + skolem:lemma5434 + skolem:lemma5435 + [ a r:Fact; r:gives {(9992 2999) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 9 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 9 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma2999 a r:Inference; + r:gives { + 3000 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3000 math:notEqualTo 0}] + skolem:lemma5436 + [ a r:Fact; r:gives {((3 0 0 0) "=<") list:sort (0 0 0 3)}] + [ a r:Fact; r:gives {((3 0 0 0) ">=") list:sort (3 0 0 0)}] + skolem:lemma5437 + skolem:lemma5438 + [ a r:Fact; r:gives {(3000 3) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 0 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 0 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3000 a r:Inference; + r:gives { + 3001 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3001 math:notEqualTo 0}] + skolem:lemma5439 + [ a r:Fact; r:gives {((3 0 0 1) "=<") list:sort (0 0 1 3)}] + [ a r:Fact; r:gives {((3 0 0 1) ">=") list:sort (3 1 0 0)}] + skolem:lemma5440 + skolem:lemma5441 + [ a r:Fact; r:gives {(3100 13) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3001]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 0 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 1 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 13]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3001 a r:Inference; + r:gives { + 3002 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3002 math:notEqualTo 0}] + skolem:lemma5442 + [ a r:Fact; r:gives {((3 0 0 2) "=<") list:sort (0 0 2 3)}] + [ a r:Fact; r:gives {((3 0 0 2) ">=") list:sort (3 2 0 0)}] + skolem:lemma4009 + skolem:lemma4010 + [ a r:Fact; r:gives {(3200 23) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3002]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 0 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3002 a r:Inference; + r:gives { + 3003 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3003 math:notEqualTo 0}] + skolem:lemma5443 + [ a r:Fact; r:gives {((3 0 0 3) "=<") list:sort (0 0 3 3)}] + [ a r:Fact; r:gives {((3 0 0 3) ">=") list:sort (3 3 0 0)}] + skolem:lemma5444 + skolem:lemma5445 + [ a r:Fact; r:gives {(3300 33) math:difference 3267}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3267 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 3267 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3003]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 0 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 33]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3003 a r:Inference; + r:gives { + 3004 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3004 math:notEqualTo 0}] + skolem:lemma5446 + [ a r:Fact; r:gives {((3 0 0 4) "=<") list:sort (0 0 3 4)}] + [ a r:Fact; r:gives {((3 0 0 4) ">=") list:sort (4 3 0 0)}] + skolem:lemma5447 + skolem:lemma5448 + [ a r:Fact; r:gives {(4300 34) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3004]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 0 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 34]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3004 a r:Inference; + r:gives { + 3005 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3005 math:notEqualTo 0}] + skolem:lemma5449 + [ a r:Fact; r:gives {((3 0 0 5) "=<") list:sort (0 0 3 5)}] + [ a r:Fact; r:gives {((3 0 0 5) ">=") list:sort (5 3 0 0)}] + skolem:lemma5450 + skolem:lemma5451 + [ a r:Fact; r:gives {(5300 35) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3005]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 0 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 35]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3005 a r:Inference; + r:gives { + 3006 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3006 math:notEqualTo 0}] + skolem:lemma5452 + [ a r:Fact; r:gives {((3 0 0 6) "=<") list:sort (0 0 3 6)}] + [ a r:Fact; r:gives {((3 0 0 6) ">=") list:sort (6 3 0 0)}] + skolem:lemma5453 + skolem:lemma5454 + [ a r:Fact; r:gives {(6300 36) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3006]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 0 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 36]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3006 a r:Inference; + r:gives { + 3007 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3007 math:notEqualTo 0}] + skolem:lemma5455 + [ a r:Fact; r:gives {((3 0 0 7) "=<") list:sort (0 0 3 7)}] + [ a r:Fact; r:gives {((3 0 0 7) ">=") list:sort (7 3 0 0)}] + skolem:lemma5456 + skolem:lemma5457 + [ a r:Fact; r:gives {(7300 37) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3007]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 0 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 37]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3007 a r:Inference; + r:gives { + 3008 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3008 math:notEqualTo 0}] + skolem:lemma5458 + [ a r:Fact; r:gives {((3 0 0 8) "=<") list:sort (0 0 3 8)}] + [ a r:Fact; r:gives {((3 0 0 8) ">=") list:sort (8 3 0 0)}] + skolem:lemma5459 + skolem:lemma5460 + [ a r:Fact; r:gives {(8300 38) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3008]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 0 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 38]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3008 a r:Inference; + r:gives { + 3009 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3009 math:notEqualTo 0}] + skolem:lemma5461 + [ a r:Fact; r:gives {((3 0 0 9) "=<") list:sort (0 0 3 9)}] + [ a r:Fact; r:gives {((3 0 0 9) ">=") list:sort (9 3 0 0)}] + skolem:lemma5462 + skolem:lemma5463 + [ a r:Fact; r:gives {(9300 39) math:difference 9261}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9261 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9261 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3009]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 0 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 39]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9261]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3009 a r:Inference; + r:gives { + 3010 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3010 math:notEqualTo 0}] + skolem:lemma5464 + [ a r:Fact; r:gives {((3 0 1 0) "=<") list:sort (0 0 1 3)}] + [ a r:Fact; r:gives {((3 0 1 0) ">=") list:sort (3 1 0 0)}] + skolem:lemma5440 + skolem:lemma5441 + [ a r:Fact; r:gives {(3100 13) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3010]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 1 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 13]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3010 a r:Inference; + r:gives { + 3011 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3011 math:notEqualTo 0}] + skolem:lemma5465 + [ a r:Fact; r:gives {((3 0 1 1) "=<") list:sort (0 1 1 3)}] + [ a r:Fact; r:gives {((3 0 1 1) ">=") list:sort (3 1 1 0)}] + skolem:lemma5466 + skolem:lemma5467 + [ a r:Fact; r:gives {(3110 113) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3011]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 1 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 113]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3110]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3011 a r:Inference; + r:gives { + 3012 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3012 math:notEqualTo 0}] + skolem:lemma5468 + [ a r:Fact; r:gives {((3 0 1 2) "=<") list:sort (0 1 2 3)}] + [ a r:Fact; r:gives {((3 0 1 2) ">=") list:sort (3 2 1 0)}] + skolem:lemma4037 + skolem:lemma4038 + [ a r:Fact; r:gives {(3210 123) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3012]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3012 a r:Inference; + r:gives { + 3013 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3013 math:notEqualTo 0}] + skolem:lemma5469 + [ a r:Fact; r:gives {((3 0 1 3) "=<") list:sort (0 1 3 3)}] + [ a r:Fact; r:gives {((3 0 1 3) ">=") list:sort (3 3 1 0)}] + skolem:lemma5470 + skolem:lemma5471 + [ a r:Fact; r:gives {(3310 133) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3013]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 133]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3013 a r:Inference; + r:gives { + 3014 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3014 math:notEqualTo 0}] + skolem:lemma5472 + [ a r:Fact; r:gives {((3 0 1 4) "=<") list:sort (0 1 3 4)}] + [ a r:Fact; r:gives {((3 0 1 4) ">=") list:sort (4 3 1 0)}] + skolem:lemma5473 + skolem:lemma5474 + [ a r:Fact; r:gives {(4310 134) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3014]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 1 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 134]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3014 a r:Inference; + r:gives { + 3015 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3015 math:notEqualTo 0}] + skolem:lemma5475 + [ a r:Fact; r:gives {((3 0 1 5) "=<") list:sort (0 1 3 5)}] + [ a r:Fact; r:gives {((3 0 1 5) ">=") list:sort (5 3 1 0)}] + skolem:lemma5476 + skolem:lemma5477 + [ a r:Fact; r:gives {(5310 135) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3015]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 1 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 135]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3015 a r:Inference; + r:gives { + 3016 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3016 math:notEqualTo 0}] + skolem:lemma5478 + [ a r:Fact; r:gives {((3 0 1 6) "=<") list:sort (0 1 3 6)}] + [ a r:Fact; r:gives {((3 0 1 6) ">=") list:sort (6 3 1 0)}] + skolem:lemma5479 + skolem:lemma5480 + [ a r:Fact; r:gives {(6310 136) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3016]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 1 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 136]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3016 a r:Inference; + r:gives { + 3017 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3017 math:notEqualTo 0}] + skolem:lemma5481 + [ a r:Fact; r:gives {((3 0 1 7) "=<") list:sort (0 1 3 7)}] + [ a r:Fact; r:gives {((3 0 1 7) ">=") list:sort (7 3 1 0)}] + skolem:lemma5482 + skolem:lemma5483 + [ a r:Fact; r:gives {(7310 137) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3017]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 1 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 137]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3017 a r:Inference; + r:gives { + 3018 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3018 math:notEqualTo 0}] + skolem:lemma5484 + [ a r:Fact; r:gives {((3 0 1 8) "=<") list:sort (0 1 3 8)}] + [ a r:Fact; r:gives {((3 0 1 8) ">=") list:sort (8 3 1 0)}] + skolem:lemma5485 + skolem:lemma5486 + [ a r:Fact; r:gives {(8310 138) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3018]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 1 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 138]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3018 a r:Inference; + r:gives { + 3019 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3019 math:notEqualTo 0}] + skolem:lemma5487 + [ a r:Fact; r:gives {((3 0 1 9) "=<") list:sort (0 1 3 9)}] + [ a r:Fact; r:gives {((3 0 1 9) ">=") list:sort (9 3 1 0)}] + skolem:lemma5488 + skolem:lemma5489 + [ a r:Fact; r:gives {(9310 139) math:difference 9171}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9171 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9171 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3019]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 1 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 139]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3019 a r:Inference; + r:gives { + 3020 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3020 math:notEqualTo 0}] + skolem:lemma5490 + [ a r:Fact; r:gives {((3 0 2 0) "=<") list:sort (0 0 2 3)}] + [ a r:Fact; r:gives {((3 0 2 0) ">=") list:sort (3 2 0 0)}] + skolem:lemma4009 + skolem:lemma4010 + [ a r:Fact; r:gives {(3200 23) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3020]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3020 a r:Inference; + r:gives { + 3021 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3021 math:notEqualTo 0}] + skolem:lemma5491 + [ a r:Fact; r:gives {((3 0 2 1) "=<") list:sort (0 1 2 3)}] + [ a r:Fact; r:gives {((3 0 2 1) ">=") list:sort (3 2 1 0)}] + skolem:lemma4037 + skolem:lemma4038 + [ a r:Fact; r:gives {(3210 123) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3021]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3021 a r:Inference; + r:gives { + 3022 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3022 math:notEqualTo 0}] + skolem:lemma5492 + [ a r:Fact; r:gives {((3 0 2 2) "=<") list:sort (0 2 2 3)}] + [ a r:Fact; r:gives {((3 0 2 2) ">=") list:sort (3 2 2 0)}] + skolem:lemma4063 + skolem:lemma4064 + [ a r:Fact; r:gives {(3220 223) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3022]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3022 a r:Inference; + r:gives { + 3023 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3023 math:notEqualTo 0}] + skolem:lemma5493 + [ a r:Fact; r:gives {((3 0 2 3) "=<") list:sort (0 2 3 3)}] + [ a r:Fact; r:gives {((3 0 2 3) ">=") list:sort (3 3 2 0)}] + skolem:lemma4087 + skolem:lemma4088 + [ a r:Fact; r:gives {(3320 233) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3023]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3023 a r:Inference; + r:gives { + 3024 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3024 math:notEqualTo 0}] + skolem:lemma5494 + [ a r:Fact; r:gives {((3 0 2 4) "=<") list:sort (0 2 3 4)}] + [ a r:Fact; r:gives {((3 0 2 4) ">=") list:sort (4 3 2 0)}] + skolem:lemma4090 + skolem:lemma4091 + [ a r:Fact; r:gives {(4320 234) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3024]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3024 a r:Inference; + r:gives { + 3025 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3025 math:notEqualTo 0}] + skolem:lemma5495 + [ a r:Fact; r:gives {((3 0 2 5) "=<") list:sort (0 2 3 5)}] + [ a r:Fact; r:gives {((3 0 2 5) ">=") list:sort (5 3 2 0)}] + skolem:lemma4093 + skolem:lemma4094 + [ a r:Fact; r:gives {(5320 235) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3025]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3025 a r:Inference; + r:gives { + 3026 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3026 math:notEqualTo 0}] + skolem:lemma5496 + [ a r:Fact; r:gives {((3 0 2 6) "=<") list:sort (0 2 3 6)}] + [ a r:Fact; r:gives {((3 0 2 6) ">=") list:sort (6 3 2 0)}] + skolem:lemma4096 + skolem:lemma4097 + [ a r:Fact; r:gives {(6320 236) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3026]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3026 a r:Inference; + r:gives { + 3027 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3027 math:notEqualTo 0}] + skolem:lemma5497 + [ a r:Fact; r:gives {((3 0 2 7) "=<") list:sort (0 2 3 7)}] + [ a r:Fact; r:gives {((3 0 2 7) ">=") list:sort (7 3 2 0)}] + skolem:lemma4099 + skolem:lemma4100 + [ a r:Fact; r:gives {(7320 237) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3027]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3027 a r:Inference; + r:gives { + 3028 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3028 math:notEqualTo 0}] + skolem:lemma5498 + [ a r:Fact; r:gives {((3 0 2 8) "=<") list:sort (0 2 3 8)}] + [ a r:Fact; r:gives {((3 0 2 8) ">=") list:sort (8 3 2 0)}] + skolem:lemma4102 + skolem:lemma4103 + [ a r:Fact; r:gives {(8320 238) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3028]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3028 a r:Inference; + r:gives { + 3029 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3029 math:notEqualTo 0}] + skolem:lemma5499 + [ a r:Fact; r:gives {((3 0 2 9) "=<") list:sort (0 2 3 9)}] + [ a r:Fact; r:gives {((3 0 2 9) ">=") list:sort (9 3 2 0)}] + skolem:lemma4105 + skolem:lemma4106 + [ a r:Fact; r:gives {(9320 239) math:difference 9081}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9081 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 9081 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3029]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3029 a r:Inference; + r:gives { + 3030 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3030 math:notEqualTo 0}] + skolem:lemma5500 + [ a r:Fact; r:gives {((3 0 3 0) "=<") list:sort (0 0 3 3)}] + [ a r:Fact; r:gives {((3 0 3 0) ">=") list:sort (3 3 0 0)}] + skolem:lemma5444 + skolem:lemma5445 + [ a r:Fact; r:gives {(3300 33) math:difference 3267}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3267 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 3267 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3030]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 33]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3030 a r:Inference; + r:gives { + 3031 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3031 math:notEqualTo 0}] + skolem:lemma5501 + [ a r:Fact; r:gives {((3 0 3 1) "=<") list:sort (0 1 3 3)}] + [ a r:Fact; r:gives {((3 0 3 1) ">=") list:sort (3 3 1 0)}] + skolem:lemma5470 + skolem:lemma5471 + [ a r:Fact; r:gives {(3310 133) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3031]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 133]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3031 a r:Inference; + r:gives { + 3032 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3032 math:notEqualTo 0}] + skolem:lemma5502 + [ a r:Fact; r:gives {((3 0 3 2) "=<") list:sort (0 2 3 3)}] + [ a r:Fact; r:gives {((3 0 3 2) ">=") list:sort (3 3 2 0)}] + skolem:lemma4087 + skolem:lemma4088 + [ a r:Fact; r:gives {(3320 233) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3032]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3032 a r:Inference; + r:gives { + 3033 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3033 math:notEqualTo 0}] + skolem:lemma5503 + [ a r:Fact; r:gives {((3 0 3 3) "=<") list:sort (0 3 3 3)}] + [ a r:Fact; r:gives {((3 0 3 3) ">=") list:sort (3 3 3 0)}] + skolem:lemma5504 + skolem:lemma5505 + [ a r:Fact; r:gives {(3330 333) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3033]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3033 a r:Inference; + r:gives { + 3034 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3034 math:notEqualTo 0}] + skolem:lemma5506 + [ a r:Fact; r:gives {((3 0 3 4) "=<") list:sort (0 3 3 4)}] + [ a r:Fact; r:gives {((3 0 3 4) ">=") list:sort (4 3 3 0)}] + skolem:lemma5507 + skolem:lemma5508 + [ a r:Fact; r:gives {(4330 334) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3034]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3034 a r:Inference; + r:gives { + 3035 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3035 math:notEqualTo 0}] + skolem:lemma5509 + [ a r:Fact; r:gives {((3 0 3 5) "=<") list:sort (0 3 3 5)}] + [ a r:Fact; r:gives {((3 0 3 5) ">=") list:sort (5 3 3 0)}] + skolem:lemma5510 + skolem:lemma5511 + [ a r:Fact; r:gives {(5330 335) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3035]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3035 a r:Inference; + r:gives { + 3036 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3036 math:notEqualTo 0}] + skolem:lemma5512 + [ a r:Fact; r:gives {((3 0 3 6) "=<") list:sort (0 3 3 6)}] + [ a r:Fact; r:gives {((3 0 3 6) ">=") list:sort (6 3 3 0)}] + skolem:lemma5513 + skolem:lemma5514 + [ a r:Fact; r:gives {(6330 336) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3036]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3036 a r:Inference; + r:gives { + 3037 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3037 math:notEqualTo 0}] + skolem:lemma5515 + [ a r:Fact; r:gives {((3 0 3 7) "=<") list:sort (0 3 3 7)}] + [ a r:Fact; r:gives {((3 0 3 7) ">=") list:sort (7 3 3 0)}] + skolem:lemma5516 + skolem:lemma5517 + [ a r:Fact; r:gives {(7330 337) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3037]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3037 a r:Inference; + r:gives { + 3038 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3038 math:notEqualTo 0}] + skolem:lemma5518 + [ a r:Fact; r:gives {((3 0 3 8) "=<") list:sort (0 3 3 8)}] + [ a r:Fact; r:gives {((3 0 3 8) ">=") list:sort (8 3 3 0)}] + skolem:lemma5519 + skolem:lemma5520 + [ a r:Fact; r:gives {(8330 338) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3038]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3038 a r:Inference; + r:gives { + 3039 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3039 math:notEqualTo 0}] + skolem:lemma5521 + [ a r:Fact; r:gives {((3 0 3 9) "=<") list:sort (0 3 3 9)}] + [ a r:Fact; r:gives {((3 0 3 9) ">=") list:sort (9 3 3 0)}] + skolem:lemma5522 + skolem:lemma5523 + [ a r:Fact; r:gives {(9330 339) math:difference 8991}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8991 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 8991 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3039]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8991]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3039 a r:Inference; + r:gives { + 3040 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3040 math:notEqualTo 0}] + skolem:lemma5524 + [ a r:Fact; r:gives {((3 0 4 0) "=<") list:sort (0 0 3 4)}] + [ a r:Fact; r:gives {((3 0 4 0) ">=") list:sort (4 3 0 0)}] + skolem:lemma5447 + skolem:lemma5448 + [ a r:Fact; r:gives {(4300 34) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3040]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 4 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 34]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3040 a r:Inference; + r:gives { + 3041 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3041 math:notEqualTo 0}] + skolem:lemma5525 + [ a r:Fact; r:gives {((3 0 4 1) "=<") list:sort (0 1 3 4)}] + [ a r:Fact; r:gives {((3 0 4 1) ">=") list:sort (4 3 1 0)}] + skolem:lemma5473 + skolem:lemma5474 + [ a r:Fact; r:gives {(4310 134) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3041]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 4 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 134]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3041 a r:Inference; + r:gives { + 3042 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3042 math:notEqualTo 0}] + skolem:lemma5526 + [ a r:Fact; r:gives {((3 0 4 2) "=<") list:sort (0 2 3 4)}] + [ a r:Fact; r:gives {((3 0 4 2) ">=") list:sort (4 3 2 0)}] + skolem:lemma4090 + skolem:lemma4091 + [ a r:Fact; r:gives {(4320 234) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3042]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3042 a r:Inference; + r:gives { + 3043 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3043 math:notEqualTo 0}] + skolem:lemma5527 + [ a r:Fact; r:gives {((3 0 4 3) "=<") list:sort (0 3 3 4)}] + [ a r:Fact; r:gives {((3 0 4 3) ">=") list:sort (4 3 3 0)}] + skolem:lemma5507 + skolem:lemma5508 + [ a r:Fact; r:gives {(4330 334) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3043]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3043 a r:Inference; + r:gives { + 3044 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3044 math:notEqualTo 0}] + skolem:lemma5528 + [ a r:Fact; r:gives {((3 0 4 4) "=<") list:sort (0 3 4 4)}] + [ a r:Fact; r:gives {((3 0 4 4) ">=") list:sort (4 4 3 0)}] + skolem:lemma5529 + skolem:lemma5530 + [ a r:Fact; r:gives {(4430 344) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3044]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3044 a r:Inference; + r:gives { + 3045 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3045 math:notEqualTo 0}] + skolem:lemma5531 + [ a r:Fact; r:gives {((3 0 4 5) "=<") list:sort (0 3 4 5)}] + [ a r:Fact; r:gives {((3 0 4 5) ">=") list:sort (5 4 3 0)}] + skolem:lemma5532 + skolem:lemma5533 + [ a r:Fact; r:gives {(5430 345) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3045]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3045 a r:Inference; + r:gives { + 3046 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3046 math:notEqualTo 0}] + skolem:lemma5534 + [ a r:Fact; r:gives {((3 0 4 6) "=<") list:sort (0 3 4 6)}] + [ a r:Fact; r:gives {((3 0 4 6) ">=") list:sort (6 4 3 0)}] + skolem:lemma5535 + skolem:lemma5536 + [ a r:Fact; r:gives {(6430 346) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3046]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3046 a r:Inference; + r:gives { + 3047 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3047 math:notEqualTo 0}] + skolem:lemma5537 + [ a r:Fact; r:gives {((3 0 4 7) "=<") list:sort (0 3 4 7)}] + [ a r:Fact; r:gives {((3 0 4 7) ">=") list:sort (7 4 3 0)}] + skolem:lemma5538 + skolem:lemma5539 + [ a r:Fact; r:gives {(7430 347) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3047]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3047 a r:Inference; + r:gives { + 3048 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3048 math:notEqualTo 0}] + skolem:lemma5540 + [ a r:Fact; r:gives {((3 0 4 8) "=<") list:sort (0 3 4 8)}] + [ a r:Fact; r:gives {((3 0 4 8) ">=") list:sort (8 4 3 0)}] + skolem:lemma5541 + skolem:lemma5542 + [ a r:Fact; r:gives {(8430 348) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3048]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3048 a r:Inference; + r:gives { + 3049 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3049 math:notEqualTo 0}] + skolem:lemma5543 + [ a r:Fact; r:gives {((3 0 4 9) "=<") list:sort (0 3 4 9)}] + [ a r:Fact; r:gives {((3 0 4 9) ">=") list:sort (9 4 3 0)}] + skolem:lemma5544 + skolem:lemma5545 + [ a r:Fact; r:gives {(9430 349) math:difference 9081}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9081 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 9081 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3049]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3049 a r:Inference; + r:gives { + 3050 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3050 math:notEqualTo 0}] + skolem:lemma5546 + [ a r:Fact; r:gives {((3 0 5 0) "=<") list:sort (0 0 3 5)}] + [ a r:Fact; r:gives {((3 0 5 0) ">=") list:sort (5 3 0 0)}] + skolem:lemma5450 + skolem:lemma5451 + [ a r:Fact; r:gives {(5300 35) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3050]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 5 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 35]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3050 a r:Inference; + r:gives { + 3051 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3051 math:notEqualTo 0}] + skolem:lemma5547 + [ a r:Fact; r:gives {((3 0 5 1) "=<") list:sort (0 1 3 5)}] + [ a r:Fact; r:gives {((3 0 5 1) ">=") list:sort (5 3 1 0)}] + skolem:lemma5476 + skolem:lemma5477 + [ a r:Fact; r:gives {(5310 135) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3051]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 5 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 135]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3051 a r:Inference; + r:gives { + 3052 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3052 math:notEqualTo 0}] + skolem:lemma5548 + [ a r:Fact; r:gives {((3 0 5 2) "=<") list:sort (0 2 3 5)}] + [ a r:Fact; r:gives {((3 0 5 2) ">=") list:sort (5 3 2 0)}] + skolem:lemma4093 + skolem:lemma4094 + [ a r:Fact; r:gives {(5320 235) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3052]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3052 a r:Inference; + r:gives { + 3053 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3053 math:notEqualTo 0}] + skolem:lemma5549 + [ a r:Fact; r:gives {((3 0 5 3) "=<") list:sort (0 3 3 5)}] + [ a r:Fact; r:gives {((3 0 5 3) ">=") list:sort (5 3 3 0)}] + skolem:lemma5510 + skolem:lemma5511 + [ a r:Fact; r:gives {(5330 335) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3053]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3053 a r:Inference; + r:gives { + 3054 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3054 math:notEqualTo 0}] + skolem:lemma5550 + [ a r:Fact; r:gives {((3 0 5 4) "=<") list:sort (0 3 4 5)}] + [ a r:Fact; r:gives {((3 0 5 4) ">=") list:sort (5 4 3 0)}] + skolem:lemma5532 + skolem:lemma5533 + [ a r:Fact; r:gives {(5430 345) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3054]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 5 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3054 a r:Inference; + r:gives { + 3055 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3055 math:notEqualTo 0}] + skolem:lemma5551 + [ a r:Fact; r:gives {((3 0 5 5) "=<") list:sort (0 3 5 5)}] + [ a r:Fact; r:gives {((3 0 5 5) ">=") list:sort (5 5 3 0)}] + skolem:lemma5552 + skolem:lemma5553 + [ a r:Fact; r:gives {(5530 355) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3055]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3055 a r:Inference; + r:gives { + 3056 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3056 math:notEqualTo 0}] + skolem:lemma5554 + [ a r:Fact; r:gives {((3 0 5 6) "=<") list:sort (0 3 5 6)}] + [ a r:Fact; r:gives {((3 0 5 6) ">=") list:sort (6 5 3 0)}] + skolem:lemma5555 + skolem:lemma5556 + [ a r:Fact; r:gives {(6530 356) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3056]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3056 a r:Inference; + r:gives { + 3057 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3057 math:notEqualTo 0}] + skolem:lemma5557 + [ a r:Fact; r:gives {((3 0 5 7) "=<") list:sort (0 3 5 7)}] + [ a r:Fact; r:gives {((3 0 5 7) ">=") list:sort (7 5 3 0)}] + skolem:lemma5558 + skolem:lemma5559 + [ a r:Fact; r:gives {(7530 357) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3057]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3057 a r:Inference; + r:gives { + 3058 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3058 math:notEqualTo 0}] + skolem:lemma5560 + [ a r:Fact; r:gives {((3 0 5 8) "=<") list:sort (0 3 5 8)}] + [ a r:Fact; r:gives {((3 0 5 8) ">=") list:sort (8 5 3 0)}] + skolem:lemma5561 + skolem:lemma5562 + [ a r:Fact; r:gives {(8530 358) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3058]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3058 a r:Inference; + r:gives { + 3059 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3059 math:notEqualTo 0}] + skolem:lemma5563 + [ a r:Fact; r:gives {((3 0 5 9) "=<") list:sort (0 3 5 9)}] + [ a r:Fact; r:gives {((3 0 5 9) ">=") list:sort (9 5 3 0)}] + skolem:lemma5564 + skolem:lemma5565 + [ a r:Fact; r:gives {(9530 359) math:difference 9171}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9171 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9171 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3059]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3059 a r:Inference; + r:gives { + 3060 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3060 math:notEqualTo 0}] + skolem:lemma5566 + [ a r:Fact; r:gives {((3 0 6 0) "=<") list:sort (0 0 3 6)}] + [ a r:Fact; r:gives {((3 0 6 0) ">=") list:sort (6 3 0 0)}] + skolem:lemma5453 + skolem:lemma5454 + [ a r:Fact; r:gives {(6300 36) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3060]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 6 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 36]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3060 a r:Inference; + r:gives { + 3061 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3061 math:notEqualTo 0}] + skolem:lemma5567 + [ a r:Fact; r:gives {((3 0 6 1) "=<") list:sort (0 1 3 6)}] + [ a r:Fact; r:gives {((3 0 6 1) ">=") list:sort (6 3 1 0)}] + skolem:lemma5479 + skolem:lemma5480 + [ a r:Fact; r:gives {(6310 136) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3061]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 6 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 136]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3061 a r:Inference; + r:gives { + 3062 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3062 math:notEqualTo 0}] + skolem:lemma5568 + [ a r:Fact; r:gives {((3 0 6 2) "=<") list:sort (0 2 3 6)}] + [ a r:Fact; r:gives {((3 0 6 2) ">=") list:sort (6 3 2 0)}] + skolem:lemma4096 + skolem:lemma4097 + [ a r:Fact; r:gives {(6320 236) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3062]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3062 a r:Inference; + r:gives { + 3063 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3063 math:notEqualTo 0}] + skolem:lemma5569 + [ a r:Fact; r:gives {((3 0 6 3) "=<") list:sort (0 3 3 6)}] + [ a r:Fact; r:gives {((3 0 6 3) ">=") list:sort (6 3 3 0)}] + skolem:lemma5513 + skolem:lemma5514 + [ a r:Fact; r:gives {(6330 336) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3063]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3063 a r:Inference; + r:gives { + 3064 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3064 math:notEqualTo 0}] + skolem:lemma5570 + [ a r:Fact; r:gives {((3 0 6 4) "=<") list:sort (0 3 4 6)}] + [ a r:Fact; r:gives {((3 0 6 4) ">=") list:sort (6 4 3 0)}] + skolem:lemma5535 + skolem:lemma5536 + [ a r:Fact; r:gives {(6430 346) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3064]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 6 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3064 a r:Inference; + r:gives { + 3065 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3065 math:notEqualTo 0}] + skolem:lemma5571 + [ a r:Fact; r:gives {((3 0 6 5) "=<") list:sort (0 3 5 6)}] + [ a r:Fact; r:gives {((3 0 6 5) ">=") list:sort (6 5 3 0)}] + skolem:lemma5555 + skolem:lemma5556 + [ a r:Fact; r:gives {(6530 356) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3065]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 6 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3065 a r:Inference; + r:gives { + 3066 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3066 math:notEqualTo 0}] + skolem:lemma5572 + [ a r:Fact; r:gives {((3 0 6 6) "=<") list:sort (0 3 6 6)}] + [ a r:Fact; r:gives {((3 0 6 6) ">=") list:sort (6 6 3 0)}] + skolem:lemma5573 + skolem:lemma5574 + [ a r:Fact; r:gives {(6630 366) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3066]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3066 a r:Inference; + r:gives { + 3067 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3067 math:notEqualTo 0}] + skolem:lemma5575 + [ a r:Fact; r:gives {((3 0 6 7) "=<") list:sort (0 3 6 7)}] + [ a r:Fact; r:gives {((3 0 6 7) ">=") list:sort (7 6 3 0)}] + skolem:lemma5576 + skolem:lemma5577 + [ a r:Fact; r:gives {(7630 367) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3067]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3067 a r:Inference; + r:gives { + 3068 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3068 math:notEqualTo 0}] + skolem:lemma5578 + [ a r:Fact; r:gives {((3 0 6 8) "=<") list:sort (0 3 6 8)}] + [ a r:Fact; r:gives {((3 0 6 8) ">=") list:sort (8 6 3 0)}] + skolem:lemma5579 + skolem:lemma5580 + [ a r:Fact; r:gives {(8630 368) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3068]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3068 a r:Inference; + r:gives { + 3069 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3069 math:notEqualTo 0}] + skolem:lemma5581 + [ a r:Fact; r:gives {((3 0 6 9) "=<") list:sort (0 3 6 9)}] + [ a r:Fact; r:gives {((3 0 6 9) ">=") list:sort (9 6 3 0)}] + skolem:lemma5582 + skolem:lemma5583 + [ a r:Fact; r:gives {(9630 369) math:difference 9261}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9261 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9261 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3069]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9261]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3069 a r:Inference; + r:gives { + 3070 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3070 math:notEqualTo 0}] + skolem:lemma5584 + [ a r:Fact; r:gives {((3 0 7 0) "=<") list:sort (0 0 3 7)}] + [ a r:Fact; r:gives {((3 0 7 0) ">=") list:sort (7 3 0 0)}] + skolem:lemma5456 + skolem:lemma5457 + [ a r:Fact; r:gives {(7300 37) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3070]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 7 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 37]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3070 a r:Inference; + r:gives { + 3071 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3071 math:notEqualTo 0}] + skolem:lemma5585 + [ a r:Fact; r:gives {((3 0 7 1) "=<") list:sort (0 1 3 7)}] + [ a r:Fact; r:gives {((3 0 7 1) ">=") list:sort (7 3 1 0)}] + skolem:lemma5482 + skolem:lemma5483 + [ a r:Fact; r:gives {(7310 137) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3071]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 7 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 137]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3071 a r:Inference; + r:gives { + 3072 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3072 math:notEqualTo 0}] + skolem:lemma5586 + [ a r:Fact; r:gives {((3 0 7 2) "=<") list:sort (0 2 3 7)}] + [ a r:Fact; r:gives {((3 0 7 2) ">=") list:sort (7 3 2 0)}] + skolem:lemma4099 + skolem:lemma4100 + [ a r:Fact; r:gives {(7320 237) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3072]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3072 a r:Inference; + r:gives { + 3073 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3073 math:notEqualTo 0}] + skolem:lemma5587 + [ a r:Fact; r:gives {((3 0 7 3) "=<") list:sort (0 3 3 7)}] + [ a r:Fact; r:gives {((3 0 7 3) ">=") list:sort (7 3 3 0)}] + skolem:lemma5516 + skolem:lemma5517 + [ a r:Fact; r:gives {(7330 337) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3073]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3073 a r:Inference; + r:gives { + 3074 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3074 math:notEqualTo 0}] + skolem:lemma5588 + [ a r:Fact; r:gives {((3 0 7 4) "=<") list:sort (0 3 4 7)}] + [ a r:Fact; r:gives {((3 0 7 4) ">=") list:sort (7 4 3 0)}] + skolem:lemma5538 + skolem:lemma5539 + [ a r:Fact; r:gives {(7430 347) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3074]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 7 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3074 a r:Inference; + r:gives { + 3075 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3075 math:notEqualTo 0}] + skolem:lemma5589 + [ a r:Fact; r:gives {((3 0 7 5) "=<") list:sort (0 3 5 7)}] + [ a r:Fact; r:gives {((3 0 7 5) ">=") list:sort (7 5 3 0)}] + skolem:lemma5558 + skolem:lemma5559 + [ a r:Fact; r:gives {(7530 357) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3075]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 7 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3075 a r:Inference; + r:gives { + 3076 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3076 math:notEqualTo 0}] + skolem:lemma5590 + [ a r:Fact; r:gives {((3 0 7 6) "=<") list:sort (0 3 6 7)}] + [ a r:Fact; r:gives {((3 0 7 6) ">=") list:sort (7 6 3 0)}] + skolem:lemma5576 + skolem:lemma5577 + [ a r:Fact; r:gives {(7630 367) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3076]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 7 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3076 a r:Inference; + r:gives { + 3077 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3077 math:notEqualTo 0}] + skolem:lemma5591 + [ a r:Fact; r:gives {((3 0 7 7) "=<") list:sort (0 3 7 7)}] + [ a r:Fact; r:gives {((3 0 7 7) ">=") list:sort (7 7 3 0)}] + skolem:lemma5592 + skolem:lemma5593 + [ a r:Fact; r:gives {(7730 377) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3077]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3077 a r:Inference; + r:gives { + 3078 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3078 math:notEqualTo 0}] + skolem:lemma5594 + [ a r:Fact; r:gives {((3 0 7 8) "=<") list:sort (0 3 7 8)}] + [ a r:Fact; r:gives {((3 0 7 8) ">=") list:sort (8 7 3 0)}] + skolem:lemma5595 + skolem:lemma5596 + [ a r:Fact; r:gives {(8730 378) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3078]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3078 a r:Inference; + r:gives { + 3079 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3079 math:notEqualTo 0}] + skolem:lemma5597 + [ a r:Fact; r:gives {((3 0 7 9) "=<") list:sort (0 3 7 9)}] + [ a r:Fact; r:gives {((3 0 7 9) ">=") list:sort (9 7 3 0)}] + skolem:lemma5598 + skolem:lemma5599 + [ a r:Fact; r:gives {(9730 379) math:difference 9351}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9351 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9351 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3079]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9351]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3079 a r:Inference; + r:gives { + 3080 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3080 math:notEqualTo 0}] + skolem:lemma5600 + [ a r:Fact; r:gives {((3 0 8 0) "=<") list:sort (0 0 3 8)}] + [ a r:Fact; r:gives {((3 0 8 0) ">=") list:sort (8 3 0 0)}] + skolem:lemma5459 + skolem:lemma5460 + [ a r:Fact; r:gives {(8300 38) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3080]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 8 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 38]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3080 a r:Inference; + r:gives { + 3081 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3081 math:notEqualTo 0}] + skolem:lemma5601 + [ a r:Fact; r:gives {((3 0 8 1) "=<") list:sort (0 1 3 8)}] + [ a r:Fact; r:gives {((3 0 8 1) ">=") list:sort (8 3 1 0)}] + skolem:lemma5485 + skolem:lemma5486 + [ a r:Fact; r:gives {(8310 138) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 8 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 138]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3081 a r:Inference; + r:gives { + 3082 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3082 math:notEqualTo 0}] + skolem:lemma5602 + [ a r:Fact; r:gives {((3 0 8 2) "=<") list:sort (0 2 3 8)}] + [ a r:Fact; r:gives {((3 0 8 2) ">=") list:sort (8 3 2 0)}] + skolem:lemma4102 + skolem:lemma4103 + [ a r:Fact; r:gives {(8320 238) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3082 a r:Inference; + r:gives { + 3083 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3083 math:notEqualTo 0}] + skolem:lemma5603 + [ a r:Fact; r:gives {((3 0 8 3) "=<") list:sort (0 3 3 8)}] + [ a r:Fact; r:gives {((3 0 8 3) ">=") list:sort (8 3 3 0)}] + skolem:lemma5519 + skolem:lemma5520 + [ a r:Fact; r:gives {(8330 338) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3083 a r:Inference; + r:gives { + 3084 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3084 math:notEqualTo 0}] + skolem:lemma5604 + [ a r:Fact; r:gives {((3 0 8 4) "=<") list:sort (0 3 4 8)}] + [ a r:Fact; r:gives {((3 0 8 4) ">=") list:sort (8 4 3 0)}] + skolem:lemma5541 + skolem:lemma5542 + [ a r:Fact; r:gives {(8430 348) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 8 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3084 a r:Inference; + r:gives { + 3085 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3085 math:notEqualTo 0}] + skolem:lemma5605 + [ a r:Fact; r:gives {((3 0 8 5) "=<") list:sort (0 3 5 8)}] + [ a r:Fact; r:gives {((3 0 8 5) ">=") list:sort (8 5 3 0)}] + skolem:lemma5561 + skolem:lemma5562 + [ a r:Fact; r:gives {(8530 358) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 8 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3085 a r:Inference; + r:gives { + 3086 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3086 math:notEqualTo 0}] + skolem:lemma5606 + [ a r:Fact; r:gives {((3 0 8 6) "=<") list:sort (0 3 6 8)}] + [ a r:Fact; r:gives {((3 0 8 6) ">=") list:sort (8 6 3 0)}] + skolem:lemma5579 + skolem:lemma5580 + [ a r:Fact; r:gives {(8630 368) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 8 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3086 a r:Inference; + r:gives { + 3087 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3087 math:notEqualTo 0}] + skolem:lemma5607 + [ a r:Fact; r:gives {((3 0 8 7) "=<") list:sort (0 3 7 8)}] + [ a r:Fact; r:gives {((3 0 8 7) ">=") list:sort (8 7 3 0)}] + skolem:lemma5595 + skolem:lemma5596 + [ a r:Fact; r:gives {(8730 378) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 8 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3087 a r:Inference; + r:gives { + 3088 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3088 math:notEqualTo 0}] + skolem:lemma5608 + [ a r:Fact; r:gives {((3 0 8 8) "=<") list:sort (0 3 8 8)}] + [ a r:Fact; r:gives {((3 0 8 8) ">=") list:sort (8 8 3 0)}] + skolem:lemma5609 + skolem:lemma5610 + [ a r:Fact; r:gives {(8830 388) math:difference 8442}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8442 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 8442 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8830]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3088 a r:Inference; + r:gives { + 3089 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3089 math:notEqualTo 0}] + skolem:lemma5611 + [ a r:Fact; r:gives {((3 0 8 9) "=<") list:sort (0 3 8 9)}] + [ a r:Fact; r:gives {((3 0 8 9) ">=") list:sort (9 8 3 0)}] + skolem:lemma5612 + skolem:lemma5613 + [ a r:Fact; r:gives {(9830 389) math:difference 9441}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9441 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9441 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3089]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9830]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9441]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3089 a r:Inference; + r:gives { + 3090 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3090 math:notEqualTo 0}] + skolem:lemma5614 + [ a r:Fact; r:gives {((3 0 9 0) "=<") list:sort (0 0 3 9)}] + [ a r:Fact; r:gives {((3 0 9 0) ">=") list:sort (9 3 0 0)}] + skolem:lemma5462 + skolem:lemma5463 + [ a r:Fact; r:gives {(9300 39) math:difference 9261}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9261 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9261 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3090]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 9 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 39]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9261]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3090 a r:Inference; + r:gives { + 3091 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3091 math:notEqualTo 0}] + skolem:lemma5615 + [ a r:Fact; r:gives {((3 0 9 1) "=<") list:sort (0 1 3 9)}] + [ a r:Fact; r:gives {((3 0 9 1) ">=") list:sort (9 3 1 0)}] + skolem:lemma5488 + skolem:lemma5489 + [ a r:Fact; r:gives {(9310 139) math:difference 9171}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9171 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9171 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3091]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 9 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 139]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3091 a r:Inference; + r:gives { + 3092 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3092 math:notEqualTo 0}] + skolem:lemma5616 + [ a r:Fact; r:gives {((3 0 9 2) "=<") list:sort (0 2 3 9)}] + [ a r:Fact; r:gives {((3 0 9 2) ">=") list:sort (9 3 2 0)}] + skolem:lemma4105 + skolem:lemma4106 + [ a r:Fact; r:gives {(9320 239) math:difference 9081}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9081 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 9081 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3092]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 9 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3092 a r:Inference; + r:gives { + 3093 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3093 math:notEqualTo 0}] + skolem:lemma5617 + [ a r:Fact; r:gives {((3 0 9 3) "=<") list:sort (0 3 3 9)}] + [ a r:Fact; r:gives {((3 0 9 3) ">=") list:sort (9 3 3 0)}] + skolem:lemma5522 + skolem:lemma5523 + [ a r:Fact; r:gives {(9330 339) math:difference 8991}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8991 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 8991 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3093]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 9 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8991]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3093 a r:Inference; + r:gives { + 3094 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3094 math:notEqualTo 0}] + skolem:lemma5618 + [ a r:Fact; r:gives {((3 0 9 4) "=<") list:sort (0 3 4 9)}] + [ a r:Fact; r:gives {((3 0 9 4) ">=") list:sort (9 4 3 0)}] + skolem:lemma5544 + skolem:lemma5545 + [ a r:Fact; r:gives {(9430 349) math:difference 9081}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9081 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 9081 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3094]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 9 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3094 a r:Inference; + r:gives { + 3095 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3095 math:notEqualTo 0}] + skolem:lemma5619 + [ a r:Fact; r:gives {((3 0 9 5) "=<") list:sort (0 3 5 9)}] + [ a r:Fact; r:gives {((3 0 9 5) ">=") list:sort (9 5 3 0)}] + skolem:lemma5564 + skolem:lemma5565 + [ a r:Fact; r:gives {(9530 359) math:difference 9171}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9171 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9171 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3095]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 9 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3095 a r:Inference; + r:gives { + 3096 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3096 math:notEqualTo 0}] + skolem:lemma5620 + [ a r:Fact; r:gives {((3 0 9 6) "=<") list:sort (0 3 6 9)}] + [ a r:Fact; r:gives {((3 0 9 6) ">=") list:sort (9 6 3 0)}] + skolem:lemma5582 + skolem:lemma5583 + [ a r:Fact; r:gives {(9630 369) math:difference 9261}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9261 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9261 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3096]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 9 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9261]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3096 a r:Inference; + r:gives { + 3097 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3097 math:notEqualTo 0}] + skolem:lemma5621 + [ a r:Fact; r:gives {((3 0 9 7) "=<") list:sort (0 3 7 9)}] + [ a r:Fact; r:gives {((3 0 9 7) ">=") list:sort (9 7 3 0)}] + skolem:lemma5598 + skolem:lemma5599 + [ a r:Fact; r:gives {(9730 379) math:difference 9351}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9351 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9351 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3097]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 9 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9351]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3097 a r:Inference; + r:gives { + 3098 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3098 math:notEqualTo 0}] + skolem:lemma5622 + [ a r:Fact; r:gives {((3 0 9 8) "=<") list:sort (0 3 8 9)}] + [ a r:Fact; r:gives {((3 0 9 8) ">=") list:sort (9 8 3 0)}] + skolem:lemma5612 + skolem:lemma5613 + [ a r:Fact; r:gives {(9830 389) math:difference 9441}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9441 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9441 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3098]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 9 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9830]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9441]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3098 a r:Inference; + r:gives { + 3099 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3099 math:notEqualTo 0}] + skolem:lemma5623 + [ a r:Fact; r:gives {((3 0 9 9) "=<") list:sort (0 3 9 9)}] + [ a r:Fact; r:gives {((3 0 9 9) ">=") list:sort (9 9 3 0)}] + skolem:lemma5624 + skolem:lemma5625 + [ a r:Fact; r:gives {(9930 399) math:difference 9531}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9531 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9531 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3099]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 0 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9930]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3099 a r:Inference; + r:gives { + 3100 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3100 math:notEqualTo 0}] + skolem:lemma5626 + [ a r:Fact; r:gives {((3 1 0 0) "=<") list:sort (0 0 1 3)}] + [ a r:Fact; r:gives {((3 1 0 0) ">=") list:sort (3 1 0 0)}] + skolem:lemma5440 + skolem:lemma5441 + [ a r:Fact; r:gives {(3100 13) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 1 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 13]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3100 a r:Inference; + r:gives { + 3101 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3101 math:notEqualTo 0}] + skolem:lemma5627 + [ a r:Fact; r:gives {((3 1 0 1) "=<") list:sort (0 1 1 3)}] + [ a r:Fact; r:gives {((3 1 0 1) ">=") list:sort (3 1 1 0)}] + skolem:lemma5466 + skolem:lemma5467 + [ a r:Fact; r:gives {(3110 113) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3101]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 0 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 1 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 113]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3110]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3101 a r:Inference; + r:gives { + 3102 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3102 math:notEqualTo 0}] + skolem:lemma5628 + [ a r:Fact; r:gives {((3 1 0 2) "=<") list:sort (0 1 2 3)}] + [ a r:Fact; r:gives {((3 1 0 2) ">=") list:sort (3 2 1 0)}] + skolem:lemma4037 + skolem:lemma4038 + [ a r:Fact; r:gives {(3210 123) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3102]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 0 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3102 a r:Inference; + r:gives { + 3103 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3103 math:notEqualTo 0}] + skolem:lemma5629 + [ a r:Fact; r:gives {((3 1 0 3) "=<") list:sort (0 1 3 3)}] + [ a r:Fact; r:gives {((3 1 0 3) ">=") list:sort (3 3 1 0)}] + skolem:lemma5470 + skolem:lemma5471 + [ a r:Fact; r:gives {(3310 133) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3103]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 0 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 133]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3103 a r:Inference; + r:gives { + 3104 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3104 math:notEqualTo 0}] + skolem:lemma5630 + [ a r:Fact; r:gives {((3 1 0 4) "=<") list:sort (0 1 3 4)}] + [ a r:Fact; r:gives {((3 1 0 4) ">=") list:sort (4 3 1 0)}] + skolem:lemma5473 + skolem:lemma5474 + [ a r:Fact; r:gives {(4310 134) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3104]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 0 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 134]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3104 a r:Inference; + r:gives { + 3105 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3105 math:notEqualTo 0}] + skolem:lemma5631 + [ a r:Fact; r:gives {((3 1 0 5) "=<") list:sort (0 1 3 5)}] + [ a r:Fact; r:gives {((3 1 0 5) ">=") list:sort (5 3 1 0)}] + skolem:lemma5476 + skolem:lemma5477 + [ a r:Fact; r:gives {(5310 135) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3105]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 0 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 135]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3105 a r:Inference; + r:gives { + 3106 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3106 math:notEqualTo 0}] + skolem:lemma5632 + [ a r:Fact; r:gives {((3 1 0 6) "=<") list:sort (0 1 3 6)}] + [ a r:Fact; r:gives {((3 1 0 6) ">=") list:sort (6 3 1 0)}] + skolem:lemma5479 + skolem:lemma5480 + [ a r:Fact; r:gives {(6310 136) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3106]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 0 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 136]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3106 a r:Inference; + r:gives { + 3107 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3107 math:notEqualTo 0}] + skolem:lemma5633 + [ a r:Fact; r:gives {((3 1 0 7) "=<") list:sort (0 1 3 7)}] + [ a r:Fact; r:gives {((3 1 0 7) ">=") list:sort (7 3 1 0)}] + skolem:lemma5482 + skolem:lemma5483 + [ a r:Fact; r:gives {(7310 137) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3107]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 0 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 137]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3107 a r:Inference; + r:gives { + 3108 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3108 math:notEqualTo 0}] + skolem:lemma5634 + [ a r:Fact; r:gives {((3 1 0 8) "=<") list:sort (0 1 3 8)}] + [ a r:Fact; r:gives {((3 1 0 8) ">=") list:sort (8 3 1 0)}] + skolem:lemma5485 + skolem:lemma5486 + [ a r:Fact; r:gives {(8310 138) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3108]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 0 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 138]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3108 a r:Inference; + r:gives { + 3109 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3109 math:notEqualTo 0}] + skolem:lemma5635 + [ a r:Fact; r:gives {((3 1 0 9) "=<") list:sort (0 1 3 9)}] + [ a r:Fact; r:gives {((3 1 0 9) ">=") list:sort (9 3 1 0)}] + skolem:lemma5488 + skolem:lemma5489 + [ a r:Fact; r:gives {(9310 139) math:difference 9171}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9171 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9171 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3109]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 0 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 139]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3109 a r:Inference; + r:gives { + 3110 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3110 math:notEqualTo 0}] + skolem:lemma5636 + [ a r:Fact; r:gives {((3 1 1 0) "=<") list:sort (0 1 1 3)}] + [ a r:Fact; r:gives {((3 1 1 0) ">=") list:sort (3 1 1 0)}] + skolem:lemma5466 + skolem:lemma5467 + [ a r:Fact; r:gives {(3110 113) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3110]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 1 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 113]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3110]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3110 a r:Inference; + r:gives { + 3111 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3111 math:notEqualTo 0}] + skolem:lemma5637 + [ a r:Fact; r:gives {((3 1 1 1) "=<") list:sort (1 1 1 3)}] + [ a r:Fact; r:gives {((3 1 1 1) ">=") list:sort (3 1 1 1)}] + skolem:lemma5638 + skolem:lemma5639 + [ a r:Fact; r:gives {(3111 1113) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3111]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 1 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1113]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3111]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3111 a r:Inference; + r:gives { + 3112 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3112 math:notEqualTo 0}] + skolem:lemma5640 + [ a r:Fact; r:gives {((3 1 1 2) "=<") list:sort (1 1 2 3)}] + [ a r:Fact; r:gives {((3 1 1 2) ">=") list:sort (3 2 1 1)}] + skolem:lemma4227 + skolem:lemma4228 + [ a r:Fact; r:gives {(3211 1123) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3112]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3112 a r:Inference; + r:gives { + 3113 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3113 math:notEqualTo 0}] + skolem:lemma5641 + [ a r:Fact; r:gives {((3 1 1 3) "=<") list:sort (1 1 3 3)}] + [ a r:Fact; r:gives {((3 1 1 3) ">=") list:sort (3 3 1 1)}] + skolem:lemma5642 + skolem:lemma5643 + [ a r:Fact; r:gives {(3311 1133) math:difference 2178}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2178 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2178 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3113]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1133]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2178]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3113 a r:Inference; + r:gives { + 3114 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3114 math:notEqualTo 0}] + skolem:lemma5644 + [ a r:Fact; r:gives {((3 1 1 4) "=<") list:sort (1 1 3 4)}] + [ a r:Fact; r:gives {((3 1 1 4) ">=") list:sort (4 3 1 1)}] + skolem:lemma5645 + skolem:lemma5646 + [ a r:Fact; r:gives {(4311 1134) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3114]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 1 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1134]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3114 a r:Inference; + r:gives { + 3115 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3115 math:notEqualTo 0}] + skolem:lemma5647 + [ a r:Fact; r:gives {((3 1 1 5) "=<") list:sort (1 1 3 5)}] + [ a r:Fact; r:gives {((3 1 1 5) ">=") list:sort (5 3 1 1)}] + skolem:lemma5648 + skolem:lemma5649 + [ a r:Fact; r:gives {(5311 1135) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3115]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 1 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1135]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3115 a r:Inference; + r:gives { + 3116 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3116 math:notEqualTo 0}] + skolem:lemma5650 + [ a r:Fact; r:gives {((3 1 1 6) "=<") list:sort (1 1 3 6)}] + [ a r:Fact; r:gives {((3 1 1 6) ">=") list:sort (6 3 1 1)}] + skolem:lemma5651 + skolem:lemma5652 + [ a r:Fact; r:gives {(6311 1136) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3116]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 1 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1136]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3116 a r:Inference; + r:gives { + 3117 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3117 math:notEqualTo 0}] + skolem:lemma5653 + [ a r:Fact; r:gives {((3 1 1 7) "=<") list:sort (1 1 3 7)}] + [ a r:Fact; r:gives {((3 1 1 7) ">=") list:sort (7 3 1 1)}] + skolem:lemma5654 + skolem:lemma5655 + [ a r:Fact; r:gives {(7311 1137) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3117]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 1 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1137]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3117 a r:Inference; + r:gives { + 3118 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3118 math:notEqualTo 0}] + skolem:lemma5656 + [ a r:Fact; r:gives {((3 1 1 8) "=<") list:sort (1 1 3 8)}] + [ a r:Fact; r:gives {((3 1 1 8) ">=") list:sort (8 3 1 1)}] + skolem:lemma5657 + skolem:lemma5658 + [ a r:Fact; r:gives {(8311 1138) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3118]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 1 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1138]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3118 a r:Inference; + r:gives { + 3119 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3119 math:notEqualTo 0}] + skolem:lemma5659 + [ a r:Fact; r:gives {((3 1 1 9) "=<") list:sort (1 1 3 9)}] + [ a r:Fact; r:gives {((3 1 1 9) ">=") list:sort (9 3 1 1)}] + skolem:lemma5660 + skolem:lemma5661 + [ a r:Fact; r:gives {(9311 1139) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3119]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 1 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1139]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3119 a r:Inference; + r:gives { + 3120 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3120 math:notEqualTo 0}] + skolem:lemma5662 + [ a r:Fact; r:gives {((3 1 2 0) "=<") list:sort (0 1 2 3)}] + [ a r:Fact; r:gives {((3 1 2 0) ">=") list:sort (3 2 1 0)}] + skolem:lemma4037 + skolem:lemma4038 + [ a r:Fact; r:gives {(3210 123) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3120]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3120 a r:Inference; + r:gives { + 3121 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3121 math:notEqualTo 0}] + skolem:lemma5663 + [ a r:Fact; r:gives {((3 1 2 1) "=<") list:sort (1 1 2 3)}] + [ a r:Fact; r:gives {((3 1 2 1) ">=") list:sort (3 2 1 1)}] + skolem:lemma4227 + skolem:lemma4228 + [ a r:Fact; r:gives {(3211 1123) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3121]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3121 a r:Inference; + r:gives { + 3122 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3122 math:notEqualTo 0}] + skolem:lemma5664 + [ a r:Fact; r:gives {((3 1 2 2) "=<") list:sort (1 2 2 3)}] + [ a r:Fact; r:gives {((3 1 2 2) ">=") list:sort (3 2 2 1)}] + skolem:lemma4253 + skolem:lemma4254 + [ a r:Fact; r:gives {(3221 1223) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3122]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3122 a r:Inference; + r:gives { + 3123 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3123 math:notEqualTo 0}] + skolem:lemma5665 + [ a r:Fact; r:gives {((3 1 2 3) "=<") list:sort (1 2 3 3)}] + [ a r:Fact; r:gives {((3 1 2 3) ">=") list:sort (3 3 2 1)}] + skolem:lemma4277 + skolem:lemma4278 + [ a r:Fact; r:gives {(3321 1233) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3123 a r:Inference; + r:gives { + 3124 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3124 math:notEqualTo 0}] + skolem:lemma5666 + [ a r:Fact; r:gives {((3 1 2 4) "=<") list:sort (1 2 3 4)}] + [ a r:Fact; r:gives {((3 1 2 4) ">=") list:sort (4 3 2 1)}] + skolem:lemma4280 + skolem:lemma4281 + [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3124 a r:Inference; + r:gives { + 3125 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3125 math:notEqualTo 0}] + skolem:lemma5667 + [ a r:Fact; r:gives {((3 1 2 5) "=<") list:sort (1 2 3 5)}] + [ a r:Fact; r:gives {((3 1 2 5) ">=") list:sort (5 3 2 1)}] + skolem:lemma4283 + skolem:lemma4284 + [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3125 a r:Inference; + r:gives { + 3126 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3126 math:notEqualTo 0}] + skolem:lemma5668 + [ a r:Fact; r:gives {((3 1 2 6) "=<") list:sort (1 2 3 6)}] + [ a r:Fact; r:gives {((3 1 2 6) ">=") list:sort (6 3 2 1)}] + skolem:lemma4286 + skolem:lemma4287 + [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3126 a r:Inference; + r:gives { + 3127 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3127 math:notEqualTo 0}] + skolem:lemma5669 + [ a r:Fact; r:gives {((3 1 2 7) "=<") list:sort (1 2 3 7)}] + [ a r:Fact; r:gives {((3 1 2 7) ">=") list:sort (7 3 2 1)}] + skolem:lemma4289 + skolem:lemma4290 + [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3127 a r:Inference; + r:gives { + 3128 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3128 math:notEqualTo 0}] + skolem:lemma5670 + [ a r:Fact; r:gives {((3 1 2 8) "=<") list:sort (1 2 3 8)}] + [ a r:Fact; r:gives {((3 1 2 8) ">=") list:sort (8 3 2 1)}] + skolem:lemma4292 + skolem:lemma4293 + [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3128 a r:Inference; + r:gives { + 3129 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3129 math:notEqualTo 0}] + skolem:lemma5671 + [ a r:Fact; r:gives {((3 1 2 9) "=<") list:sort (1 2 3 9)}] + [ a r:Fact; r:gives {((3 1 2 9) ">=") list:sort (9 3 2 1)}] + skolem:lemma4295 + skolem:lemma4296 + [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3129 a r:Inference; + r:gives { + 3130 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3130 math:notEqualTo 0}] + skolem:lemma5672 + [ a r:Fact; r:gives {((3 1 3 0) "=<") list:sort (0 1 3 3)}] + [ a r:Fact; r:gives {((3 1 3 0) ">=") list:sort (3 3 1 0)}] + skolem:lemma5470 + skolem:lemma5471 + [ a r:Fact; r:gives {(3310 133) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3130]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 133]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3130 a r:Inference; + r:gives { + 3131 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3131 math:notEqualTo 0}] + skolem:lemma5673 + [ a r:Fact; r:gives {((3 1 3 1) "=<") list:sort (1 1 3 3)}] + [ a r:Fact; r:gives {((3 1 3 1) ">=") list:sort (3 3 1 1)}] + skolem:lemma5642 + skolem:lemma5643 + [ a r:Fact; r:gives {(3311 1133) math:difference 2178}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2178 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2178 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3131]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1133]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2178]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3131 a r:Inference; + r:gives { + 3132 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3132 math:notEqualTo 0}] + skolem:lemma5674 + [ a r:Fact; r:gives {((3 1 3 2) "=<") list:sort (1 2 3 3)}] + [ a r:Fact; r:gives {((3 1 3 2) ">=") list:sort (3 3 2 1)}] + skolem:lemma4277 + skolem:lemma4278 + [ a r:Fact; r:gives {(3321 1233) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3132]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3132 a r:Inference; + r:gives { + 3133 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3133 math:notEqualTo 0}] + skolem:lemma5675 + [ a r:Fact; r:gives {((3 1 3 3) "=<") list:sort (1 3 3 3)}] + [ a r:Fact; r:gives {((3 1 3 3) ">=") list:sort (3 3 3 1)}] + skolem:lemma5676 + skolem:lemma5677 + [ a r:Fact; r:gives {(3331 1333) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3133]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3133 a r:Inference; + r:gives { + 3134 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3134 math:notEqualTo 0}] + skolem:lemma5678 + [ a r:Fact; r:gives {((3 1 3 4) "=<") list:sort (1 3 3 4)}] + [ a r:Fact; r:gives {((3 1 3 4) ">=") list:sort (4 3 3 1)}] + skolem:lemma5679 + skolem:lemma5680 + [ a r:Fact; r:gives {(4331 1334) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3134]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3134 a r:Inference; + r:gives { + 3135 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3135 math:notEqualTo 0}] + skolem:lemma5681 + [ a r:Fact; r:gives {((3 1 3 5) "=<") list:sort (1 3 3 5)}] + [ a r:Fact; r:gives {((3 1 3 5) ">=") list:sort (5 3 3 1)}] + skolem:lemma5682 + skolem:lemma5683 + [ a r:Fact; r:gives {(5331 1335) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3135]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3135 a r:Inference; + r:gives { + 3136 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3136 math:notEqualTo 0}] + skolem:lemma5684 + [ a r:Fact; r:gives {((3 1 3 6) "=<") list:sort (1 3 3 6)}] + [ a r:Fact; r:gives {((3 1 3 6) ">=") list:sort (6 3 3 1)}] + skolem:lemma5685 + skolem:lemma5686 + [ a r:Fact; r:gives {(6331 1336) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3136]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3136 a r:Inference; + r:gives { + 3137 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3137 math:notEqualTo 0}] + skolem:lemma5687 + [ a r:Fact; r:gives {((3 1 3 7) "=<") list:sort (1 3 3 7)}] + [ a r:Fact; r:gives {((3 1 3 7) ">=") list:sort (7 3 3 1)}] + skolem:lemma5688 + skolem:lemma5689 + [ a r:Fact; r:gives {(7331 1337) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3137]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3137 a r:Inference; + r:gives { + 3138 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3138 math:notEqualTo 0}] + skolem:lemma5690 + [ a r:Fact; r:gives {((3 1 3 8) "=<") list:sort (1 3 3 8)}] + [ a r:Fact; r:gives {((3 1 3 8) ">=") list:sort (8 3 3 1)}] + skolem:lemma5691 + skolem:lemma5692 + [ a r:Fact; r:gives {(8331 1338) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3138]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3138 a r:Inference; + r:gives { + 3139 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3139 math:notEqualTo 0}] + skolem:lemma5693 + [ a r:Fact; r:gives {((3 1 3 9) "=<") list:sort (1 3 3 9)}] + [ a r:Fact; r:gives {((3 1 3 9) ">=") list:sort (9 3 3 1)}] + skolem:lemma5694 + skolem:lemma5695 + [ a r:Fact; r:gives {(9331 1339) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3139]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3139 a r:Inference; + r:gives { + 3140 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3140 math:notEqualTo 0}] + skolem:lemma5696 + [ a r:Fact; r:gives {((3 1 4 0) "=<") list:sort (0 1 3 4)}] + [ a r:Fact; r:gives {((3 1 4 0) ">=") list:sort (4 3 1 0)}] + skolem:lemma5473 + skolem:lemma5474 + [ a r:Fact; r:gives {(4310 134) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3140]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 4 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 134]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3140 a r:Inference; + r:gives { + 3141 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3141 math:notEqualTo 0}] + skolem:lemma5697 + [ a r:Fact; r:gives {((3 1 4 1) "=<") list:sort (1 1 3 4)}] + [ a r:Fact; r:gives {((3 1 4 1) ">=") list:sort (4 3 1 1)}] + skolem:lemma5645 + skolem:lemma5646 + [ a r:Fact; r:gives {(4311 1134) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3141]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 4 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1134]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3141 a r:Inference; + r:gives { + 3142 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3142 math:notEqualTo 0}] + skolem:lemma5698 + [ a r:Fact; r:gives {((3 1 4 2) "=<") list:sort (1 2 3 4)}] + [ a r:Fact; r:gives {((3 1 4 2) ">=") list:sort (4 3 2 1)}] + skolem:lemma4280 + skolem:lemma4281 + [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3142]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3142 a r:Inference; + r:gives { + 3143 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3143 math:notEqualTo 0}] + skolem:lemma5699 + [ a r:Fact; r:gives {((3 1 4 3) "=<") list:sort (1 3 3 4)}] + [ a r:Fact; r:gives {((3 1 4 3) ">=") list:sort (4 3 3 1)}] + skolem:lemma5679 + skolem:lemma5680 + [ a r:Fact; r:gives {(4331 1334) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3143]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3143 a r:Inference; + r:gives { + 3144 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3144 math:notEqualTo 0}] + skolem:lemma5700 + [ a r:Fact; r:gives {((3 1 4 4) "=<") list:sort (1 3 4 4)}] + [ a r:Fact; r:gives {((3 1 4 4) ">=") list:sort (4 4 3 1)}] + skolem:lemma5701 + skolem:lemma5702 + [ a r:Fact; r:gives {(4431 1344) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3144]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3144 a r:Inference; + r:gives { + 3145 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3145 math:notEqualTo 0}] + skolem:lemma5703 + [ a r:Fact; r:gives {((3 1 4 5) "=<") list:sort (1 3 4 5)}] + [ a r:Fact; r:gives {((3 1 4 5) ">=") list:sort (5 4 3 1)}] + skolem:lemma5704 + skolem:lemma5705 + [ a r:Fact; r:gives {(5431 1345) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3145]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3145 a r:Inference; + r:gives { + 3146 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3146 math:notEqualTo 0}] + skolem:lemma5706 + [ a r:Fact; r:gives {((3 1 4 6) "=<") list:sort (1 3 4 6)}] + [ a r:Fact; r:gives {((3 1 4 6) ">=") list:sort (6 4 3 1)}] + skolem:lemma5707 + skolem:lemma5708 + [ a r:Fact; r:gives {(6431 1346) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3146]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3146 a r:Inference; + r:gives { + 3147 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3147 math:notEqualTo 0}] + skolem:lemma5709 + [ a r:Fact; r:gives {((3 1 4 7) "=<") list:sort (1 3 4 7)}] + [ a r:Fact; r:gives {((3 1 4 7) ">=") list:sort (7 4 3 1)}] + skolem:lemma5710 + skolem:lemma5711 + [ a r:Fact; r:gives {(7431 1347) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3147]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3147 a r:Inference; + r:gives { + 3148 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3148 math:notEqualTo 0}] + skolem:lemma5712 + [ a r:Fact; r:gives {((3 1 4 8) "=<") list:sort (1 3 4 8)}] + [ a r:Fact; r:gives {((3 1 4 8) ">=") list:sort (8 4 3 1)}] + skolem:lemma5713 + skolem:lemma5714 + [ a r:Fact; r:gives {(8431 1348) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3148]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3148 a r:Inference; + r:gives { + 3149 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3149 math:notEqualTo 0}] + skolem:lemma5715 + [ a r:Fact; r:gives {((3 1 4 9) "=<") list:sort (1 3 4 9)}] + [ a r:Fact; r:gives {((3 1 4 9) ">=") list:sort (9 4 3 1)}] + skolem:lemma5716 + skolem:lemma5717 + [ a r:Fact; r:gives {(9431 1349) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3149]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3149 a r:Inference; + r:gives { + 3150 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3150 math:notEqualTo 0}] + skolem:lemma5718 + [ a r:Fact; r:gives {((3 1 5 0) "=<") list:sort (0 1 3 5)}] + [ a r:Fact; r:gives {((3 1 5 0) ">=") list:sort (5 3 1 0)}] + skolem:lemma5476 + skolem:lemma5477 + [ a r:Fact; r:gives {(5310 135) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3150]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 5 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 135]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3150 a r:Inference; + r:gives { + 3151 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3151 math:notEqualTo 0}] + skolem:lemma5719 + [ a r:Fact; r:gives {((3 1 5 1) "=<") list:sort (1 1 3 5)}] + [ a r:Fact; r:gives {((3 1 5 1) ">=") list:sort (5 3 1 1)}] + skolem:lemma5648 + skolem:lemma5649 + [ a r:Fact; r:gives {(5311 1135) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3151]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 5 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1135]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3151 a r:Inference; + r:gives { + 3152 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3152 math:notEqualTo 0}] + skolem:lemma5720 + [ a r:Fact; r:gives {((3 1 5 2) "=<") list:sort (1 2 3 5)}] + [ a r:Fact; r:gives {((3 1 5 2) ">=") list:sort (5 3 2 1)}] + skolem:lemma4283 + skolem:lemma4284 + [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3152]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3152 a r:Inference; + r:gives { + 3153 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3153 math:notEqualTo 0}] + skolem:lemma5721 + [ a r:Fact; r:gives {((3 1 5 3) "=<") list:sort (1 3 3 5)}] + [ a r:Fact; r:gives {((3 1 5 3) ">=") list:sort (5 3 3 1)}] + skolem:lemma5682 + skolem:lemma5683 + [ a r:Fact; r:gives {(5331 1335) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3153]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3153 a r:Inference; + r:gives { + 3154 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3154 math:notEqualTo 0}] + skolem:lemma5722 + [ a r:Fact; r:gives {((3 1 5 4) "=<") list:sort (1 3 4 5)}] + [ a r:Fact; r:gives {((3 1 5 4) ">=") list:sort (5 4 3 1)}] + skolem:lemma5704 + skolem:lemma5705 + [ a r:Fact; r:gives {(5431 1345) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3154]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 5 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3154 a r:Inference; + r:gives { + 3155 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3155 math:notEqualTo 0}] + skolem:lemma5723 + [ a r:Fact; r:gives {((3 1 5 5) "=<") list:sort (1 3 5 5)}] + [ a r:Fact; r:gives {((3 1 5 5) ">=") list:sort (5 5 3 1)}] + skolem:lemma5724 + skolem:lemma5725 + [ a r:Fact; r:gives {(5531 1355) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3155]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3155 a r:Inference; + r:gives { + 3156 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3156 math:notEqualTo 0}] + skolem:lemma5726 + [ a r:Fact; r:gives {((3 1 5 6) "=<") list:sort (1 3 5 6)}] + [ a r:Fact; r:gives {((3 1 5 6) ">=") list:sort (6 5 3 1)}] + skolem:lemma5727 + skolem:lemma5728 + [ a r:Fact; r:gives {(6531 1356) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3156]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3156 a r:Inference; + r:gives { + 3157 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3157 math:notEqualTo 0}] + skolem:lemma5729 + [ a r:Fact; r:gives {((3 1 5 7) "=<") list:sort (1 3 5 7)}] + [ a r:Fact; r:gives {((3 1 5 7) ">=") list:sort (7 5 3 1)}] + skolem:lemma5730 + skolem:lemma5731 + [ a r:Fact; r:gives {(7531 1357) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3157]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3157 a r:Inference; + r:gives { + 3158 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3158 math:notEqualTo 0}] + skolem:lemma5732 + [ a r:Fact; r:gives {((3 1 5 8) "=<") list:sort (1 3 5 8)}] + [ a r:Fact; r:gives {((3 1 5 8) ">=") list:sort (8 5 3 1)}] + skolem:lemma5733 + skolem:lemma5734 + [ a r:Fact; r:gives {(8531 1358) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3158]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3158 a r:Inference; + r:gives { + 3159 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3159 math:notEqualTo 0}] + skolem:lemma5735 + [ a r:Fact; r:gives {((3 1 5 9) "=<") list:sort (1 3 5 9)}] + [ a r:Fact; r:gives {((3 1 5 9) ">=") list:sort (9 5 3 1)}] + skolem:lemma5736 + skolem:lemma5737 + [ a r:Fact; r:gives {(9531 1359) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3159]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3159 a r:Inference; + r:gives { + 3160 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3160 math:notEqualTo 0}] + skolem:lemma5738 + [ a r:Fact; r:gives {((3 1 6 0) "=<") list:sort (0 1 3 6)}] + [ a r:Fact; r:gives {((3 1 6 0) ">=") list:sort (6 3 1 0)}] + skolem:lemma5479 + skolem:lemma5480 + [ a r:Fact; r:gives {(6310 136) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3160]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 6 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 136]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3160 a r:Inference; + r:gives { + 3161 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3161 math:notEqualTo 0}] + skolem:lemma5739 + [ a r:Fact; r:gives {((3 1 6 1) "=<") list:sort (1 1 3 6)}] + [ a r:Fact; r:gives {((3 1 6 1) ">=") list:sort (6 3 1 1)}] + skolem:lemma5651 + skolem:lemma5652 + [ a r:Fact; r:gives {(6311 1136) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3161]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 6 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1136]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3161 a r:Inference; + r:gives { + 3162 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3162 math:notEqualTo 0}] + skolem:lemma5740 + [ a r:Fact; r:gives {((3 1 6 2) "=<") list:sort (1 2 3 6)}] + [ a r:Fact; r:gives {((3 1 6 2) ">=") list:sort (6 3 2 1)}] + skolem:lemma4286 + skolem:lemma4287 + [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3162]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3162 a r:Inference; + r:gives { + 3163 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3163 math:notEqualTo 0}] + skolem:lemma5741 + [ a r:Fact; r:gives {((3 1 6 3) "=<") list:sort (1 3 3 6)}] + [ a r:Fact; r:gives {((3 1 6 3) ">=") list:sort (6 3 3 1)}] + skolem:lemma5685 + skolem:lemma5686 + [ a r:Fact; r:gives {(6331 1336) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3163]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3163 a r:Inference; + r:gives { + 3164 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3164 math:notEqualTo 0}] + skolem:lemma5742 + [ a r:Fact; r:gives {((3 1 6 4) "=<") list:sort (1 3 4 6)}] + [ a r:Fact; r:gives {((3 1 6 4) ">=") list:sort (6 4 3 1)}] + skolem:lemma5707 + skolem:lemma5708 + [ a r:Fact; r:gives {(6431 1346) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3164]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 6 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3164 a r:Inference; + r:gives { + 3165 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3165 math:notEqualTo 0}] + skolem:lemma5743 + [ a r:Fact; r:gives {((3 1 6 5) "=<") list:sort (1 3 5 6)}] + [ a r:Fact; r:gives {((3 1 6 5) ">=") list:sort (6 5 3 1)}] + skolem:lemma5727 + skolem:lemma5728 + [ a r:Fact; r:gives {(6531 1356) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3165]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 6 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3165 a r:Inference; + r:gives { + 3166 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3166 math:notEqualTo 0}] + skolem:lemma5744 + [ a r:Fact; r:gives {((3 1 6 6) "=<") list:sort (1 3 6 6)}] + [ a r:Fact; r:gives {((3 1 6 6) ">=") list:sort (6 6 3 1)}] + skolem:lemma5745 + skolem:lemma5746 + [ a r:Fact; r:gives {(6631 1366) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3166]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3166 a r:Inference; + r:gives { + 3167 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3167 math:notEqualTo 0}] + skolem:lemma5747 + [ a r:Fact; r:gives {((3 1 6 7) "=<") list:sort (1 3 6 7)}] + [ a r:Fact; r:gives {((3 1 6 7) ">=") list:sort (7 6 3 1)}] + skolem:lemma5748 + skolem:lemma5749 + [ a r:Fact; r:gives {(7631 1367) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3167]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3167 a r:Inference; + r:gives { + 3168 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3168 math:notEqualTo 0}] + skolem:lemma5750 + [ a r:Fact; r:gives {((3 1 6 8) "=<") list:sort (1 3 6 8)}] + [ a r:Fact; r:gives {((3 1 6 8) ">=") list:sort (8 6 3 1)}] + skolem:lemma5751 + skolem:lemma5752 + [ a r:Fact; r:gives {(8631 1368) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3168]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3168 a r:Inference; + r:gives { + 3169 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3169 math:notEqualTo 0}] + skolem:lemma5753 + [ a r:Fact; r:gives {((3 1 6 9) "=<") list:sort (1 3 6 9)}] + [ a r:Fact; r:gives {((3 1 6 9) ">=") list:sort (9 6 3 1)}] + skolem:lemma5754 + skolem:lemma5755 + [ a r:Fact; r:gives {(9631 1369) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3169]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3169 a r:Inference; + r:gives { + 3170 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3170 math:notEqualTo 0}] + skolem:lemma5756 + [ a r:Fact; r:gives {((3 1 7 0) "=<") list:sort (0 1 3 7)}] + [ a r:Fact; r:gives {((3 1 7 0) ">=") list:sort (7 3 1 0)}] + skolem:lemma5482 + skolem:lemma5483 + [ a r:Fact; r:gives {(7310 137) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3170]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 7 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 137]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3170 a r:Inference; + r:gives { + 3171 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3171 math:notEqualTo 0}] + skolem:lemma5757 + [ a r:Fact; r:gives {((3 1 7 1) "=<") list:sort (1 1 3 7)}] + [ a r:Fact; r:gives {((3 1 7 1) ">=") list:sort (7 3 1 1)}] + skolem:lemma5654 + skolem:lemma5655 + [ a r:Fact; r:gives {(7311 1137) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 7 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1137]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3171 a r:Inference; + r:gives { + 3172 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3172 math:notEqualTo 0}] + skolem:lemma5758 + [ a r:Fact; r:gives {((3 1 7 2) "=<") list:sort (1 2 3 7)}] + [ a r:Fact; r:gives {((3 1 7 2) ">=") list:sort (7 3 2 1)}] + skolem:lemma4289 + skolem:lemma4290 + [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3172 a r:Inference; + r:gives { + 3173 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3173 math:notEqualTo 0}] + skolem:lemma5759 + [ a r:Fact; r:gives {((3 1 7 3) "=<") list:sort (1 3 3 7)}] + [ a r:Fact; r:gives {((3 1 7 3) ">=") list:sort (7 3 3 1)}] + skolem:lemma5688 + skolem:lemma5689 + [ a r:Fact; r:gives {(7331 1337) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3173 a r:Inference; + r:gives { + 3174 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3174 math:notEqualTo 0}] + skolem:lemma5760 + [ a r:Fact; r:gives {((3 1 7 4) "=<") list:sort (1 3 4 7)}] + [ a r:Fact; r:gives {((3 1 7 4) ">=") list:sort (7 4 3 1)}] + skolem:lemma5710 + skolem:lemma5711 + [ a r:Fact; r:gives {(7431 1347) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 7 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3174 a r:Inference; + r:gives { + 3175 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3175 math:notEqualTo 0}] + skolem:lemma5761 + [ a r:Fact; r:gives {((3 1 7 5) "=<") list:sort (1 3 5 7)}] + [ a r:Fact; r:gives {((3 1 7 5) ">=") list:sort (7 5 3 1)}] + skolem:lemma5730 + skolem:lemma5731 + [ a r:Fact; r:gives {(7531 1357) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 7 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3175 a r:Inference; + r:gives { + 3176 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3176 math:notEqualTo 0}] + skolem:lemma5762 + [ a r:Fact; r:gives {((3 1 7 6) "=<") list:sort (1 3 6 7)}] + [ a r:Fact; r:gives {((3 1 7 6) ">=") list:sort (7 6 3 1)}] + skolem:lemma5748 + skolem:lemma5749 + [ a r:Fact; r:gives {(7631 1367) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 7 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3176 a r:Inference; + r:gives { + 3177 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3177 math:notEqualTo 0}] + skolem:lemma5763 + [ a r:Fact; r:gives {((3 1 7 7) "=<") list:sort (1 3 7 7)}] + [ a r:Fact; r:gives {((3 1 7 7) ">=") list:sort (7 7 3 1)}] + skolem:lemma5764 + skolem:lemma5765 + [ a r:Fact; r:gives {(7731 1377) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7731]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3177 a r:Inference; + r:gives { + 3178 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3178 math:notEqualTo 0}] + skolem:lemma5766 + [ a r:Fact; r:gives {((3 1 7 8) "=<") list:sort (1 3 7 8)}] + [ a r:Fact; r:gives {((3 1 7 8) ">=") list:sort (8 7 3 1)}] + skolem:lemma5767 + skolem:lemma5768 + [ a r:Fact; r:gives {(8731 1378) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3178]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8731]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3178 a r:Inference; + r:gives { + 3179 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3179 math:notEqualTo 0}] + skolem:lemma5769 + [ a r:Fact; r:gives {((3 1 7 9) "=<") list:sort (1 3 7 9)}] + [ a r:Fact; r:gives {((3 1 7 9) ">=") list:sort (9 7 3 1)}] + skolem:lemma5770 + skolem:lemma5771 + [ a r:Fact; r:gives {(9731 1379) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3179]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9731]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3179 a r:Inference; + r:gives { + 3180 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3180 math:notEqualTo 0}] + skolem:lemma5772 + [ a r:Fact; r:gives {((3 1 8 0) "=<") list:sort (0 1 3 8)}] + [ a r:Fact; r:gives {((3 1 8 0) ">=") list:sort (8 3 1 0)}] + skolem:lemma5485 + skolem:lemma5486 + [ a r:Fact; r:gives {(8310 138) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3180]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 8 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 138]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3180 a r:Inference; + r:gives { + 3181 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3181 math:notEqualTo 0}] + skolem:lemma5773 + [ a r:Fact; r:gives {((3 1 8 1) "=<") list:sort (1 1 3 8)}] + [ a r:Fact; r:gives {((3 1 8 1) ">=") list:sort (8 3 1 1)}] + skolem:lemma5657 + skolem:lemma5658 + [ a r:Fact; r:gives {(8311 1138) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3181]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 8 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1138]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3181 a r:Inference; + r:gives { + 3182 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3182 math:notEqualTo 0}] + skolem:lemma5774 + [ a r:Fact; r:gives {((3 1 8 2) "=<") list:sort (1 2 3 8)}] + [ a r:Fact; r:gives {((3 1 8 2) ">=") list:sort (8 3 2 1)}] + skolem:lemma4292 + skolem:lemma4293 + [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3182]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3182 a r:Inference; + r:gives { + 3183 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3183 math:notEqualTo 0}] + skolem:lemma5775 + [ a r:Fact; r:gives {((3 1 8 3) "=<") list:sort (1 3 3 8)}] + [ a r:Fact; r:gives {((3 1 8 3) ">=") list:sort (8 3 3 1)}] + skolem:lemma5691 + skolem:lemma5692 + [ a r:Fact; r:gives {(8331 1338) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3183]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3183 a r:Inference; + r:gives { + 3184 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3184 math:notEqualTo 0}] + skolem:lemma5776 + [ a r:Fact; r:gives {((3 1 8 4) "=<") list:sort (1 3 4 8)}] + [ a r:Fact; r:gives {((3 1 8 4) ">=") list:sort (8 4 3 1)}] + skolem:lemma5713 + skolem:lemma5714 + [ a r:Fact; r:gives {(8431 1348) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3184]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 8 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3184 a r:Inference; + r:gives { + 3185 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3185 math:notEqualTo 0}] + skolem:lemma5777 + [ a r:Fact; r:gives {((3 1 8 5) "=<") list:sort (1 3 5 8)}] + [ a r:Fact; r:gives {((3 1 8 5) ">=") list:sort (8 5 3 1)}] + skolem:lemma5733 + skolem:lemma5734 + [ a r:Fact; r:gives {(8531 1358) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3185]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 8 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3185 a r:Inference; + r:gives { + 3186 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3186 math:notEqualTo 0}] + skolem:lemma5778 + [ a r:Fact; r:gives {((3 1 8 6) "=<") list:sort (1 3 6 8)}] + [ a r:Fact; r:gives {((3 1 8 6) ">=") list:sort (8 6 3 1)}] + skolem:lemma5751 + skolem:lemma5752 + [ a r:Fact; r:gives {(8631 1368) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3186]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 8 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3186 a r:Inference; + r:gives { + 3187 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3187 math:notEqualTo 0}] + skolem:lemma5779 + [ a r:Fact; r:gives {((3 1 8 7) "=<") list:sort (1 3 7 8)}] + [ a r:Fact; r:gives {((3 1 8 7) ">=") list:sort (8 7 3 1)}] + skolem:lemma5767 + skolem:lemma5768 + [ a r:Fact; r:gives {(8731 1378) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3187]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 8 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8731]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3187 a r:Inference; + r:gives { + 3188 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3188 math:notEqualTo 0}] + skolem:lemma5780 + [ a r:Fact; r:gives {((3 1 8 8) "=<") list:sort (1 3 8 8)}] + [ a r:Fact; r:gives {((3 1 8 8) ">=") list:sort (8 8 3 1)}] + skolem:lemma5781 + skolem:lemma5782 + [ a r:Fact; r:gives {(8831 1388) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3188]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8831]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3188 a r:Inference; + r:gives { + 3189 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3189 math:notEqualTo 0}] + skolem:lemma5783 + [ a r:Fact; r:gives {((3 1 8 9) "=<") list:sort (1 3 8 9)}] + [ a r:Fact; r:gives {((3 1 8 9) ">=") list:sort (9 8 3 1)}] + skolem:lemma5784 + skolem:lemma5785 + [ a r:Fact; r:gives {(9831 1389) math:difference 8442}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8442 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 8442 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3189]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9831]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3189 a r:Inference; + r:gives { + 3190 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3190 math:notEqualTo 0}] + skolem:lemma5786 + [ a r:Fact; r:gives {((3 1 9 0) "=<") list:sort (0 1 3 9)}] + [ a r:Fact; r:gives {((3 1 9 0) ">=") list:sort (9 3 1 0)}] + skolem:lemma5488 + skolem:lemma5489 + [ a r:Fact; r:gives {(9310 139) math:difference 9171}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9171 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9171 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3190]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 9 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 139]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3190 a r:Inference; + r:gives { + 3191 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3191 math:notEqualTo 0}] + skolem:lemma5787 + [ a r:Fact; r:gives {((3 1 9 1) "=<") list:sort (1 1 3 9)}] + [ a r:Fact; r:gives {((3 1 9 1) ">=") list:sort (9 3 1 1)}] + skolem:lemma5660 + skolem:lemma5661 + [ a r:Fact; r:gives {(9311 1139) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3191]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 9 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1139]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3191 a r:Inference; + r:gives { + 3192 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3192 math:notEqualTo 0}] + skolem:lemma5788 + [ a r:Fact; r:gives {((3 1 9 2) "=<") list:sort (1 2 3 9)}] + [ a r:Fact; r:gives {((3 1 9 2) ">=") list:sort (9 3 2 1)}] + skolem:lemma4295 + skolem:lemma4296 + [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3192]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 9 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3192 a r:Inference; + r:gives { + 3193 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3193 math:notEqualTo 0}] + skolem:lemma5789 + [ a r:Fact; r:gives {((3 1 9 3) "=<") list:sort (1 3 3 9)}] + [ a r:Fact; r:gives {((3 1 9 3) ">=") list:sort (9 3 3 1)}] + skolem:lemma5694 + skolem:lemma5695 + [ a r:Fact; r:gives {(9331 1339) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3193]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 9 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3193 a r:Inference; + r:gives { + 3194 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3194 math:notEqualTo 0}] + skolem:lemma5790 + [ a r:Fact; r:gives {((3 1 9 4) "=<") list:sort (1 3 4 9)}] + [ a r:Fact; r:gives {((3 1 9 4) ">=") list:sort (9 4 3 1)}] + skolem:lemma5716 + skolem:lemma5717 + [ a r:Fact; r:gives {(9431 1349) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3194]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 9 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3194 a r:Inference; + r:gives { + 3195 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3195 math:notEqualTo 0}] + skolem:lemma5791 + [ a r:Fact; r:gives {((3 1 9 5) "=<") list:sort (1 3 5 9)}] + [ a r:Fact; r:gives {((3 1 9 5) ">=") list:sort (9 5 3 1)}] + skolem:lemma5736 + skolem:lemma5737 + [ a r:Fact; r:gives {(9531 1359) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3195]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 9 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3195 a r:Inference; + r:gives { + 3196 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3196 math:notEqualTo 0}] + skolem:lemma5792 + [ a r:Fact; r:gives {((3 1 9 6) "=<") list:sort (1 3 6 9)}] + [ a r:Fact; r:gives {((3 1 9 6) ">=") list:sort (9 6 3 1)}] + skolem:lemma5754 + skolem:lemma5755 + [ a r:Fact; r:gives {(9631 1369) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3196]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 9 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3196 a r:Inference; + r:gives { + 3197 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3197 math:notEqualTo 0}] + skolem:lemma5793 + [ a r:Fact; r:gives {((3 1 9 7) "=<") list:sort (1 3 7 9)}] + [ a r:Fact; r:gives {((3 1 9 7) ">=") list:sort (9 7 3 1)}] + skolem:lemma5770 + skolem:lemma5771 + [ a r:Fact; r:gives {(9731 1379) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3197]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 9 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9731]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3197 a r:Inference; + r:gives { + 3198 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3198 math:notEqualTo 0}] + skolem:lemma5794 + [ a r:Fact; r:gives {((3 1 9 8) "=<") list:sort (1 3 8 9)}] + [ a r:Fact; r:gives {((3 1 9 8) ">=") list:sort (9 8 3 1)}] + skolem:lemma5784 + skolem:lemma5785 + [ a r:Fact; r:gives {(9831 1389) math:difference 8442}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8442 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 8442 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3198]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 9 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9831]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3198 a r:Inference; + r:gives { + 3199 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3199 math:notEqualTo 0}] + skolem:lemma5795 + [ a r:Fact; r:gives {((3 1 9 9) "=<") list:sort (1 3 9 9)}] + [ a r:Fact; r:gives {((3 1 9 9) ">=") list:sort (9 9 3 1)}] + skolem:lemma5796 + skolem:lemma5797 + [ a r:Fact; r:gives {(9931 1399) math:difference 8532}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8532 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8532 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3199]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 1 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9931]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3199 a r:Inference; + r:gives { + 3200 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3200 math:notEqualTo 0}] + skolem:lemma5798 + [ a r:Fact; r:gives {((3 2 0 0) "=<") list:sort (0 0 2 3)}] + [ a r:Fact; r:gives {((3 2 0 0) ">=") list:sort (3 2 0 0)}] + skolem:lemma4009 + skolem:lemma4010 + [ a r:Fact; r:gives {(3200 23) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3200 a r:Inference; + r:gives { + 3201 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3201 math:notEqualTo 0}] + skolem:lemma5799 + [ a r:Fact; r:gives {((3 2 0 1) "=<") list:sort (0 1 2 3)}] + [ a r:Fact; r:gives {((3 2 0 1) ">=") list:sort (3 2 1 0)}] + skolem:lemma4037 + skolem:lemma4038 + [ a r:Fact; r:gives {(3210 123) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3201]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 0 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3201 a r:Inference; + r:gives { + 3202 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3202 math:notEqualTo 0}] + skolem:lemma5800 + [ a r:Fact; r:gives {((3 2 0 2) "=<") list:sort (0 2 2 3)}] + [ a r:Fact; r:gives {((3 2 0 2) ">=") list:sort (3 2 2 0)}] + skolem:lemma4063 + skolem:lemma4064 + [ a r:Fact; r:gives {(3220 223) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3202]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 0 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3202 a r:Inference; + r:gives { + 3203 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3203 math:notEqualTo 0}] + skolem:lemma5801 + [ a r:Fact; r:gives {((3 2 0 3) "=<") list:sort (0 2 3 3)}] + [ a r:Fact; r:gives {((3 2 0 3) ">=") list:sort (3 3 2 0)}] + skolem:lemma4087 + skolem:lemma4088 + [ a r:Fact; r:gives {(3320 233) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3203]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 0 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3203 a r:Inference; + r:gives { + 3204 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3204 math:notEqualTo 0}] + skolem:lemma5802 + [ a r:Fact; r:gives {((3 2 0 4) "=<") list:sort (0 2 3 4)}] + [ a r:Fact; r:gives {((3 2 0 4) ">=") list:sort (4 3 2 0)}] + skolem:lemma4090 + skolem:lemma4091 + [ a r:Fact; r:gives {(4320 234) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3204]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 0 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3204 a r:Inference; + r:gives { + 3205 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3205 math:notEqualTo 0}] + skolem:lemma5803 + [ a r:Fact; r:gives {((3 2 0 5) "=<") list:sort (0 2 3 5)}] + [ a r:Fact; r:gives {((3 2 0 5) ">=") list:sort (5 3 2 0)}] + skolem:lemma4093 + skolem:lemma4094 + [ a r:Fact; r:gives {(5320 235) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3205]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 0 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3205 a r:Inference; + r:gives { + 3206 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3206 math:notEqualTo 0}] + skolem:lemma5804 + [ a r:Fact; r:gives {((3 2 0 6) "=<") list:sort (0 2 3 6)}] + [ a r:Fact; r:gives {((3 2 0 6) ">=") list:sort (6 3 2 0)}] + skolem:lemma4096 + skolem:lemma4097 + [ a r:Fact; r:gives {(6320 236) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3206]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 0 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3206 a r:Inference; + r:gives { + 3207 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3207 math:notEqualTo 0}] + skolem:lemma5805 + [ a r:Fact; r:gives {((3 2 0 7) "=<") list:sort (0 2 3 7)}] + [ a r:Fact; r:gives {((3 2 0 7) ">=") list:sort (7 3 2 0)}] + skolem:lemma4099 + skolem:lemma4100 + [ a r:Fact; r:gives {(7320 237) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3207]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 0 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3207 a r:Inference; + r:gives { + 3208 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3208 math:notEqualTo 0}] + skolem:lemma5806 + [ a r:Fact; r:gives {((3 2 0 8) "=<") list:sort (0 2 3 8)}] + [ a r:Fact; r:gives {((3 2 0 8) ">=") list:sort (8 3 2 0)}] + skolem:lemma4102 + skolem:lemma4103 + [ a r:Fact; r:gives {(8320 238) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3208]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 0 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3208 a r:Inference; + r:gives { + 3209 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3209 math:notEqualTo 0}] + skolem:lemma5807 + [ a r:Fact; r:gives {((3 2 0 9) "=<") list:sort (0 2 3 9)}] + [ a r:Fact; r:gives {((3 2 0 9) ">=") list:sort (9 3 2 0)}] + skolem:lemma4105 + skolem:lemma4106 + [ a r:Fact; r:gives {(9320 239) math:difference 9081}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9081 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 9081 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3209]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 0 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3209 a r:Inference; + r:gives { + 3210 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3210 math:notEqualTo 0}] + skolem:lemma5808 + [ a r:Fact; r:gives {((3 2 1 0) "=<") list:sort (0 1 2 3)}] + [ a r:Fact; r:gives {((3 2 1 0) ">=") list:sort (3 2 1 0)}] + skolem:lemma4037 + skolem:lemma4038 + [ a r:Fact; r:gives {(3210 123) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3210 a r:Inference; + r:gives { + 3211 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3211 math:notEqualTo 0}] + skolem:lemma5809 + [ a r:Fact; r:gives {((3 2 1 1) "=<") list:sort (1 1 2 3)}] + [ a r:Fact; r:gives {((3 2 1 1) ">=") list:sort (3 2 1 1)}] + skolem:lemma4227 + skolem:lemma4228 + [ a r:Fact; r:gives {(3211 1123) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3211 a r:Inference; + r:gives { + 3212 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3212 math:notEqualTo 0}] + skolem:lemma5810 + [ a r:Fact; r:gives {((3 2 1 2) "=<") list:sort (1 2 2 3)}] + [ a r:Fact; r:gives {((3 2 1 2) ">=") list:sort (3 2 2 1)}] + skolem:lemma4253 + skolem:lemma4254 + [ a r:Fact; r:gives {(3221 1223) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3212]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3212 a r:Inference; + r:gives { + 3213 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3213 math:notEqualTo 0}] + skolem:lemma5811 + [ a r:Fact; r:gives {((3 2 1 3) "=<") list:sort (1 2 3 3)}] + [ a r:Fact; r:gives {((3 2 1 3) ">=") list:sort (3 3 2 1)}] + skolem:lemma4277 + skolem:lemma4278 + [ a r:Fact; r:gives {(3321 1233) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3213]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3213 a r:Inference; + r:gives { + 3214 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3214 math:notEqualTo 0}] + skolem:lemma5812 + [ a r:Fact; r:gives {((3 2 1 4) "=<") list:sort (1 2 3 4)}] + [ a r:Fact; r:gives {((3 2 1 4) ">=") list:sort (4 3 2 1)}] + skolem:lemma4280 + skolem:lemma4281 + [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3214]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 1 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3214 a r:Inference; + r:gives { + 3215 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3215 math:notEqualTo 0}] + skolem:lemma5813 + [ a r:Fact; r:gives {((3 2 1 5) "=<") list:sort (1 2 3 5)}] + [ a r:Fact; r:gives {((3 2 1 5) ">=") list:sort (5 3 2 1)}] + skolem:lemma4283 + skolem:lemma4284 + [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3215]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 1 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3215 a r:Inference; + r:gives { + 3216 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3216 math:notEqualTo 0}] + skolem:lemma5814 + [ a r:Fact; r:gives {((3 2 1 6) "=<") list:sort (1 2 3 6)}] + [ a r:Fact; r:gives {((3 2 1 6) ">=") list:sort (6 3 2 1)}] + skolem:lemma4286 + skolem:lemma4287 + [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3216]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 1 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3216 a r:Inference; + r:gives { + 3217 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3217 math:notEqualTo 0}] + skolem:lemma5815 + [ a r:Fact; r:gives {((3 2 1 7) "=<") list:sort (1 2 3 7)}] + [ a r:Fact; r:gives {((3 2 1 7) ">=") list:sort (7 3 2 1)}] + skolem:lemma4289 + skolem:lemma4290 + [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3217]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 1 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3217 a r:Inference; + r:gives { + 3218 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3218 math:notEqualTo 0}] + skolem:lemma5816 + [ a r:Fact; r:gives {((3 2 1 8) "=<") list:sort (1 2 3 8)}] + [ a r:Fact; r:gives {((3 2 1 8) ">=") list:sort (8 3 2 1)}] + skolem:lemma4292 + skolem:lemma4293 + [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3218]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 1 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3218 a r:Inference; + r:gives { + 3219 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3219 math:notEqualTo 0}] + skolem:lemma5817 + [ a r:Fact; r:gives {((3 2 1 9) "=<") list:sort (1 2 3 9)}] + [ a r:Fact; r:gives {((3 2 1 9) ">=") list:sort (9 3 2 1)}] + skolem:lemma4295 + skolem:lemma4296 + [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3219]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 1 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3219 a r:Inference; + r:gives { + 3220 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3220 math:notEqualTo 0}] + skolem:lemma5818 + [ a r:Fact; r:gives {((3 2 2 0) "=<") list:sort (0 2 2 3)}] + [ a r:Fact; r:gives {((3 2 2 0) ">=") list:sort (3 2 2 0)}] + skolem:lemma4063 + skolem:lemma4064 + [ a r:Fact; r:gives {(3220 223) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3220 a r:Inference; + r:gives { + 3221 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3221 math:notEqualTo 0}] + skolem:lemma5819 + [ a r:Fact; r:gives {((3 2 2 1) "=<") list:sort (1 2 2 3)}] + [ a r:Fact; r:gives {((3 2 2 1) ">=") list:sort (3 2 2 1)}] + skolem:lemma4253 + skolem:lemma4254 + [ a r:Fact; r:gives {(3221 1223) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3221 a r:Inference; + r:gives { + 3222 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3222 math:notEqualTo 0}] + skolem:lemma5820 + [ a r:Fact; r:gives {((3 2 2 2) "=<") list:sort (2 2 2 3)}] + [ a r:Fact; r:gives {((3 2 2 2) ">=") list:sort (3 2 2 2)}] + skolem:lemma4422 + skolem:lemma4423 + [ a r:Fact; r:gives {(3222 2223) math:difference 999}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 999 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 999 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 2 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3222 a r:Inference; + r:gives { + 3223 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3223 math:notEqualTo 0}] + skolem:lemma5821 + [ a r:Fact; r:gives {((3 2 2 3) "=<") list:sort (2 2 3 3)}] + [ a r:Fact; r:gives {((3 2 2 3) ">=") list:sort (3 3 2 2)}] + skolem:lemma4446 + skolem:lemma4447 + [ a r:Fact; r:gives {(3322 2233) math:difference 1089}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1089 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1089 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1089]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3223 a r:Inference; + r:gives { + 3224 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3224 math:notEqualTo 0}] + skolem:lemma5822 + [ a r:Fact; r:gives {((3 2 2 4) "=<") list:sort (2 2 3 4)}] + [ a r:Fact; r:gives {((3 2 2 4) ">=") list:sort (4 3 2 2)}] + skolem:lemma4449 + skolem:lemma4450 + [ a r:Fact; r:gives {(4322 2234) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3224 a r:Inference; + r:gives { + 3225 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3225 math:notEqualTo 0}] + skolem:lemma5823 + [ a r:Fact; r:gives {((3 2 2 5) "=<") list:sort (2 2 3 5)}] + [ a r:Fact; r:gives {((3 2 2 5) ">=") list:sort (5 3 2 2)}] + skolem:lemma4452 + skolem:lemma4453 + [ a r:Fact; r:gives {(5322 2235) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3225 a r:Inference; + r:gives { + 3226 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3226 math:notEqualTo 0}] + skolem:lemma5824 + [ a r:Fact; r:gives {((3 2 2 6) "=<") list:sort (2 2 3 6)}] + [ a r:Fact; r:gives {((3 2 2 6) ">=") list:sort (6 3 2 2)}] + skolem:lemma4455 + skolem:lemma4456 + [ a r:Fact; r:gives {(6322 2236) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3226 a r:Inference; + r:gives { + 3227 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3227 math:notEqualTo 0}] + skolem:lemma5825 + [ a r:Fact; r:gives {((3 2 2 7) "=<") list:sort (2 2 3 7)}] + [ a r:Fact; r:gives {((3 2 2 7) ">=") list:sort (7 3 2 2)}] + skolem:lemma4458 + skolem:lemma4459 + [ a r:Fact; r:gives {(7322 2237) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3227 a r:Inference; + r:gives { + 3228 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3228 math:notEqualTo 0}] + skolem:lemma5826 + [ a r:Fact; r:gives {((3 2 2 8) "=<") list:sort (2 2 3 8)}] + [ a r:Fact; r:gives {((3 2 2 8) ">=") list:sort (8 3 2 2)}] + skolem:lemma4461 + skolem:lemma4462 + [ a r:Fact; r:gives {(8322 2238) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3228 a r:Inference; + r:gives { + 3229 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3229 math:notEqualTo 0}] + skolem:lemma5827 + [ a r:Fact; r:gives {((3 2 2 9) "=<") list:sort (2 2 3 9)}] + [ a r:Fact; r:gives {((3 2 2 9) ">=") list:sort (9 3 2 2)}] + skolem:lemma4464 + skolem:lemma4465 + [ a r:Fact; r:gives {(9322 2239) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3229 a r:Inference; + r:gives { + 3230 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3230 math:notEqualTo 0}] + skolem:lemma5828 + [ a r:Fact; r:gives {((3 2 3 0) "=<") list:sort (0 2 3 3)}] + [ a r:Fact; r:gives {((3 2 3 0) ">=") list:sort (3 3 2 0)}] + skolem:lemma4087 + skolem:lemma4088 + [ a r:Fact; r:gives {(3320 233) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3230]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3230 a r:Inference; + r:gives { + 3231 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3231 math:notEqualTo 0}] + skolem:lemma5829 + [ a r:Fact; r:gives {((3 2 3 1) "=<") list:sort (1 2 3 3)}] + [ a r:Fact; r:gives {((3 2 3 1) ">=") list:sort (3 3 2 1)}] + skolem:lemma4277 + skolem:lemma4278 + [ a r:Fact; r:gives {(3321 1233) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3231]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3231 a r:Inference; + r:gives { + 3232 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3232 math:notEqualTo 0}] + skolem:lemma5830 + [ a r:Fact; r:gives {((3 2 3 2) "=<") list:sort (2 2 3 3)}] + [ a r:Fact; r:gives {((3 2 3 2) ">=") list:sort (3 3 2 2)}] + skolem:lemma4446 + skolem:lemma4447 + [ a r:Fact; r:gives {(3322 2233) math:difference 1089}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1089 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1089 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3232]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1089]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3232 a r:Inference; + r:gives { + 3233 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3233 math:notEqualTo 0}] + skolem:lemma5831 + [ a r:Fact; r:gives {((3 2 3 3) "=<") list:sort (2 3 3 3)}] + [ a r:Fact; r:gives {((3 2 3 3) ">=") list:sort (3 3 3 2)}] + skolem:lemma4602 + skolem:lemma4603 + [ a r:Fact; r:gives {(3332 2333) math:difference 999}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 999 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 999 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3233 a r:Inference; + r:gives { + 3234 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3234 math:notEqualTo 0}] + skolem:lemma5832 + [ a r:Fact; r:gives {((3 2 3 4) "=<") list:sort (2 3 3 4)}] + [ a r:Fact; r:gives {((3 2 3 4) ">=") list:sort (4 3 3 2)}] + skolem:lemma4605 + skolem:lemma4606 + [ a r:Fact; r:gives {(4332 2334) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3234 a r:Inference; + r:gives { + 3235 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3235 math:notEqualTo 0}] + skolem:lemma5833 + [ a r:Fact; r:gives {((3 2 3 5) "=<") list:sort (2 3 3 5)}] + [ a r:Fact; r:gives {((3 2 3 5) ">=") list:sort (5 3 3 2)}] + skolem:lemma4608 + skolem:lemma4609 + [ a r:Fact; r:gives {(5332 2335) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3235 a r:Inference; + r:gives { + 3236 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3236 math:notEqualTo 0}] + skolem:lemma5834 + [ a r:Fact; r:gives {((3 2 3 6) "=<") list:sort (2 3 3 6)}] + [ a r:Fact; r:gives {((3 2 3 6) ">=") list:sort (6 3 3 2)}] + skolem:lemma4611 + skolem:lemma4612 + [ a r:Fact; r:gives {(6332 2336) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3236 a r:Inference; + r:gives { + 3237 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3237 math:notEqualTo 0}] + skolem:lemma5835 + [ a r:Fact; r:gives {((3 2 3 7) "=<") list:sort (2 3 3 7)}] + [ a r:Fact; r:gives {((3 2 3 7) ">=") list:sort (7 3 3 2)}] + skolem:lemma4614 + skolem:lemma4615 + [ a r:Fact; r:gives {(7332 2337) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3237 a r:Inference; + r:gives { + 3238 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3238 math:notEqualTo 0}] + skolem:lemma5836 + [ a r:Fact; r:gives {((3 2 3 8) "=<") list:sort (2 3 3 8)}] + [ a r:Fact; r:gives {((3 2 3 8) ">=") list:sort (8 3 3 2)}] + skolem:lemma4617 + skolem:lemma4618 + [ a r:Fact; r:gives {(8332 2338) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3238 a r:Inference; + r:gives { + 3239 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3239 math:notEqualTo 0}] + skolem:lemma5837 + [ a r:Fact; r:gives {((3 2 3 9) "=<") list:sort (2 3 3 9)}] + [ a r:Fact; r:gives {((3 2 3 9) ">=") list:sort (9 3 3 2)}] + skolem:lemma4620 + skolem:lemma4621 + [ a r:Fact; r:gives {(9332 2339) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3239 a r:Inference; + r:gives { + 3240 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3240 math:notEqualTo 0}] + skolem:lemma5838 + [ a r:Fact; r:gives {((3 2 4 0) "=<") list:sort (0 2 3 4)}] + [ a r:Fact; r:gives {((3 2 4 0) ">=") list:sort (4 3 2 0)}] + skolem:lemma4090 + skolem:lemma4091 + [ a r:Fact; r:gives {(4320 234) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3240]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 4 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3240 a r:Inference; + r:gives { + 3241 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3241 math:notEqualTo 0}] + skolem:lemma5839 + [ a r:Fact; r:gives {((3 2 4 1) "=<") list:sort (1 2 3 4)}] + [ a r:Fact; r:gives {((3 2 4 1) ">=") list:sort (4 3 2 1)}] + skolem:lemma4280 + skolem:lemma4281 + [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3241]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 4 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3241 a r:Inference; + r:gives { + 3242 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3242 math:notEqualTo 0}] + skolem:lemma5840 + [ a r:Fact; r:gives {((3 2 4 2) "=<") list:sort (2 2 3 4)}] + [ a r:Fact; r:gives {((3 2 4 2) ">=") list:sort (4 3 2 2)}] + skolem:lemma4449 + skolem:lemma4450 + [ a r:Fact; r:gives {(4322 2234) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3242]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3242 a r:Inference; + r:gives { + 3243 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3243 math:notEqualTo 0}] + skolem:lemma5841 + [ a r:Fact; r:gives {((3 2 4 3) "=<") list:sort (2 3 3 4)}] + [ a r:Fact; r:gives {((3 2 4 3) ">=") list:sort (4 3 3 2)}] + skolem:lemma4605 + skolem:lemma4606 + [ a r:Fact; r:gives {(4332 2334) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3243]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3243 a r:Inference; + r:gives { + 3244 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3244 math:notEqualTo 0}] + skolem:lemma5842 + [ a r:Fact; r:gives {((3 2 4 4) "=<") list:sort (2 3 4 4)}] + [ a r:Fact; r:gives {((3 2 4 4) ">=") list:sort (4 4 3 2)}] + skolem:lemma4627 + skolem:lemma4628 + [ a r:Fact; r:gives {(4432 2344) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3244 a r:Inference; + r:gives { + 3245 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3245 math:notEqualTo 0}] + skolem:lemma5843 + [ a r:Fact; r:gives {((3 2 4 5) "=<") list:sort (2 3 4 5)}] + [ a r:Fact; r:gives {((3 2 4 5) ">=") list:sort (5 4 3 2)}] + skolem:lemma4630 + skolem:lemma4631 + [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3245 a r:Inference; + r:gives { + 3246 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3246 math:notEqualTo 0}] + skolem:lemma5844 + [ a r:Fact; r:gives {((3 2 4 6) "=<") list:sort (2 3 4 6)}] + [ a r:Fact; r:gives {((3 2 4 6) ">=") list:sort (6 4 3 2)}] + skolem:lemma4633 + skolem:lemma4634 + [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3246 a r:Inference; + r:gives { + 3247 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3247 math:notEqualTo 0}] + skolem:lemma5845 + [ a r:Fact; r:gives {((3 2 4 7) "=<") list:sort (2 3 4 7)}] + [ a r:Fact; r:gives {((3 2 4 7) ">=") list:sort (7 4 3 2)}] + skolem:lemma4636 + skolem:lemma4637 + [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3247 a r:Inference; + r:gives { + 3248 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3248 math:notEqualTo 0}] + skolem:lemma5846 + [ a r:Fact; r:gives {((3 2 4 8) "=<") list:sort (2 3 4 8)}] + [ a r:Fact; r:gives {((3 2 4 8) ">=") list:sort (8 4 3 2)}] + skolem:lemma4639 + skolem:lemma4640 + [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3248 a r:Inference; + r:gives { + 3249 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3249 math:notEqualTo 0}] + skolem:lemma5847 + [ a r:Fact; r:gives {((3 2 4 9) "=<") list:sort (2 3 4 9)}] + [ a r:Fact; r:gives {((3 2 4 9) ">=") list:sort (9 4 3 2)}] + skolem:lemma4642 + skolem:lemma4643 + [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3249 a r:Inference; + r:gives { + 3250 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3250 math:notEqualTo 0}] + skolem:lemma5848 + [ a r:Fact; r:gives {((3 2 5 0) "=<") list:sort (0 2 3 5)}] + [ a r:Fact; r:gives {((3 2 5 0) ">=") list:sort (5 3 2 0)}] + skolem:lemma4093 + skolem:lemma4094 + [ a r:Fact; r:gives {(5320 235) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3250]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 5 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3250 a r:Inference; + r:gives { + 3251 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3251 math:notEqualTo 0}] + skolem:lemma5849 + [ a r:Fact; r:gives {((3 2 5 1) "=<") list:sort (1 2 3 5)}] + [ a r:Fact; r:gives {((3 2 5 1) ">=") list:sort (5 3 2 1)}] + skolem:lemma4283 + skolem:lemma4284 + [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3251]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 5 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3251 a r:Inference; + r:gives { + 3252 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3252 math:notEqualTo 0}] + skolem:lemma5850 + [ a r:Fact; r:gives {((3 2 5 2) "=<") list:sort (2 2 3 5)}] + [ a r:Fact; r:gives {((3 2 5 2) ">=") list:sort (5 3 2 2)}] + skolem:lemma4452 + skolem:lemma4453 + [ a r:Fact; r:gives {(5322 2235) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3252]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3252 a r:Inference; + r:gives { + 3253 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3253 math:notEqualTo 0}] + skolem:lemma5851 + [ a r:Fact; r:gives {((3 2 5 3) "=<") list:sort (2 3 3 5)}] + [ a r:Fact; r:gives {((3 2 5 3) ">=") list:sort (5 3 3 2)}] + skolem:lemma4608 + skolem:lemma4609 + [ a r:Fact; r:gives {(5332 2335) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3253]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3253 a r:Inference; + r:gives { + 3254 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3254 math:notEqualTo 0}] + skolem:lemma5852 + [ a r:Fact; r:gives {((3 2 5 4) "=<") list:sort (2 3 4 5)}] + [ a r:Fact; r:gives {((3 2 5 4) ">=") list:sort (5 4 3 2)}] + skolem:lemma4630 + skolem:lemma4631 + [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3254]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 5 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3254 a r:Inference; + r:gives { + 3255 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3255 math:notEqualTo 0}] + skolem:lemma5853 + [ a r:Fact; r:gives {((3 2 5 5) "=<") list:sort (2 3 5 5)}] + [ a r:Fact; r:gives {((3 2 5 5) ">=") list:sort (5 5 3 2)}] + skolem:lemma4650 + skolem:lemma4651 + [ a r:Fact; r:gives {(5532 2355) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3255 a r:Inference; + r:gives { + 3256 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3256 math:notEqualTo 0}] + skolem:lemma5854 + [ a r:Fact; r:gives {((3 2 5 6) "=<") list:sort (2 3 5 6)}] + [ a r:Fact; r:gives {((3 2 5 6) ">=") list:sort (6 5 3 2)}] + skolem:lemma4653 + skolem:lemma4654 + [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3256 a r:Inference; + r:gives { + 3257 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3257 math:notEqualTo 0}] + skolem:lemma5855 + [ a r:Fact; r:gives {((3 2 5 7) "=<") list:sort (2 3 5 7)}] + [ a r:Fact; r:gives {((3 2 5 7) ">=") list:sort (7 5 3 2)}] + skolem:lemma4656 + skolem:lemma4657 + [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3257 a r:Inference; + r:gives { + 3258 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3258 math:notEqualTo 0}] + skolem:lemma5856 + [ a r:Fact; r:gives {((3 2 5 8) "=<") list:sort (2 3 5 8)}] + [ a r:Fact; r:gives {((3 2 5 8) ">=") list:sort (8 5 3 2)}] + skolem:lemma4659 + skolem:lemma4660 + [ a r:Fact; r:gives {(8532 2358) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3258 a r:Inference; + r:gives { + 3259 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3259 math:notEqualTo 0}] + skolem:lemma5857 + [ a r:Fact; r:gives {((3 2 5 9) "=<") list:sort (2 3 5 9)}] + [ a r:Fact; r:gives {((3 2 5 9) ">=") list:sort (9 5 3 2)}] + skolem:lemma4662 + skolem:lemma4663 + [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3259 a r:Inference; + r:gives { + 3260 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3260 math:notEqualTo 0}] + skolem:lemma5858 + [ a r:Fact; r:gives {((3 2 6 0) "=<") list:sort (0 2 3 6)}] + [ a r:Fact; r:gives {((3 2 6 0) ">=") list:sort (6 3 2 0)}] + skolem:lemma4096 + skolem:lemma4097 + [ a r:Fact; r:gives {(6320 236) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3260]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 6 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3260 a r:Inference; + r:gives { + 3261 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3261 math:notEqualTo 0}] + skolem:lemma5859 + [ a r:Fact; r:gives {((3 2 6 1) "=<") list:sort (1 2 3 6)}] + [ a r:Fact; r:gives {((3 2 6 1) ">=") list:sort (6 3 2 1)}] + skolem:lemma4286 + skolem:lemma4287 + [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3261]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 6 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3261 a r:Inference; + r:gives { + 3262 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3262 math:notEqualTo 0}] + skolem:lemma5860 + [ a r:Fact; r:gives {((3 2 6 2) "=<") list:sort (2 2 3 6)}] + [ a r:Fact; r:gives {((3 2 6 2) ">=") list:sort (6 3 2 2)}] + skolem:lemma4455 + skolem:lemma4456 + [ a r:Fact; r:gives {(6322 2236) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3262 a r:Inference; + r:gives { + 3263 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3263 math:notEqualTo 0}] + skolem:lemma5861 + [ a r:Fact; r:gives {((3 2 6 3) "=<") list:sort (2 3 3 6)}] + [ a r:Fact; r:gives {((3 2 6 3) ">=") list:sort (6 3 3 2)}] + skolem:lemma4611 + skolem:lemma4612 + [ a r:Fact; r:gives {(6332 2336) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3263 a r:Inference; + r:gives { + 3264 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3264 math:notEqualTo 0}] + skolem:lemma5862 + [ a r:Fact; r:gives {((3 2 6 4) "=<") list:sort (2 3 4 6)}] + [ a r:Fact; r:gives {((3 2 6 4) ">=") list:sort (6 4 3 2)}] + skolem:lemma4633 + skolem:lemma4634 + [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 6 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3264 a r:Inference; + r:gives { + 3265 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3265 math:notEqualTo 0}] + skolem:lemma5863 + [ a r:Fact; r:gives {((3 2 6 5) "=<") list:sort (2 3 5 6)}] + [ a r:Fact; r:gives {((3 2 6 5) ">=") list:sort (6 5 3 2)}] + skolem:lemma4653 + skolem:lemma4654 + [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 6 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3265 a r:Inference; + r:gives { + 3266 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3266 math:notEqualTo 0}] + skolem:lemma5864 + [ a r:Fact; r:gives {((3 2 6 6) "=<") list:sort (2 3 6 6)}] + [ a r:Fact; r:gives {((3 2 6 6) ">=") list:sort (6 6 3 2)}] + skolem:lemma4671 + skolem:lemma4672 + [ a r:Fact; r:gives {(6632 2366) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3266 a r:Inference; + r:gives { + 3267 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3267 math:notEqualTo 0}] + skolem:lemma5865 + [ a r:Fact; r:gives {((3 2 6 7) "=<") list:sort (2 3 6 7)}] + [ a r:Fact; r:gives {((3 2 6 7) ">=") list:sort (7 6 3 2)}] + skolem:lemma4674 + skolem:lemma4675 + [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3267 a r:Inference; + r:gives { + 3268 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3268 math:notEqualTo 0}] + skolem:lemma5866 + [ a r:Fact; r:gives {((3 2 6 8) "=<") list:sort (2 3 6 8)}] + [ a r:Fact; r:gives {((3 2 6 8) ">=") list:sort (8 6 3 2)}] + skolem:lemma4677 + skolem:lemma4678 + [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3268 a r:Inference; + r:gives { + 3269 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3269 math:notEqualTo 0}] + skolem:lemma5867 + [ a r:Fact; r:gives {((3 2 6 9) "=<") list:sort (2 3 6 9)}] + [ a r:Fact; r:gives {((3 2 6 9) ">=") list:sort (9 6 3 2)}] + skolem:lemma4680 + skolem:lemma4681 + [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3269 a r:Inference; + r:gives { + 3270 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3270 math:notEqualTo 0}] + skolem:lemma5868 + [ a r:Fact; r:gives {((3 2 7 0) "=<") list:sort (0 2 3 7)}] + [ a r:Fact; r:gives {((3 2 7 0) ">=") list:sort (7 3 2 0)}] + skolem:lemma4099 + skolem:lemma4100 + [ a r:Fact; r:gives {(7320 237) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3270]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 7 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3270 a r:Inference; + r:gives { + 3271 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3271 math:notEqualTo 0}] + skolem:lemma5869 + [ a r:Fact; r:gives {((3 2 7 1) "=<") list:sort (1 2 3 7)}] + [ a r:Fact; r:gives {((3 2 7 1) ">=") list:sort (7 3 2 1)}] + skolem:lemma4289 + skolem:lemma4290 + [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3271]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 7 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3271 a r:Inference; + r:gives { + 3272 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3272 math:notEqualTo 0}] + skolem:lemma5870 + [ a r:Fact; r:gives {((3 2 7 2) "=<") list:sort (2 2 3 7)}] + [ a r:Fact; r:gives {((3 2 7 2) ">=") list:sort (7 3 2 2)}] + skolem:lemma4458 + skolem:lemma4459 + [ a r:Fact; r:gives {(7322 2237) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3272]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3272 a r:Inference; + r:gives { + 3273 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3273 math:notEqualTo 0}] + skolem:lemma5871 + [ a r:Fact; r:gives {((3 2 7 3) "=<") list:sort (2 3 3 7)}] + [ a r:Fact; r:gives {((3 2 7 3) ">=") list:sort (7 3 3 2)}] + skolem:lemma4614 + skolem:lemma4615 + [ a r:Fact; r:gives {(7332 2337) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3273]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3273 a r:Inference; + r:gives { + 3274 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3274 math:notEqualTo 0}] + skolem:lemma5872 + [ a r:Fact; r:gives {((3 2 7 4) "=<") list:sort (2 3 4 7)}] + [ a r:Fact; r:gives {((3 2 7 4) ">=") list:sort (7 4 3 2)}] + skolem:lemma4636 + skolem:lemma4637 + [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3274]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 7 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3274 a r:Inference; + r:gives { + 3275 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3275 math:notEqualTo 0}] + skolem:lemma5873 + [ a r:Fact; r:gives {((3 2 7 5) "=<") list:sort (2 3 5 7)}] + [ a r:Fact; r:gives {((3 2 7 5) ">=") list:sort (7 5 3 2)}] + skolem:lemma4656 + skolem:lemma4657 + [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3275]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 7 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3275 a r:Inference; + r:gives { + 3276 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3276 math:notEqualTo 0}] + skolem:lemma5874 + [ a r:Fact; r:gives {((3 2 7 6) "=<") list:sort (2 3 6 7)}] + [ a r:Fact; r:gives {((3 2 7 6) ">=") list:sort (7 6 3 2)}] + skolem:lemma4674 + skolem:lemma4675 + [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3276]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 7 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3276 a r:Inference; + r:gives { + 3277 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3277 math:notEqualTo 0}] + skolem:lemma5875 + [ a r:Fact; r:gives {((3 2 7 7) "=<") list:sort (2 3 7 7)}] + [ a r:Fact; r:gives {((3 2 7 7) ">=") list:sort (7 7 3 2)}] + skolem:lemma4690 + skolem:lemma4691 + [ a r:Fact; r:gives {(7732 2377) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3277]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3277 a r:Inference; + r:gives { + 3278 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3278 math:notEqualTo 0}] + skolem:lemma5876 + [ a r:Fact; r:gives {((3 2 7 8) "=<") list:sort (2 3 7 8)}] + [ a r:Fact; r:gives {((3 2 7 8) ">=") list:sort (8 7 3 2)}] + skolem:lemma4693 + skolem:lemma4694 + [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3278 a r:Inference; + r:gives { + 3279 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3279 math:notEqualTo 0}] + skolem:lemma5877 + [ a r:Fact; r:gives {((3 2 7 9) "=<") list:sort (2 3 7 9)}] + [ a r:Fact; r:gives {((3 2 7 9) ">=") list:sort (9 7 3 2)}] + skolem:lemma4696 + skolem:lemma4697 + [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3279 a r:Inference; + r:gives { + 3280 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3280 math:notEqualTo 0}] + skolem:lemma5878 + [ a r:Fact; r:gives {((3 2 8 0) "=<") list:sort (0 2 3 8)}] + [ a r:Fact; r:gives {((3 2 8 0) ">=") list:sort (8 3 2 0)}] + skolem:lemma4102 + skolem:lemma4103 + [ a r:Fact; r:gives {(8320 238) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3280]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 8 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3280 a r:Inference; + r:gives { + 3281 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3281 math:notEqualTo 0}] + skolem:lemma5879 + [ a r:Fact; r:gives {((3 2 8 1) "=<") list:sort (1 2 3 8)}] + [ a r:Fact; r:gives {((3 2 8 1) ">=") list:sort (8 3 2 1)}] + skolem:lemma4292 + skolem:lemma4293 + [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3281]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 8 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3281 a r:Inference; + r:gives { + 3282 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3282 math:notEqualTo 0}] + skolem:lemma5880 + [ a r:Fact; r:gives {((3 2 8 2) "=<") list:sort (2 2 3 8)}] + [ a r:Fact; r:gives {((3 2 8 2) ">=") list:sort (8 3 2 2)}] + skolem:lemma4461 + skolem:lemma4462 + [ a r:Fact; r:gives {(8322 2238) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3282]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3282 a r:Inference; + r:gives { + 3283 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3283 math:notEqualTo 0}] + skolem:lemma5881 + [ a r:Fact; r:gives {((3 2 8 3) "=<") list:sort (2 3 3 8)}] + [ a r:Fact; r:gives {((3 2 8 3) ">=") list:sort (8 3 3 2)}] + skolem:lemma4617 + skolem:lemma4618 + [ a r:Fact; r:gives {(8332 2338) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3283]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3283 a r:Inference; + r:gives { + 3284 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3284 math:notEqualTo 0}] + skolem:lemma5882 + [ a r:Fact; r:gives {((3 2 8 4) "=<") list:sort (2 3 4 8)}] + [ a r:Fact; r:gives {((3 2 8 4) ">=") list:sort (8 4 3 2)}] + skolem:lemma4639 + skolem:lemma4640 + [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3284]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 8 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3284 a r:Inference; + r:gives { + 3285 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3285 math:notEqualTo 0}] + skolem:lemma5883 + [ a r:Fact; r:gives {((3 2 8 5) "=<") list:sort (2 3 5 8)}] + [ a r:Fact; r:gives {((3 2 8 5) ">=") list:sort (8 5 3 2)}] + skolem:lemma4659 + skolem:lemma4660 + [ a r:Fact; r:gives {(8532 2358) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3285]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 8 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3285 a r:Inference; + r:gives { + 3286 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3286 math:notEqualTo 0}] + skolem:lemma5884 + [ a r:Fact; r:gives {((3 2 8 6) "=<") list:sort (2 3 6 8)}] + [ a r:Fact; r:gives {((3 2 8 6) ">=") list:sort (8 6 3 2)}] + skolem:lemma4677 + skolem:lemma4678 + [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3286]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 8 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3286 a r:Inference; + r:gives { + 3287 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3287 math:notEqualTo 0}] + skolem:lemma5885 + [ a r:Fact; r:gives {((3 2 8 7) "=<") list:sort (2 3 7 8)}] + [ a r:Fact; r:gives {((3 2 8 7) ">=") list:sort (8 7 3 2)}] + skolem:lemma4693 + skolem:lemma4694 + [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3287]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 8 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3287 a r:Inference; + r:gives { + 3288 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3288 math:notEqualTo 0}] + skolem:lemma5886 + [ a r:Fact; r:gives {((3 2 8 8) "=<") list:sort (2 3 8 8)}] + [ a r:Fact; r:gives {((3 2 8 8) ">=") list:sort (8 8 3 2)}] + skolem:lemma4707 + skolem:lemma4708 + [ a r:Fact; r:gives {(8832 2388) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3288]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3288 a r:Inference; + r:gives { + 3289 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3289 math:notEqualTo 0}] + skolem:lemma5887 + [ a r:Fact; r:gives {((3 2 8 9) "=<") list:sort (2 3 8 9)}] + [ a r:Fact; r:gives {((3 2 8 9) ">=") list:sort (9 8 3 2)}] + skolem:lemma4710 + skolem:lemma4711 + [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3289 a r:Inference; + r:gives { + 3290 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3290 math:notEqualTo 0}] + skolem:lemma5888 + [ a r:Fact; r:gives {((3 2 9 0) "=<") list:sort (0 2 3 9)}] + [ a r:Fact; r:gives {((3 2 9 0) ">=") list:sort (9 3 2 0)}] + skolem:lemma4105 + skolem:lemma4106 + [ a r:Fact; r:gives {(9320 239) math:difference 9081}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9081 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 9081 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3290]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 9 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3290 a r:Inference; + r:gives { + 3291 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3291 math:notEqualTo 0}] + skolem:lemma5889 + [ a r:Fact; r:gives {((3 2 9 1) "=<") list:sort (1 2 3 9)}] + [ a r:Fact; r:gives {((3 2 9 1) ">=") list:sort (9 3 2 1)}] + skolem:lemma4295 + skolem:lemma4296 + [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3291]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 9 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3291 a r:Inference; + r:gives { + 3292 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3292 math:notEqualTo 0}] + skolem:lemma5890 + [ a r:Fact; r:gives {((3 2 9 2) "=<") list:sort (2 2 3 9)}] + [ a r:Fact; r:gives {((3 2 9 2) ">=") list:sort (9 3 2 2)}] + skolem:lemma4464 + skolem:lemma4465 + [ a r:Fact; r:gives {(9322 2239) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3292]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 9 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3292 a r:Inference; + r:gives { + 3293 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3293 math:notEqualTo 0}] + skolem:lemma5891 + [ a r:Fact; r:gives {((3 2 9 3) "=<") list:sort (2 3 3 9)}] + [ a r:Fact; r:gives {((3 2 9 3) ">=") list:sort (9 3 3 2)}] + skolem:lemma4620 + skolem:lemma4621 + [ a r:Fact; r:gives {(9332 2339) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3293]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 9 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3293 a r:Inference; + r:gives { + 3294 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3294 math:notEqualTo 0}] + skolem:lemma5892 + [ a r:Fact; r:gives {((3 2 9 4) "=<") list:sort (2 3 4 9)}] + [ a r:Fact; r:gives {((3 2 9 4) ">=") list:sort (9 4 3 2)}] + skolem:lemma4642 + skolem:lemma4643 + [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3294]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 9 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3294 a r:Inference; + r:gives { + 3295 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3295 math:notEqualTo 0}] + skolem:lemma5893 + [ a r:Fact; r:gives {((3 2 9 5) "=<") list:sort (2 3 5 9)}] + [ a r:Fact; r:gives {((3 2 9 5) ">=") list:sort (9 5 3 2)}] + skolem:lemma4662 + skolem:lemma4663 + [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3295]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 9 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3295 a r:Inference; + r:gives { + 3296 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3296 math:notEqualTo 0}] + skolem:lemma5894 + [ a r:Fact; r:gives {((3 2 9 6) "=<") list:sort (2 3 6 9)}] + [ a r:Fact; r:gives {((3 2 9 6) ">=") list:sort (9 6 3 2)}] + skolem:lemma4680 + skolem:lemma4681 + [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3296]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 9 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3296 a r:Inference; + r:gives { + 3297 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3297 math:notEqualTo 0}] + skolem:lemma5895 + [ a r:Fact; r:gives {((3 2 9 7) "=<") list:sort (2 3 7 9)}] + [ a r:Fact; r:gives {((3 2 9 7) ">=") list:sort (9 7 3 2)}] + skolem:lemma4696 + skolem:lemma4697 + [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3297]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 9 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3297 a r:Inference; + r:gives { + 3298 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3298 math:notEqualTo 0}] + skolem:lemma5896 + [ a r:Fact; r:gives {((3 2 9 8) "=<") list:sort (2 3 8 9)}] + [ a r:Fact; r:gives {((3 2 9 8) ">=") list:sort (9 8 3 2)}] + skolem:lemma4710 + skolem:lemma4711 + [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3298]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 9 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3298 a r:Inference; + r:gives { + 3299 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3299 math:notEqualTo 0}] + skolem:lemma5897 + [ a r:Fact; r:gives {((3 2 9 9) "=<") list:sort (2 3 9 9)}] + [ a r:Fact; r:gives {((3 2 9 9) ">=") list:sort (9 9 3 2)}] + skolem:lemma4722 + skolem:lemma4723 + [ a r:Fact; r:gives {(9932 2399) math:difference 7533}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7533 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7533 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 2 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9932]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3299 a r:Inference; + r:gives { + 3300 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3300 math:notEqualTo 0}] + skolem:lemma5898 + [ a r:Fact; r:gives {((3 3 0 0) "=<") list:sort (0 0 3 3)}] + [ a r:Fact; r:gives {((3 3 0 0) ">=") list:sort (3 3 0 0)}] + skolem:lemma5444 + skolem:lemma5445 + [ a r:Fact; r:gives {(3300 33) math:difference 3267}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3267 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 3267 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 33]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3300 a r:Inference; + r:gives { + 3301 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3301 math:notEqualTo 0}] + skolem:lemma5899 + [ a r:Fact; r:gives {((3 3 0 1) "=<") list:sort (0 1 3 3)}] + [ a r:Fact; r:gives {((3 3 0 1) ">=") list:sort (3 3 1 0)}] + skolem:lemma5470 + skolem:lemma5471 + [ a r:Fact; r:gives {(3310 133) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3301]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 0 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 133]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3301 a r:Inference; + r:gives { + 3302 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3302 math:notEqualTo 0}] + skolem:lemma5900 + [ a r:Fact; r:gives {((3 3 0 2) "=<") list:sort (0 2 3 3)}] + [ a r:Fact; r:gives {((3 3 0 2) ">=") list:sort (3 3 2 0)}] + skolem:lemma4087 + skolem:lemma4088 + [ a r:Fact; r:gives {(3320 233) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3302]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 0 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3302 a r:Inference; + r:gives { + 3303 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3303 math:notEqualTo 0}] + skolem:lemma5901 + [ a r:Fact; r:gives {((3 3 0 3) "=<") list:sort (0 3 3 3)}] + [ a r:Fact; r:gives {((3 3 0 3) ">=") list:sort (3 3 3 0)}] + skolem:lemma5504 + skolem:lemma5505 + [ a r:Fact; r:gives {(3330 333) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3303]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 0 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3303 a r:Inference; + r:gives { + 3304 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3304 math:notEqualTo 0}] + skolem:lemma5902 + [ a r:Fact; r:gives {((3 3 0 4) "=<") list:sort (0 3 3 4)}] + [ a r:Fact; r:gives {((3 3 0 4) ">=") list:sort (4 3 3 0)}] + skolem:lemma5507 + skolem:lemma5508 + [ a r:Fact; r:gives {(4330 334) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3304]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 0 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3304 a r:Inference; + r:gives { + 3305 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3305 math:notEqualTo 0}] + skolem:lemma5903 + [ a r:Fact; r:gives {((3 3 0 5) "=<") list:sort (0 3 3 5)}] + [ a r:Fact; r:gives {((3 3 0 5) ">=") list:sort (5 3 3 0)}] + skolem:lemma5510 + skolem:lemma5511 + [ a r:Fact; r:gives {(5330 335) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3305]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 0 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3305 a r:Inference; + r:gives { + 3306 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3306 math:notEqualTo 0}] + skolem:lemma5904 + [ a r:Fact; r:gives {((3 3 0 6) "=<") list:sort (0 3 3 6)}] + [ a r:Fact; r:gives {((3 3 0 6) ">=") list:sort (6 3 3 0)}] + skolem:lemma5513 + skolem:lemma5514 + [ a r:Fact; r:gives {(6330 336) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3306]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 0 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3306 a r:Inference; + r:gives { + 3307 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3307 math:notEqualTo 0}] + skolem:lemma5905 + [ a r:Fact; r:gives {((3 3 0 7) "=<") list:sort (0 3 3 7)}] + [ a r:Fact; r:gives {((3 3 0 7) ">=") list:sort (7 3 3 0)}] + skolem:lemma5516 + skolem:lemma5517 + [ a r:Fact; r:gives {(7330 337) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3307]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 0 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3307 a r:Inference; + r:gives { + 3308 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3308 math:notEqualTo 0}] + skolem:lemma5906 + [ a r:Fact; r:gives {((3 3 0 8) "=<") list:sort (0 3 3 8)}] + [ a r:Fact; r:gives {((3 3 0 8) ">=") list:sort (8 3 3 0)}] + skolem:lemma5519 + skolem:lemma5520 + [ a r:Fact; r:gives {(8330 338) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3308]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 0 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3308 a r:Inference; + r:gives { + 3309 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3309 math:notEqualTo 0}] + skolem:lemma5907 + [ a r:Fact; r:gives {((3 3 0 9) "=<") list:sort (0 3 3 9)}] + [ a r:Fact; r:gives {((3 3 0 9) ">=") list:sort (9 3 3 0)}] + skolem:lemma5522 + skolem:lemma5523 + [ a r:Fact; r:gives {(9330 339) math:difference 8991}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8991 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 8991 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3309]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 0 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8991]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3309 a r:Inference; + r:gives { + 3310 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3310 math:notEqualTo 0}] + skolem:lemma5908 + [ a r:Fact; r:gives {((3 3 1 0) "=<") list:sort (0 1 3 3)}] + [ a r:Fact; r:gives {((3 3 1 0) ">=") list:sort (3 3 1 0)}] + skolem:lemma5470 + skolem:lemma5471 + [ a r:Fact; r:gives {(3310 133) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 133]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3310 a r:Inference; + r:gives { + 3311 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3311 math:notEqualTo 0}] + skolem:lemma5909 + [ a r:Fact; r:gives {((3 3 1 1) "=<") list:sort (1 1 3 3)}] + [ a r:Fact; r:gives {((3 3 1 1) ">=") list:sort (3 3 1 1)}] + skolem:lemma5642 + skolem:lemma5643 + [ a r:Fact; r:gives {(3311 1133) math:difference 2178}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2178 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2178 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1133]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2178]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3311 a r:Inference; + r:gives { + 3312 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3312 math:notEqualTo 0}] + skolem:lemma5910 + [ a r:Fact; r:gives {((3 3 1 2) "=<") list:sort (1 2 3 3)}] + [ a r:Fact; r:gives {((3 3 1 2) ">=") list:sort (3 3 2 1)}] + skolem:lemma4277 + skolem:lemma4278 + [ a r:Fact; r:gives {(3321 1233) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3312]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3312 a r:Inference; + r:gives { + 3313 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3313 math:notEqualTo 0}] + skolem:lemma5911 + [ a r:Fact; r:gives {((3 3 1 3) "=<") list:sort (1 3 3 3)}] + [ a r:Fact; r:gives {((3 3 1 3) ">=") list:sort (3 3 3 1)}] + skolem:lemma5676 + skolem:lemma5677 + [ a r:Fact; r:gives {(3331 1333) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3313]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3313 a r:Inference; + r:gives { + 3314 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3314 math:notEqualTo 0}] + skolem:lemma5912 + [ a r:Fact; r:gives {((3 3 1 4) "=<") list:sort (1 3 3 4)}] + [ a r:Fact; r:gives {((3 3 1 4) ">=") list:sort (4 3 3 1)}] + skolem:lemma5679 + skolem:lemma5680 + [ a r:Fact; r:gives {(4331 1334) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3314]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 1 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3314 a r:Inference; + r:gives { + 3315 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3315 math:notEqualTo 0}] + skolem:lemma5913 + [ a r:Fact; r:gives {((3 3 1 5) "=<") list:sort (1 3 3 5)}] + [ a r:Fact; r:gives {((3 3 1 5) ">=") list:sort (5 3 3 1)}] + skolem:lemma5682 + skolem:lemma5683 + [ a r:Fact; r:gives {(5331 1335) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3315]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 1 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3315 a r:Inference; + r:gives { + 3316 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3316 math:notEqualTo 0}] + skolem:lemma5914 + [ a r:Fact; r:gives {((3 3 1 6) "=<") list:sort (1 3 3 6)}] + [ a r:Fact; r:gives {((3 3 1 6) ">=") list:sort (6 3 3 1)}] + skolem:lemma5685 + skolem:lemma5686 + [ a r:Fact; r:gives {(6331 1336) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3316]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 1 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3316 a r:Inference; + r:gives { + 3317 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3317 math:notEqualTo 0}] + skolem:lemma5915 + [ a r:Fact; r:gives {((3 3 1 7) "=<") list:sort (1 3 3 7)}] + [ a r:Fact; r:gives {((3 3 1 7) ">=") list:sort (7 3 3 1)}] + skolem:lemma5688 + skolem:lemma5689 + [ a r:Fact; r:gives {(7331 1337) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3317]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 1 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3317 a r:Inference; + r:gives { + 3318 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3318 math:notEqualTo 0}] + skolem:lemma5916 + [ a r:Fact; r:gives {((3 3 1 8) "=<") list:sort (1 3 3 8)}] + [ a r:Fact; r:gives {((3 3 1 8) ">=") list:sort (8 3 3 1)}] + skolem:lemma5691 + skolem:lemma5692 + [ a r:Fact; r:gives {(8331 1338) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3318]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 1 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3318 a r:Inference; + r:gives { + 3319 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3319 math:notEqualTo 0}] + skolem:lemma5917 + [ a r:Fact; r:gives {((3 3 1 9) "=<") list:sort (1 3 3 9)}] + [ a r:Fact; r:gives {((3 3 1 9) ">=") list:sort (9 3 3 1)}] + skolem:lemma5694 + skolem:lemma5695 + [ a r:Fact; r:gives {(9331 1339) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3319]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 1 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3319 a r:Inference; + r:gives { + 3320 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3320 math:notEqualTo 0}] + skolem:lemma5918 + [ a r:Fact; r:gives {((3 3 2 0) "=<") list:sort (0 2 3 3)}] + [ a r:Fact; r:gives {((3 3 2 0) ">=") list:sort (3 3 2 0)}] + skolem:lemma4087 + skolem:lemma4088 + [ a r:Fact; r:gives {(3320 233) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3320 a r:Inference; + r:gives { + 3321 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3321 math:notEqualTo 0}] + skolem:lemma5919 + [ a r:Fact; r:gives {((3 3 2 1) "=<") list:sort (1 2 3 3)}] + [ a r:Fact; r:gives {((3 3 2 1) ">=") list:sort (3 3 2 1)}] + skolem:lemma4277 + skolem:lemma4278 + [ a r:Fact; r:gives {(3321 1233) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3321 a r:Inference; + r:gives { + 3322 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3322 math:notEqualTo 0}] + skolem:lemma5920 + [ a r:Fact; r:gives {((3 3 2 2) "=<") list:sort (2 2 3 3)}] + [ a r:Fact; r:gives {((3 3 2 2) ">=") list:sort (3 3 2 2)}] + skolem:lemma4446 + skolem:lemma4447 + [ a r:Fact; r:gives {(3322 2233) math:difference 1089}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1089 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1089 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1089]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3322 a r:Inference; + r:gives { + 3323 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3323 math:notEqualTo 0}] + skolem:lemma5921 + [ a r:Fact; r:gives {((3 3 2 3) "=<") list:sort (2 3 3 3)}] + [ a r:Fact; r:gives {((3 3 2 3) ">=") list:sort (3 3 3 2)}] + skolem:lemma4602 + skolem:lemma4603 + [ a r:Fact; r:gives {(3332 2333) math:difference 999}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 999 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 999 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3323]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3323 a r:Inference; + r:gives { + 3324 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3324 math:notEqualTo 0}] + skolem:lemma5922 + [ a r:Fact; r:gives {((3 3 2 4) "=<") list:sort (2 3 3 4)}] + [ a r:Fact; r:gives {((3 3 2 4) ">=") list:sort (4 3 3 2)}] + skolem:lemma4605 + skolem:lemma4606 + [ a r:Fact; r:gives {(4332 2334) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3324]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3324 a r:Inference; + r:gives { + 3325 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3325 math:notEqualTo 0}] + skolem:lemma5923 + [ a r:Fact; r:gives {((3 3 2 5) "=<") list:sort (2 3 3 5)}] + [ a r:Fact; r:gives {((3 3 2 5) ">=") list:sort (5 3 3 2)}] + skolem:lemma4608 + skolem:lemma4609 + [ a r:Fact; r:gives {(5332 2335) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3325]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3325 a r:Inference; + r:gives { + 3326 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3326 math:notEqualTo 0}] + skolem:lemma5924 + [ a r:Fact; r:gives {((3 3 2 6) "=<") list:sort (2 3 3 6)}] + [ a r:Fact; r:gives {((3 3 2 6) ">=") list:sort (6 3 3 2)}] + skolem:lemma4611 + skolem:lemma4612 + [ a r:Fact; r:gives {(6332 2336) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3326]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3326 a r:Inference; + r:gives { + 3327 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3327 math:notEqualTo 0}] + skolem:lemma5925 + [ a r:Fact; r:gives {((3 3 2 7) "=<") list:sort (2 3 3 7)}] + [ a r:Fact; r:gives {((3 3 2 7) ">=") list:sort (7 3 3 2)}] + skolem:lemma4614 + skolem:lemma4615 + [ a r:Fact; r:gives {(7332 2337) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3327]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3327 a r:Inference; + r:gives { + 3328 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3328 math:notEqualTo 0}] + skolem:lemma5926 + [ a r:Fact; r:gives {((3 3 2 8) "=<") list:sort (2 3 3 8)}] + [ a r:Fact; r:gives {((3 3 2 8) ">=") list:sort (8 3 3 2)}] + skolem:lemma4617 + skolem:lemma4618 + [ a r:Fact; r:gives {(8332 2338) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3328]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3328 a r:Inference; + r:gives { + 3329 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3329 math:notEqualTo 0}] + skolem:lemma5927 + [ a r:Fact; r:gives {((3 3 2 9) "=<") list:sort (2 3 3 9)}] + [ a r:Fact; r:gives {((3 3 2 9) ">=") list:sort (9 3 3 2)}] + skolem:lemma4620 + skolem:lemma4621 + [ a r:Fact; r:gives {(9332 2339) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3329]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3329 a r:Inference; + r:gives { + 3330 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3330 math:notEqualTo 0}] + skolem:lemma5928 + [ a r:Fact; r:gives {((3 3 3 0) "=<") list:sort (0 3 3 3)}] + [ a r:Fact; r:gives {((3 3 3 0) ">=") list:sort (3 3 3 0)}] + skolem:lemma5504 + skolem:lemma5505 + [ a r:Fact; r:gives {(3330 333) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3330 a r:Inference; + r:gives { + 3331 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3331 math:notEqualTo 0}] + skolem:lemma5929 + [ a r:Fact; r:gives {((3 3 3 1) "=<") list:sort (1 3 3 3)}] + [ a r:Fact; r:gives {((3 3 3 1) ">=") list:sort (3 3 3 1)}] + skolem:lemma5676 + skolem:lemma5677 + [ a r:Fact; r:gives {(3331 1333) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3331 a r:Inference; + r:gives { + 3332 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3332 math:notEqualTo 0}] + skolem:lemma5930 + [ a r:Fact; r:gives {((3 3 3 2) "=<") list:sort (2 3 3 3)}] + [ a r:Fact; r:gives {((3 3 3 2) ">=") list:sort (3 3 3 2)}] + skolem:lemma4602 + skolem:lemma4603 + [ a r:Fact; r:gives {(3332 2333) math:difference 999}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 999 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 999 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (3 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3332 a r:Inference; + r:gives { + 3334 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3334 math:notEqualTo 0}] + skolem:lemma5931 + [ a r:Fact; r:gives {((3 3 3 4) "=<") list:sort (3 3 3 4)}] + [ a r:Fact; r:gives {((3 3 3 4) ">=") list:sort (4 3 3 3)}] + skolem:lemma5932 + skolem:lemma5933 + [ a r:Fact; r:gives {(4333 3334) math:difference 999}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 999 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 999 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3333 a r:Inference; + r:gives { + 3335 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3335 math:notEqualTo 0}] + skolem:lemma5934 + [ a r:Fact; r:gives {((3 3 3 5) "=<") list:sort (3 3 3 5)}] + [ a r:Fact; r:gives {((3 3 3 5) ">=") list:sort (5 3 3 3)}] + skolem:lemma5935 + skolem:lemma5936 + [ a r:Fact; r:gives {(5333 3335) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3334 a r:Inference; + r:gives { + 3336 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3336 math:notEqualTo 0}] + skolem:lemma5937 + [ a r:Fact; r:gives {((3 3 3 6) "=<") list:sort (3 3 3 6)}] + [ a r:Fact; r:gives {((3 3 3 6) ">=") list:sort (6 3 3 3)}] + skolem:lemma5938 + skolem:lemma5939 + [ a r:Fact; r:gives {(6333 3336) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3335 a r:Inference; + r:gives { + 3337 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3337 math:notEqualTo 0}] + skolem:lemma5940 + [ a r:Fact; r:gives {((3 3 3 7) "=<") list:sort (3 3 3 7)}] + [ a r:Fact; r:gives {((3 3 3 7) ">=") list:sort (7 3 3 3)}] + skolem:lemma5941 + skolem:lemma5942 + [ a r:Fact; r:gives {(7333 3337) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3336 a r:Inference; + r:gives { + 3338 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3338 math:notEqualTo 0}] + skolem:lemma5943 + [ a r:Fact; r:gives {((3 3 3 8) "=<") list:sort (3 3 3 8)}] + [ a r:Fact; r:gives {((3 3 3 8) ">=") list:sort (8 3 3 3)}] + skolem:lemma5944 + skolem:lemma5945 + [ a r:Fact; r:gives {(8333 3338) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3337 a r:Inference; + r:gives { + 3339 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3339 math:notEqualTo 0}] + skolem:lemma5946 + [ a r:Fact; r:gives {((3 3 3 9) "=<") list:sort (3 3 3 9)}] + [ a r:Fact; r:gives {((3 3 3 9) ">=") list:sort (9 3 3 3)}] + skolem:lemma5947 + skolem:lemma5948 + [ a r:Fact; r:gives {(9333 3339) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3338 a r:Inference; + r:gives { + 3340 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3340 math:notEqualTo 0}] + skolem:lemma5949 + [ a r:Fact; r:gives {((3 3 4 0) "=<") list:sort (0 3 3 4)}] + [ a r:Fact; r:gives {((3 3 4 0) ">=") list:sort (4 3 3 0)}] + skolem:lemma5507 + skolem:lemma5508 + [ a r:Fact; r:gives {(4330 334) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3340]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 4 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3339 a r:Inference; + r:gives { + 3341 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3341 math:notEqualTo 0}] + skolem:lemma5950 + [ a r:Fact; r:gives {((3 3 4 1) "=<") list:sort (1 3 3 4)}] + [ a r:Fact; r:gives {((3 3 4 1) ">=") list:sort (4 3 3 1)}] + skolem:lemma5679 + skolem:lemma5680 + [ a r:Fact; r:gives {(4331 1334) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3341]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 4 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3340 a r:Inference; + r:gives { + 3342 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3342 math:notEqualTo 0}] + skolem:lemma5951 + [ a r:Fact; r:gives {((3 3 4 2) "=<") list:sort (2 3 3 4)}] + [ a r:Fact; r:gives {((3 3 4 2) ">=") list:sort (4 3 3 2)}] + skolem:lemma4605 + skolem:lemma4606 + [ a r:Fact; r:gives {(4332 2334) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3342]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3341 a r:Inference; + r:gives { + 3343 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3343 math:notEqualTo 0}] + skolem:lemma5952 + [ a r:Fact; r:gives {((3 3 4 3) "=<") list:sort (3 3 3 4)}] + [ a r:Fact; r:gives {((3 3 4 3) ">=") list:sort (4 3 3 3)}] + skolem:lemma5932 + skolem:lemma5933 + [ a r:Fact; r:gives {(4333 3334) math:difference 999}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 999 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 999 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3343]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3342 a r:Inference; + r:gives { + 3344 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3344 math:notEqualTo 0}] + skolem:lemma5953 + [ a r:Fact; r:gives {((3 3 4 4) "=<") list:sort (3 3 4 4)}] + [ a r:Fact; r:gives {((3 3 4 4) ">=") list:sort (4 4 3 3)}] + skolem:lemma5954 + skolem:lemma5955 + [ a r:Fact; r:gives {(4433 3344) math:difference 1089}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1089 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1089 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1089]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3343 a r:Inference; + r:gives { + 3345 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3345 math:notEqualTo 0}] + skolem:lemma5956 + [ a r:Fact; r:gives {((3 3 4 5) "=<") list:sort (3 3 4 5)}] + [ a r:Fact; r:gives {((3 3 4 5) ">=") list:sort (5 4 3 3)}] + skolem:lemma5957 + skolem:lemma5958 + [ a r:Fact; r:gives {(5433 3345) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3344 a r:Inference; + r:gives { + 3346 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3346 math:notEqualTo 0}] + skolem:lemma5959 + [ a r:Fact; r:gives {((3 3 4 6) "=<") list:sort (3 3 4 6)}] + [ a r:Fact; r:gives {((3 3 4 6) ">=") list:sort (6 4 3 3)}] + skolem:lemma5960 + skolem:lemma5961 + [ a r:Fact; r:gives {(6433 3346) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3345 a r:Inference; + r:gives { + 3347 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3347 math:notEqualTo 0}] + skolem:lemma5962 + [ a r:Fact; r:gives {((3 3 4 7) "=<") list:sort (3 3 4 7)}] + [ a r:Fact; r:gives {((3 3 4 7) ">=") list:sort (7 4 3 3)}] + skolem:lemma5963 + skolem:lemma5964 + [ a r:Fact; r:gives {(7433 3347) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3346 a r:Inference; + r:gives { + 3348 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3348 math:notEqualTo 0}] + skolem:lemma5965 + [ a r:Fact; r:gives {((3 3 4 8) "=<") list:sort (3 3 4 8)}] + [ a r:Fact; r:gives {((3 3 4 8) ">=") list:sort (8 4 3 3)}] + skolem:lemma5966 + skolem:lemma5967 + [ a r:Fact; r:gives {(8433 3348) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3347 a r:Inference; + r:gives { + 3349 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3349 math:notEqualTo 0}] + skolem:lemma5968 + [ a r:Fact; r:gives {((3 3 4 9) "=<") list:sort (3 3 4 9)}] + [ a r:Fact; r:gives {((3 3 4 9) ">=") list:sort (9 4 3 3)}] + skolem:lemma5969 + skolem:lemma5970 + [ a r:Fact; r:gives {(9433 3349) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3348 a r:Inference; + r:gives { + 3350 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3350 math:notEqualTo 0}] + skolem:lemma5971 + [ a r:Fact; r:gives {((3 3 5 0) "=<") list:sort (0 3 3 5)}] + [ a r:Fact; r:gives {((3 3 5 0) ">=") list:sort (5 3 3 0)}] + skolem:lemma5510 + skolem:lemma5511 + [ a r:Fact; r:gives {(5330 335) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3350]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 5 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3349 a r:Inference; + r:gives { + 3351 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3351 math:notEqualTo 0}] + skolem:lemma5972 + [ a r:Fact; r:gives {((3 3 5 1) "=<") list:sort (1 3 3 5)}] + [ a r:Fact; r:gives {((3 3 5 1) ">=") list:sort (5 3 3 1)}] + skolem:lemma5682 + skolem:lemma5683 + [ a r:Fact; r:gives {(5331 1335) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3351]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 5 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3350 a r:Inference; + r:gives { + 3352 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3352 math:notEqualTo 0}] + skolem:lemma5973 + [ a r:Fact; r:gives {((3 3 5 2) "=<") list:sort (2 3 3 5)}] + [ a r:Fact; r:gives {((3 3 5 2) ">=") list:sort (5 3 3 2)}] + skolem:lemma4608 + skolem:lemma4609 + [ a r:Fact; r:gives {(5332 2335) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3351 a r:Inference; + r:gives { + 3353 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3353 math:notEqualTo 0}] + skolem:lemma5974 + [ a r:Fact; r:gives {((3 3 5 3) "=<") list:sort (3 3 3 5)}] + [ a r:Fact; r:gives {((3 3 5 3) ">=") list:sort (5 3 3 3)}] + skolem:lemma5935 + skolem:lemma5936 + [ a r:Fact; r:gives {(5333 3335) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3352 a r:Inference; + r:gives { + 3354 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3354 math:notEqualTo 0}] + skolem:lemma5975 + [ a r:Fact; r:gives {((3 3 5 4) "=<") list:sort (3 3 4 5)}] + [ a r:Fact; r:gives {((3 3 5 4) ">=") list:sort (5 4 3 3)}] + skolem:lemma5957 + skolem:lemma5958 + [ a r:Fact; r:gives {(5433 3345) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 5 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3353 a r:Inference; + r:gives { + 3355 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3355 math:notEqualTo 0}] + skolem:lemma5976 + [ a r:Fact; r:gives {((3 3 5 5) "=<") list:sort (3 3 5 5)}] + [ a r:Fact; r:gives {((3 3 5 5) ">=") list:sort (5 5 3 3)}] + skolem:lemma5977 + skolem:lemma5978 + [ a r:Fact; r:gives {(5533 3355) math:difference 2178}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2178 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2178 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2178]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3354 a r:Inference; + r:gives { + 3356 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3356 math:notEqualTo 0}] + skolem:lemma5979 + [ a r:Fact; r:gives {((3 3 5 6) "=<") list:sort (3 3 5 6)}] + [ a r:Fact; r:gives {((3 3 5 6) ">=") list:sort (6 5 3 3)}] + skolem:lemma5980 + skolem:lemma5981 + [ a r:Fact; r:gives {(6533 3356) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3355 a r:Inference; + r:gives { + 3357 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3357 math:notEqualTo 0}] + skolem:lemma5982 + [ a r:Fact; r:gives {((3 3 5 7) "=<") list:sort (3 3 5 7)}] + [ a r:Fact; r:gives {((3 3 5 7) ">=") list:sort (7 5 3 3)}] + skolem:lemma5983 + skolem:lemma5984 + [ a r:Fact; r:gives {(7533 3357) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3356 a r:Inference; + r:gives { + 3358 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3358 math:notEqualTo 0}] + skolem:lemma5985 + [ a r:Fact; r:gives {((3 3 5 8) "=<") list:sort (3 3 5 8)}] + [ a r:Fact; r:gives {((3 3 5 8) ">=") list:sort (8 5 3 3)}] + skolem:lemma5986 + skolem:lemma5987 + [ a r:Fact; r:gives {(8533 3358) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3357 a r:Inference; + r:gives { + 3359 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3359 math:notEqualTo 0}] + skolem:lemma5988 + [ a r:Fact; r:gives {((3 3 5 9) "=<") list:sort (3 3 5 9)}] + [ a r:Fact; r:gives {((3 3 5 9) ">=") list:sort (9 5 3 3)}] + skolem:lemma5989 + skolem:lemma5990 + [ a r:Fact; r:gives {(9533 3359) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3358 a r:Inference; + r:gives { + 3360 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3360 math:notEqualTo 0}] + skolem:lemma5991 + [ a r:Fact; r:gives {((3 3 6 0) "=<") list:sort (0 3 3 6)}] + [ a r:Fact; r:gives {((3 3 6 0) ">=") list:sort (6 3 3 0)}] + skolem:lemma5513 + skolem:lemma5514 + [ a r:Fact; r:gives {(6330 336) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3360]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 6 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3359 a r:Inference; + r:gives { + 3361 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3361 math:notEqualTo 0}] + skolem:lemma5992 + [ a r:Fact; r:gives {((3 3 6 1) "=<") list:sort (1 3 3 6)}] + [ a r:Fact; r:gives {((3 3 6 1) ">=") list:sort (6 3 3 1)}] + skolem:lemma5685 + skolem:lemma5686 + [ a r:Fact; r:gives {(6331 1336) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3361]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 6 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3360 a r:Inference; + r:gives { + 3362 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3362 math:notEqualTo 0}] + skolem:lemma5993 + [ a r:Fact; r:gives {((3 3 6 2) "=<") list:sort (2 3 3 6)}] + [ a r:Fact; r:gives {((3 3 6 2) ">=") list:sort (6 3 3 2)}] + skolem:lemma4611 + skolem:lemma4612 + [ a r:Fact; r:gives {(6332 2336) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3362]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3361 a r:Inference; + r:gives { + 3363 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3363 math:notEqualTo 0}] + skolem:lemma5994 + [ a r:Fact; r:gives {((3 3 6 3) "=<") list:sort (3 3 3 6)}] + [ a r:Fact; r:gives {((3 3 6 3) ">=") list:sort (6 3 3 3)}] + skolem:lemma5938 + skolem:lemma5939 + [ a r:Fact; r:gives {(6333 3336) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3363]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3362 a r:Inference; + r:gives { + 3364 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3364 math:notEqualTo 0}] + skolem:lemma5995 + [ a r:Fact; r:gives {((3 3 6 4) "=<") list:sort (3 3 4 6)}] + [ a r:Fact; r:gives {((3 3 6 4) ">=") list:sort (6 4 3 3)}] + skolem:lemma5960 + skolem:lemma5961 + [ a r:Fact; r:gives {(6433 3346) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3364]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 6 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3363 a r:Inference; + r:gives { + 3365 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3365 math:notEqualTo 0}] + skolem:lemma5996 + [ a r:Fact; r:gives {((3 3 6 5) "=<") list:sort (3 3 5 6)}] + [ a r:Fact; r:gives {((3 3 6 5) ">=") list:sort (6 5 3 3)}] + skolem:lemma5980 + skolem:lemma5981 + [ a r:Fact; r:gives {(6533 3356) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3365]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 6 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3364 a r:Inference; + r:gives { + 3366 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3366 math:notEqualTo 0}] + skolem:lemma5997 + [ a r:Fact; r:gives {((3 3 6 6) "=<") list:sort (3 3 6 6)}] + [ a r:Fact; r:gives {((3 3 6 6) ">=") list:sort (6 6 3 3)}] + skolem:lemma5998 + skolem:lemma5999 + [ a r:Fact; r:gives {(6633 3366) math:difference 3267}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3267 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 3267 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3365 a r:Inference; + r:gives { + 3367 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3367 math:notEqualTo 0}] + skolem:lemma6000 + [ a r:Fact; r:gives {((3 3 6 7) "=<") list:sort (3 3 6 7)}] + [ a r:Fact; r:gives {((3 3 6 7) ">=") list:sort (7 6 3 3)}] + skolem:lemma6001 + skolem:lemma6002 + [ a r:Fact; r:gives {(7633 3367) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3366 a r:Inference; + r:gives { + 3368 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3368 math:notEqualTo 0}] + skolem:lemma6003 + [ a r:Fact; r:gives {((3 3 6 8) "=<") list:sort (3 3 6 8)}] + [ a r:Fact; r:gives {((3 3 6 8) ">=") list:sort (8 6 3 3)}] + skolem:lemma6004 + skolem:lemma6005 + [ a r:Fact; r:gives {(8633 3368) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3367 a r:Inference; + r:gives { + 3369 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3369 math:notEqualTo 0}] + skolem:lemma6006 + [ a r:Fact; r:gives {((3 3 6 9) "=<") list:sort (3 3 6 9)}] + [ a r:Fact; r:gives {((3 3 6 9) ">=") list:sort (9 6 3 3)}] + skolem:lemma6007 + skolem:lemma6008 + [ a r:Fact; r:gives {(9633 3369) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3368 a r:Inference; + r:gives { + 3370 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3370 math:notEqualTo 0}] + skolem:lemma6009 + [ a r:Fact; r:gives {((3 3 7 0) "=<") list:sort (0 3 3 7)}] + [ a r:Fact; r:gives {((3 3 7 0) ">=") list:sort (7 3 3 0)}] + skolem:lemma5516 + skolem:lemma5517 + [ a r:Fact; r:gives {(7330 337) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3370]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 7 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3369 a r:Inference; + r:gives { + 3371 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3371 math:notEqualTo 0}] + skolem:lemma6010 + [ a r:Fact; r:gives {((3 3 7 1) "=<") list:sort (1 3 3 7)}] + [ a r:Fact; r:gives {((3 3 7 1) ">=") list:sort (7 3 3 1)}] + skolem:lemma5688 + skolem:lemma5689 + [ a r:Fact; r:gives {(7331 1337) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3371]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 7 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3370 a r:Inference; + r:gives { + 3372 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3372 math:notEqualTo 0}] + skolem:lemma6011 + [ a r:Fact; r:gives {((3 3 7 2) "=<") list:sort (2 3 3 7)}] + [ a r:Fact; r:gives {((3 3 7 2) ">=") list:sort (7 3 3 2)}] + skolem:lemma4614 + skolem:lemma4615 + [ a r:Fact; r:gives {(7332 2337) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3372]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3371 a r:Inference; + r:gives { + 3373 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3373 math:notEqualTo 0}] + skolem:lemma6012 + [ a r:Fact; r:gives {((3 3 7 3) "=<") list:sort (3 3 3 7)}] + [ a r:Fact; r:gives {((3 3 7 3) ">=") list:sort (7 3 3 3)}] + skolem:lemma5941 + skolem:lemma5942 + [ a r:Fact; r:gives {(7333 3337) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3373]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3372 a r:Inference; + r:gives { + 3374 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3374 math:notEqualTo 0}] + skolem:lemma6013 + [ a r:Fact; r:gives {((3 3 7 4) "=<") list:sort (3 3 4 7)}] + [ a r:Fact; r:gives {((3 3 7 4) ">=") list:sort (7 4 3 3)}] + skolem:lemma5963 + skolem:lemma5964 + [ a r:Fact; r:gives {(7433 3347) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3374]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 7 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3373 a r:Inference; + r:gives { + 3375 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3375 math:notEqualTo 0}] + skolem:lemma6014 + [ a r:Fact; r:gives {((3 3 7 5) "=<") list:sort (3 3 5 7)}] + [ a r:Fact; r:gives {((3 3 7 5) ">=") list:sort (7 5 3 3)}] + skolem:lemma5983 + skolem:lemma5984 + [ a r:Fact; r:gives {(7533 3357) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3375]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 7 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3374 a r:Inference; + r:gives { + 3376 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3376 math:notEqualTo 0}] + skolem:lemma6015 + [ a r:Fact; r:gives {((3 3 7 6) "=<") list:sort (3 3 6 7)}] + [ a r:Fact; r:gives {((3 3 7 6) ">=") list:sort (7 6 3 3)}] + skolem:lemma6001 + skolem:lemma6002 + [ a r:Fact; r:gives {(7633 3367) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3376]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 7 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3375 a r:Inference; + r:gives { + 3377 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3377 math:notEqualTo 0}] + skolem:lemma6016 + [ a r:Fact; r:gives {((3 3 7 7) "=<") list:sort (3 3 7 7)}] + [ a r:Fact; r:gives {((3 3 7 7) ">=") list:sort (7 7 3 3)}] + skolem:lemma6017 + skolem:lemma6018 + [ a r:Fact; r:gives {(7733 3377) math:difference 4356}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4356 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 4356 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3376 a r:Inference; + r:gives { + 3378 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3378 math:notEqualTo 0}] + skolem:lemma6019 + [ a r:Fact; r:gives {((3 3 7 8) "=<") list:sort (3 3 7 8)}] + [ a r:Fact; r:gives {((3 3 7 8) ">=") list:sort (8 7 3 3)}] + skolem:lemma6020 + skolem:lemma6021 + [ a r:Fact; r:gives {(8733 3378) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3377 a r:Inference; + r:gives { + 3379 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3379 math:notEqualTo 0}] + skolem:lemma6022 + [ a r:Fact; r:gives {((3 3 7 9) "=<") list:sort (3 3 7 9)}] + [ a r:Fact; r:gives {((3 3 7 9) ">=") list:sort (9 7 3 3)}] + skolem:lemma6023 + skolem:lemma6024 + [ a r:Fact; r:gives {(9733 3379) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3378 a r:Inference; + r:gives { + 3380 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3380 math:notEqualTo 0}] + skolem:lemma6025 + [ a r:Fact; r:gives {((3 3 8 0) "=<") list:sort (0 3 3 8)}] + [ a r:Fact; r:gives {((3 3 8 0) ">=") list:sort (8 3 3 0)}] + skolem:lemma5519 + skolem:lemma5520 + [ a r:Fact; r:gives {(8330 338) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3380]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 8 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3379 a r:Inference; + r:gives { + 3381 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3381 math:notEqualTo 0}] + skolem:lemma6026 + [ a r:Fact; r:gives {((3 3 8 1) "=<") list:sort (1 3 3 8)}] + [ a r:Fact; r:gives {((3 3 8 1) ">=") list:sort (8 3 3 1)}] + skolem:lemma5691 + skolem:lemma5692 + [ a r:Fact; r:gives {(8331 1338) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3381]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 8 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3380 a r:Inference; + r:gives { + 3382 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3382 math:notEqualTo 0}] + skolem:lemma6027 + [ a r:Fact; r:gives {((3 3 8 2) "=<") list:sort (2 3 3 8)}] + [ a r:Fact; r:gives {((3 3 8 2) ">=") list:sort (8 3 3 2)}] + skolem:lemma4617 + skolem:lemma4618 + [ a r:Fact; r:gives {(8332 2338) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3382]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3381 a r:Inference; + r:gives { + 3383 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3383 math:notEqualTo 0}] + skolem:lemma6028 + [ a r:Fact; r:gives {((3 3 8 3) "=<") list:sort (3 3 3 8)}] + [ a r:Fact; r:gives {((3 3 8 3) ">=") list:sort (8 3 3 3)}] + skolem:lemma5944 + skolem:lemma5945 + [ a r:Fact; r:gives {(8333 3338) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3383]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3382 a r:Inference; + r:gives { + 3384 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3384 math:notEqualTo 0}] + skolem:lemma6029 + [ a r:Fact; r:gives {((3 3 8 4) "=<") list:sort (3 3 4 8)}] + [ a r:Fact; r:gives {((3 3 8 4) ">=") list:sort (8 4 3 3)}] + skolem:lemma5966 + skolem:lemma5967 + [ a r:Fact; r:gives {(8433 3348) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3384]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 8 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3383 a r:Inference; + r:gives { + 3385 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3385 math:notEqualTo 0}] + skolem:lemma6030 + [ a r:Fact; r:gives {((3 3 8 5) "=<") list:sort (3 3 5 8)}] + [ a r:Fact; r:gives {((3 3 8 5) ">=") list:sort (8 5 3 3)}] + skolem:lemma5986 + skolem:lemma5987 + [ a r:Fact; r:gives {(8533 3358) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3385]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 8 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3384 a r:Inference; + r:gives { + 3386 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3386 math:notEqualTo 0}] + skolem:lemma6031 + [ a r:Fact; r:gives {((3 3 8 6) "=<") list:sort (3 3 6 8)}] + [ a r:Fact; r:gives {((3 3 8 6) ">=") list:sort (8 6 3 3)}] + skolem:lemma6004 + skolem:lemma6005 + [ a r:Fact; r:gives {(8633 3368) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3386]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 8 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3385 a r:Inference; + r:gives { + 3387 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3387 math:notEqualTo 0}] + skolem:lemma6032 + [ a r:Fact; r:gives {((3 3 8 7) "=<") list:sort (3 3 7 8)}] + [ a r:Fact; r:gives {((3 3 8 7) ">=") list:sort (8 7 3 3)}] + skolem:lemma6020 + skolem:lemma6021 + [ a r:Fact; r:gives {(8733 3378) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3387]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 8 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3386 a r:Inference; + r:gives { + 3388 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3388 math:notEqualTo 0}] + skolem:lemma6033 + [ a r:Fact; r:gives {((3 3 8 8) "=<") list:sort (3 3 8 8)}] + [ a r:Fact; r:gives {((3 3 8 8) ">=") list:sort (8 8 3 3)}] + skolem:lemma6034 + skolem:lemma6035 + [ a r:Fact; r:gives {(8833 3388) math:difference 5445}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5445 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5445 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8833]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5445]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3387 a r:Inference; + r:gives { + 3389 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3389 math:notEqualTo 0}] + skolem:lemma6036 + [ a r:Fact; r:gives {((3 3 8 9) "=<") list:sort (3 3 8 9)}] + [ a r:Fact; r:gives {((3 3 8 9) ">=") list:sort (9 8 3 3)}] + skolem:lemma6037 + skolem:lemma6038 + [ a r:Fact; r:gives {(9833 3389) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9833]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3388 a r:Inference; + r:gives { + 3390 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3390 math:notEqualTo 0}] + skolem:lemma6039 + [ a r:Fact; r:gives {((3 3 9 0) "=<") list:sort (0 3 3 9)}] + [ a r:Fact; r:gives {((3 3 9 0) ">=") list:sort (9 3 3 0)}] + skolem:lemma5522 + skolem:lemma5523 + [ a r:Fact; r:gives {(9330 339) math:difference 8991}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8991 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 8991 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3390]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 9 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8991]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3389 a r:Inference; + r:gives { + 3391 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3391 math:notEqualTo 0}] + skolem:lemma6040 + [ a r:Fact; r:gives {((3 3 9 1) "=<") list:sort (1 3 3 9)}] + [ a r:Fact; r:gives {((3 3 9 1) ">=") list:sort (9 3 3 1)}] + skolem:lemma5694 + skolem:lemma5695 + [ a r:Fact; r:gives {(9331 1339) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3391]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 9 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3390 a r:Inference; + r:gives { + 3392 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3392 math:notEqualTo 0}] + skolem:lemma6041 + [ a r:Fact; r:gives {((3 3 9 2) "=<") list:sort (2 3 3 9)}] + [ a r:Fact; r:gives {((3 3 9 2) ">=") list:sort (9 3 3 2)}] + skolem:lemma4620 + skolem:lemma4621 + [ a r:Fact; r:gives {(9332 2339) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3392]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 9 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3391 a r:Inference; + r:gives { + 3393 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3393 math:notEqualTo 0}] + skolem:lemma6042 + [ a r:Fact; r:gives {((3 3 9 3) "=<") list:sort (3 3 3 9)}] + [ a r:Fact; r:gives {((3 3 9 3) ">=") list:sort (9 3 3 3)}] + skolem:lemma5947 + skolem:lemma5948 + [ a r:Fact; r:gives {(9333 3339) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3393]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 9 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3392 a r:Inference; + r:gives { + 3394 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3394 math:notEqualTo 0}] + skolem:lemma6043 + [ a r:Fact; r:gives {((3 3 9 4) "=<") list:sort (3 3 4 9)}] + [ a r:Fact; r:gives {((3 3 9 4) ">=") list:sort (9 4 3 3)}] + skolem:lemma5969 + skolem:lemma5970 + [ a r:Fact; r:gives {(9433 3349) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3394]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 9 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3393 a r:Inference; + r:gives { + 3395 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3395 math:notEqualTo 0}] + skolem:lemma6044 + [ a r:Fact; r:gives {((3 3 9 5) "=<") list:sort (3 3 5 9)}] + [ a r:Fact; r:gives {((3 3 9 5) ">=") list:sort (9 5 3 3)}] + skolem:lemma5989 + skolem:lemma5990 + [ a r:Fact; r:gives {(9533 3359) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3395]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 9 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3394 a r:Inference; + r:gives { + 3396 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3396 math:notEqualTo 0}] + skolem:lemma6045 + [ a r:Fact; r:gives {((3 3 9 6) "=<") list:sort (3 3 6 9)}] + [ a r:Fact; r:gives {((3 3 9 6) ">=") list:sort (9 6 3 3)}] + skolem:lemma6007 + skolem:lemma6008 + [ a r:Fact; r:gives {(9633 3369) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3396]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 9 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3395 a r:Inference; + r:gives { + 3397 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3397 math:notEqualTo 0}] + skolem:lemma6046 + [ a r:Fact; r:gives {((3 3 9 7) "=<") list:sort (3 3 7 9)}] + [ a r:Fact; r:gives {((3 3 9 7) ">=") list:sort (9 7 3 3)}] + skolem:lemma6023 + skolem:lemma6024 + [ a r:Fact; r:gives {(9733 3379) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3397]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 9 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3396 a r:Inference; + r:gives { + 3398 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3398 math:notEqualTo 0}] + skolem:lemma6047 + [ a r:Fact; r:gives {((3 3 9 8) "=<") list:sort (3 3 8 9)}] + [ a r:Fact; r:gives {((3 3 9 8) ">=") list:sort (9 8 3 3)}] + skolem:lemma6037 + skolem:lemma6038 + [ a r:Fact; r:gives {(9833 3389) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3398]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 9 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9833]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3397 a r:Inference; + r:gives { + 3399 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3399 math:notEqualTo 0}] + skolem:lemma6048 + [ a r:Fact; r:gives {((3 3 9 9) "=<") list:sort (3 3 9 9)}] + [ a r:Fact; r:gives {((3 3 9 9) ">=") list:sort (9 9 3 3)}] + skolem:lemma6049 + skolem:lemma6050 + [ a r:Fact; r:gives {(9933 3399) math:difference 6534}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6534 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6534 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 3 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9933]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6534]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3398 a r:Inference; + r:gives { + 3400 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3400 math:notEqualTo 0}] + skolem:lemma6051 + [ a r:Fact; r:gives {((3 4 0 0) "=<") list:sort (0 0 3 4)}] + [ a r:Fact; r:gives {((3 4 0 0) ">=") list:sort (4 3 0 0)}] + skolem:lemma5447 + skolem:lemma5448 + [ a r:Fact; r:gives {(4300 34) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 34]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3399 a r:Inference; + r:gives { + 3401 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3401 math:notEqualTo 0}] + skolem:lemma6052 + [ a r:Fact; r:gives {((3 4 0 1) "=<") list:sort (0 1 3 4)}] + [ a r:Fact; r:gives {((3 4 0 1) ">=") list:sort (4 3 1 0)}] + skolem:lemma5473 + skolem:lemma5474 + [ a r:Fact; r:gives {(4310 134) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3401]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 0 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 134]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3400 a r:Inference; + r:gives { + 3402 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3402 math:notEqualTo 0}] + skolem:lemma6053 + [ a r:Fact; r:gives {((3 4 0 2) "=<") list:sort (0 2 3 4)}] + [ a r:Fact; r:gives {((3 4 0 2) ">=") list:sort (4 3 2 0)}] + skolem:lemma4090 + skolem:lemma4091 + [ a r:Fact; r:gives {(4320 234) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3402]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 0 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3401 a r:Inference; + r:gives { + 3403 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3403 math:notEqualTo 0}] + skolem:lemma6054 + [ a r:Fact; r:gives {((3 4 0 3) "=<") list:sort (0 3 3 4)}] + [ a r:Fact; r:gives {((3 4 0 3) ">=") list:sort (4 3 3 0)}] + skolem:lemma5507 + skolem:lemma5508 + [ a r:Fact; r:gives {(4330 334) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3403]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 0 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3402 a r:Inference; + r:gives { + 3404 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3404 math:notEqualTo 0}] + skolem:lemma6055 + [ a r:Fact; r:gives {((3 4 0 4) "=<") list:sort (0 3 4 4)}] + [ a r:Fact; r:gives {((3 4 0 4) ">=") list:sort (4 4 3 0)}] + skolem:lemma5529 + skolem:lemma5530 + [ a r:Fact; r:gives {(4430 344) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3404]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 0 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3403 a r:Inference; + r:gives { + 3405 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3405 math:notEqualTo 0}] + skolem:lemma6056 + [ a r:Fact; r:gives {((3 4 0 5) "=<") list:sort (0 3 4 5)}] + [ a r:Fact; r:gives {((3 4 0 5) ">=") list:sort (5 4 3 0)}] + skolem:lemma5532 + skolem:lemma5533 + [ a r:Fact; r:gives {(5430 345) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3405]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 0 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3404 a r:Inference; + r:gives { + 3406 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3406 math:notEqualTo 0}] + skolem:lemma6057 + [ a r:Fact; r:gives {((3 4 0 6) "=<") list:sort (0 3 4 6)}] + [ a r:Fact; r:gives {((3 4 0 6) ">=") list:sort (6 4 3 0)}] + skolem:lemma5535 + skolem:lemma5536 + [ a r:Fact; r:gives {(6430 346) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3406]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 0 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3405 a r:Inference; + r:gives { + 3407 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3407 math:notEqualTo 0}] + skolem:lemma6058 + [ a r:Fact; r:gives {((3 4 0 7) "=<") list:sort (0 3 4 7)}] + [ a r:Fact; r:gives {((3 4 0 7) ">=") list:sort (7 4 3 0)}] + skolem:lemma5538 + skolem:lemma5539 + [ a r:Fact; r:gives {(7430 347) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3407]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 0 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3406 a r:Inference; + r:gives { + 3408 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3408 math:notEqualTo 0}] + skolem:lemma6059 + [ a r:Fact; r:gives {((3 4 0 8) "=<") list:sort (0 3 4 8)}] + [ a r:Fact; r:gives {((3 4 0 8) ">=") list:sort (8 4 3 0)}] + skolem:lemma5541 + skolem:lemma5542 + [ a r:Fact; r:gives {(8430 348) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3408]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 0 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3407 a r:Inference; + r:gives { + 3409 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3409 math:notEqualTo 0}] + skolem:lemma6060 + [ a r:Fact; r:gives {((3 4 0 9) "=<") list:sort (0 3 4 9)}] + [ a r:Fact; r:gives {((3 4 0 9) ">=") list:sort (9 4 3 0)}] + skolem:lemma5544 + skolem:lemma5545 + [ a r:Fact; r:gives {(9430 349) math:difference 9081}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9081 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 9081 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3409]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 0 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3408 a r:Inference; + r:gives { + 3410 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3410 math:notEqualTo 0}] + skolem:lemma6061 + [ a r:Fact; r:gives {((3 4 1 0) "=<") list:sort (0 1 3 4)}] + [ a r:Fact; r:gives {((3 4 1 0) ">=") list:sort (4 3 1 0)}] + skolem:lemma5473 + skolem:lemma5474 + [ a r:Fact; r:gives {(4310 134) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3410]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 134]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3409 a r:Inference; + r:gives { + 3411 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3411 math:notEqualTo 0}] + skolem:lemma6062 + [ a r:Fact; r:gives {((3 4 1 1) "=<") list:sort (1 1 3 4)}] + [ a r:Fact; r:gives {((3 4 1 1) ">=") list:sort (4 3 1 1)}] + skolem:lemma5645 + skolem:lemma5646 + [ a r:Fact; r:gives {(4311 1134) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3411]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1134]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3410 a r:Inference; + r:gives { + 3412 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3412 math:notEqualTo 0}] + skolem:lemma6063 + [ a r:Fact; r:gives {((3 4 1 2) "=<") list:sort (1 2 3 4)}] + [ a r:Fact; r:gives {((3 4 1 2) ">=") list:sort (4 3 2 1)}] + skolem:lemma4280 + skolem:lemma4281 + [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3412]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3411 a r:Inference; + r:gives { + 3413 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3413 math:notEqualTo 0}] + skolem:lemma6064 + [ a r:Fact; r:gives {((3 4 1 3) "=<") list:sort (1 3 3 4)}] + [ a r:Fact; r:gives {((3 4 1 3) ">=") list:sort (4 3 3 1)}] + skolem:lemma5679 + skolem:lemma5680 + [ a r:Fact; r:gives {(4331 1334) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3413]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3412 a r:Inference; + r:gives { + 3414 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3414 math:notEqualTo 0}] + skolem:lemma6065 + [ a r:Fact; r:gives {((3 4 1 4) "=<") list:sort (1 3 4 4)}] + [ a r:Fact; r:gives {((3 4 1 4) ">=") list:sort (4 4 3 1)}] + skolem:lemma5701 + skolem:lemma5702 + [ a r:Fact; r:gives {(4431 1344) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3414]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 1 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3413 a r:Inference; + r:gives { + 3415 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3415 math:notEqualTo 0}] + skolem:lemma6066 + [ a r:Fact; r:gives {((3 4 1 5) "=<") list:sort (1 3 4 5)}] + [ a r:Fact; r:gives {((3 4 1 5) ">=") list:sort (5 4 3 1)}] + skolem:lemma5704 + skolem:lemma5705 + [ a r:Fact; r:gives {(5431 1345) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3415]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 1 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3414 a r:Inference; + r:gives { + 3416 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3416 math:notEqualTo 0}] + skolem:lemma6067 + [ a r:Fact; r:gives {((3 4 1 6) "=<") list:sort (1 3 4 6)}] + [ a r:Fact; r:gives {((3 4 1 6) ">=") list:sort (6 4 3 1)}] + skolem:lemma5707 + skolem:lemma5708 + [ a r:Fact; r:gives {(6431 1346) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3416]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 1 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3415 a r:Inference; + r:gives { + 3417 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3417 math:notEqualTo 0}] + skolem:lemma6068 + [ a r:Fact; r:gives {((3 4 1 7) "=<") list:sort (1 3 4 7)}] + [ a r:Fact; r:gives {((3 4 1 7) ">=") list:sort (7 4 3 1)}] + skolem:lemma5710 + skolem:lemma5711 + [ a r:Fact; r:gives {(7431 1347) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3417]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 1 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3416 a r:Inference; + r:gives { + 3418 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3418 math:notEqualTo 0}] + skolem:lemma6069 + [ a r:Fact; r:gives {((3 4 1 8) "=<") list:sort (1 3 4 8)}] + [ a r:Fact; r:gives {((3 4 1 8) ">=") list:sort (8 4 3 1)}] + skolem:lemma5713 + skolem:lemma5714 + [ a r:Fact; r:gives {(8431 1348) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3418]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 1 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3417 a r:Inference; + r:gives { + 3419 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3419 math:notEqualTo 0}] + skolem:lemma6070 + [ a r:Fact; r:gives {((3 4 1 9) "=<") list:sort (1 3 4 9)}] + [ a r:Fact; r:gives {((3 4 1 9) ">=") list:sort (9 4 3 1)}] + skolem:lemma5716 + skolem:lemma5717 + [ a r:Fact; r:gives {(9431 1349) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3419]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 1 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3418 a r:Inference; + r:gives { + 3420 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3420 math:notEqualTo 0}] + skolem:lemma6071 + [ a r:Fact; r:gives {((3 4 2 0) "=<") list:sort (0 2 3 4)}] + [ a r:Fact; r:gives {((3 4 2 0) ">=") list:sort (4 3 2 0)}] + skolem:lemma4090 + skolem:lemma4091 + [ a r:Fact; r:gives {(4320 234) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3419 a r:Inference; + r:gives { + 3421 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3421 math:notEqualTo 0}] + skolem:lemma6072 + [ a r:Fact; r:gives {((3 4 2 1) "=<") list:sort (1 2 3 4)}] + [ a r:Fact; r:gives {((3 4 2 1) ">=") list:sort (4 3 2 1)}] + skolem:lemma4280 + skolem:lemma4281 + [ a r:Fact; r:gives {(4321 1234) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3420 a r:Inference; + r:gives { + 3422 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3422 math:notEqualTo 0}] + skolem:lemma6073 + [ a r:Fact; r:gives {((3 4 2 2) "=<") list:sort (2 2 3 4)}] + [ a r:Fact; r:gives {((3 4 2 2) ">=") list:sort (4 3 2 2)}] + skolem:lemma4449 + skolem:lemma4450 + [ a r:Fact; r:gives {(4322 2234) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3421 a r:Inference; + r:gives { + 3423 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3423 math:notEqualTo 0}] + skolem:lemma6074 + [ a r:Fact; r:gives {((3 4 2 3) "=<") list:sort (2 3 3 4)}] + [ a r:Fact; r:gives {((3 4 2 3) ">=") list:sort (4 3 3 2)}] + skolem:lemma4605 + skolem:lemma4606 + [ a r:Fact; r:gives {(4332 2334) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3423]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3422 a r:Inference; + r:gives { + 3424 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3424 math:notEqualTo 0}] + skolem:lemma6075 + [ a r:Fact; r:gives {((3 4 2 4) "=<") list:sort (2 3 4 4)}] + [ a r:Fact; r:gives {((3 4 2 4) ">=") list:sort (4 4 3 2)}] + skolem:lemma4627 + skolem:lemma4628 + [ a r:Fact; r:gives {(4432 2344) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3424]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3423 a r:Inference; + r:gives { + 3425 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3425 math:notEqualTo 0}] + skolem:lemma6076 + [ a r:Fact; r:gives {((3 4 2 5) "=<") list:sort (2 3 4 5)}] + [ a r:Fact; r:gives {((3 4 2 5) ">=") list:sort (5 4 3 2)}] + skolem:lemma4630 + skolem:lemma4631 + [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3425]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3424 a r:Inference; + r:gives { + 3426 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3426 math:notEqualTo 0}] + skolem:lemma6077 + [ a r:Fact; r:gives {((3 4 2 6) "=<") list:sort (2 3 4 6)}] + [ a r:Fact; r:gives {((3 4 2 6) ">=") list:sort (6 4 3 2)}] + skolem:lemma4633 + skolem:lemma4634 + [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3426]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3425 a r:Inference; + r:gives { + 3427 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3427 math:notEqualTo 0}] + skolem:lemma6078 + [ a r:Fact; r:gives {((3 4 2 7) "=<") list:sort (2 3 4 7)}] + [ a r:Fact; r:gives {((3 4 2 7) ">=") list:sort (7 4 3 2)}] + skolem:lemma4636 + skolem:lemma4637 + [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3427]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3426 a r:Inference; + r:gives { + 3428 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3428 math:notEqualTo 0}] + skolem:lemma6079 + [ a r:Fact; r:gives {((3 4 2 8) "=<") list:sort (2 3 4 8)}] + [ a r:Fact; r:gives {((3 4 2 8) ">=") list:sort (8 4 3 2)}] + skolem:lemma4639 + skolem:lemma4640 + [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3428]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3427 a r:Inference; + r:gives { + 3429 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3429 math:notEqualTo 0}] + skolem:lemma6080 + [ a r:Fact; r:gives {((3 4 2 9) "=<") list:sort (2 3 4 9)}] + [ a r:Fact; r:gives {((3 4 2 9) ">=") list:sort (9 4 3 2)}] + skolem:lemma4642 + skolem:lemma4643 + [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3429]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3428 a r:Inference; + r:gives { + 3430 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3430 math:notEqualTo 0}] + skolem:lemma6081 + [ a r:Fact; r:gives {((3 4 3 0) "=<") list:sort (0 3 3 4)}] + [ a r:Fact; r:gives {((3 4 3 0) ">=") list:sort (4 3 3 0)}] + skolem:lemma5507 + skolem:lemma5508 + [ a r:Fact; r:gives {(4330 334) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3429 a r:Inference; + r:gives { + 3431 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3431 math:notEqualTo 0}] + skolem:lemma6082 + [ a r:Fact; r:gives {((3 4 3 1) "=<") list:sort (1 3 3 4)}] + [ a r:Fact; r:gives {((3 4 3 1) ">=") list:sort (4 3 3 1)}] + skolem:lemma5679 + skolem:lemma5680 + [ a r:Fact; r:gives {(4331 1334) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3430 a r:Inference; + r:gives { + 3432 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3432 math:notEqualTo 0}] + skolem:lemma6083 + [ a r:Fact; r:gives {((3 4 3 2) "=<") list:sort (2 3 3 4)}] + [ a r:Fact; r:gives {((3 4 3 2) ">=") list:sort (4 3 3 2)}] + skolem:lemma4605 + skolem:lemma4606 + [ a r:Fact; r:gives {(4332 2334) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3431 a r:Inference; + r:gives { + 3433 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3433 math:notEqualTo 0}] + skolem:lemma6084 + [ a r:Fact; r:gives {((3 4 3 3) "=<") list:sort (3 3 3 4)}] + [ a r:Fact; r:gives {((3 4 3 3) ">=") list:sort (4 3 3 3)}] + skolem:lemma5932 + skolem:lemma5933 + [ a r:Fact; r:gives {(4333 3334) math:difference 999}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 999 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 999 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3432 a r:Inference; + r:gives { + 3434 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3434 math:notEqualTo 0}] + skolem:lemma6085 + [ a r:Fact; r:gives {((3 4 3 4) "=<") list:sort (3 3 4 4)}] + [ a r:Fact; r:gives {((3 4 3 4) ">=") list:sort (4 4 3 3)}] + skolem:lemma5954 + skolem:lemma5955 + [ a r:Fact; r:gives {(4433 3344) math:difference 1089}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1089 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1089 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3434]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1089]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3433 a r:Inference; + r:gives { + 3435 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3435 math:notEqualTo 0}] + skolem:lemma6086 + [ a r:Fact; r:gives {((3 4 3 5) "=<") list:sort (3 3 4 5)}] + [ a r:Fact; r:gives {((3 4 3 5) ">=") list:sort (5 4 3 3)}] + skolem:lemma5957 + skolem:lemma5958 + [ a r:Fact; r:gives {(5433 3345) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3435]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3434 a r:Inference; + r:gives { + 3436 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3436 math:notEqualTo 0}] + skolem:lemma6087 + [ a r:Fact; r:gives {((3 4 3 6) "=<") list:sort (3 3 4 6)}] + [ a r:Fact; r:gives {((3 4 3 6) ">=") list:sort (6 4 3 3)}] + skolem:lemma5960 + skolem:lemma5961 + [ a r:Fact; r:gives {(6433 3346) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3436]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3435 a r:Inference; + r:gives { + 3437 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3437 math:notEqualTo 0}] + skolem:lemma6088 + [ a r:Fact; r:gives {((3 4 3 7) "=<") list:sort (3 3 4 7)}] + [ a r:Fact; r:gives {((3 4 3 7) ">=") list:sort (7 4 3 3)}] + skolem:lemma5963 + skolem:lemma5964 + [ a r:Fact; r:gives {(7433 3347) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3437]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3436 a r:Inference; + r:gives { + 3438 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3438 math:notEqualTo 0}] + skolem:lemma6089 + [ a r:Fact; r:gives {((3 4 3 8) "=<") list:sort (3 3 4 8)}] + [ a r:Fact; r:gives {((3 4 3 8) ">=") list:sort (8 4 3 3)}] + skolem:lemma5966 + skolem:lemma5967 + [ a r:Fact; r:gives {(8433 3348) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3438]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3437 a r:Inference; + r:gives { + 3439 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3439 math:notEqualTo 0}] + skolem:lemma6090 + [ a r:Fact; r:gives {((3 4 3 9) "=<") list:sort (3 3 4 9)}] + [ a r:Fact; r:gives {((3 4 3 9) ">=") list:sort (9 4 3 3)}] + skolem:lemma5969 + skolem:lemma5970 + [ a r:Fact; r:gives {(9433 3349) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3439]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3438 a r:Inference; + r:gives { + 3440 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3440 math:notEqualTo 0}] + skolem:lemma6091 + [ a r:Fact; r:gives {((3 4 4 0) "=<") list:sort (0 3 4 4)}] + [ a r:Fact; r:gives {((3 4 4 0) ">=") list:sort (4 4 3 0)}] + skolem:lemma5529 + skolem:lemma5530 + [ a r:Fact; r:gives {(4430 344) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3440]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 4 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3439 a r:Inference; + r:gives { + 3441 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3441 math:notEqualTo 0}] + skolem:lemma6092 + [ a r:Fact; r:gives {((3 4 4 1) "=<") list:sort (1 3 4 4)}] + [ a r:Fact; r:gives {((3 4 4 1) ">=") list:sort (4 4 3 1)}] + skolem:lemma5701 + skolem:lemma5702 + [ a r:Fact; r:gives {(4431 1344) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3441]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 4 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3440 a r:Inference; + r:gives { + 3442 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3442 math:notEqualTo 0}] + skolem:lemma6093 + [ a r:Fact; r:gives {((3 4 4 2) "=<") list:sort (2 3 4 4)}] + [ a r:Fact; r:gives {((3 4 4 2) ">=") list:sort (4 4 3 2)}] + skolem:lemma4627 + skolem:lemma4628 + [ a r:Fact; r:gives {(4432 2344) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3441 a r:Inference; + r:gives { + 3443 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3443 math:notEqualTo 0}] + skolem:lemma6094 + [ a r:Fact; r:gives {((3 4 4 3) "=<") list:sort (3 3 4 4)}] + [ a r:Fact; r:gives {((3 4 4 3) ">=") list:sort (4 4 3 3)}] + skolem:lemma5954 + skolem:lemma5955 + [ a r:Fact; r:gives {(4433 3344) math:difference 1089}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1089 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1089 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1089]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3442 a r:Inference; + r:gives { + 3444 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3444 math:notEqualTo 0}] + skolem:lemma6095 + [ a r:Fact; r:gives {((3 4 4 4) "=<") list:sort (3 4 4 4)}] + [ a r:Fact; r:gives {((3 4 4 4) ">=") list:sort (4 4 4 3)}] + skolem:lemma6096 + skolem:lemma6097 + [ a r:Fact; r:gives {(4443 3444) math:difference 999}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 999 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 999 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (4 4 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3443 a r:Inference; + r:gives { + 3445 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3445 math:notEqualTo 0}] + skolem:lemma6098 + [ a r:Fact; r:gives {((3 4 4 5) "=<") list:sort (3 4 4 5)}] + [ a r:Fact; r:gives {((3 4 4 5) ">=") list:sort (5 4 4 3)}] + skolem:lemma6099 + skolem:lemma6100 + [ a r:Fact; r:gives {(5443 3445) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3445]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3445]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3444 a r:Inference; + r:gives { + 3446 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3446 math:notEqualTo 0}] + skolem:lemma6101 + [ a r:Fact; r:gives {((3 4 4 6) "=<") list:sort (3 4 4 6)}] + [ a r:Fact; r:gives {((3 4 4 6) ">=") list:sort (6 4 4 3)}] + skolem:lemma6102 + skolem:lemma6103 + [ a r:Fact; r:gives {(6443 3446) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3446]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3446]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3445 a r:Inference; + r:gives { + 3447 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3447 math:notEqualTo 0}] + skolem:lemma6104 + [ a r:Fact; r:gives {((3 4 4 7) "=<") list:sort (3 4 4 7)}] + [ a r:Fact; r:gives {((3 4 4 7) ">=") list:sort (7 4 4 3)}] + skolem:lemma6105 + skolem:lemma6106 + [ a r:Fact; r:gives {(7443 3447) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3447]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3447]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3446 a r:Inference; + r:gives { + 3448 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3448 math:notEqualTo 0}] + skolem:lemma6107 + [ a r:Fact; r:gives {((3 4 4 8) "=<") list:sort (3 4 4 8)}] + [ a r:Fact; r:gives {((3 4 4 8) ">=") list:sort (8 4 4 3)}] + skolem:lemma6108 + skolem:lemma6109 + [ a r:Fact; r:gives {(8443 3448) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3448]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3448]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3447 a r:Inference; + r:gives { + 3449 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3449 math:notEqualTo 0}] + skolem:lemma6110 + [ a r:Fact; r:gives {((3 4 4 9) "=<") list:sort (3 4 4 9)}] + [ a r:Fact; r:gives {((3 4 4 9) ">=") list:sort (9 4 4 3)}] + skolem:lemma6111 + skolem:lemma6112 + [ a r:Fact; r:gives {(9443 3449) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3449]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3449]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3448 a r:Inference; + r:gives { + 3450 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3450 math:notEqualTo 0}] + skolem:lemma6113 + [ a r:Fact; r:gives {((3 4 5 0) "=<") list:sort (0 3 4 5)}] + [ a r:Fact; r:gives {((3 4 5 0) ">=") list:sort (5 4 3 0)}] + skolem:lemma5532 + skolem:lemma5533 + [ a r:Fact; r:gives {(5430 345) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3450]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 5 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3449 a r:Inference; + r:gives { + 3451 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3451 math:notEqualTo 0}] + skolem:lemma6114 + [ a r:Fact; r:gives {((3 4 5 1) "=<") list:sort (1 3 4 5)}] + [ a r:Fact; r:gives {((3 4 5 1) ">=") list:sort (5 4 3 1)}] + skolem:lemma5704 + skolem:lemma5705 + [ a r:Fact; r:gives {(5431 1345) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3451]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 5 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3450 a r:Inference; + r:gives { + 3452 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3452 math:notEqualTo 0}] + skolem:lemma6115 + [ a r:Fact; r:gives {((3 4 5 2) "=<") list:sort (2 3 4 5)}] + [ a r:Fact; r:gives {((3 4 5 2) ">=") list:sort (5 4 3 2)}] + skolem:lemma4630 + skolem:lemma4631 + [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3452]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3451 a r:Inference; + r:gives { + 3453 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3453 math:notEqualTo 0}] + skolem:lemma6116 + [ a r:Fact; r:gives {((3 4 5 3) "=<") list:sort (3 3 4 5)}] + [ a r:Fact; r:gives {((3 4 5 3) ">=") list:sort (5 4 3 3)}] + skolem:lemma5957 + skolem:lemma5958 + [ a r:Fact; r:gives {(5433 3345) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3453]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3452 a r:Inference; + r:gives { + 3454 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3454 math:notEqualTo 0}] + skolem:lemma6117 + [ a r:Fact; r:gives {((3 4 5 4) "=<") list:sort (3 4 4 5)}] + [ a r:Fact; r:gives {((3 4 5 4) ">=") list:sort (5 4 4 3)}] + skolem:lemma6099 + skolem:lemma6100 + [ a r:Fact; r:gives {(5443 3445) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3454]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 5 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3445]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3453 a r:Inference; + r:gives { + 3455 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3455 math:notEqualTo 0}] + skolem:lemma6118 + [ a r:Fact; r:gives {((3 4 5 5) "=<") list:sort (3 4 5 5)}] + [ a r:Fact; r:gives {((3 4 5 5) ">=") list:sort (5 5 4 3)}] + skolem:lemma6119 + skolem:lemma6120 + [ a r:Fact; r:gives {(5543 3455) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3455]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3455]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3454 a r:Inference; + r:gives { + 3456 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3456 math:notEqualTo 0}] + skolem:lemma6121 + [ a r:Fact; r:gives {((3 4 5 6) "=<") list:sort (3 4 5 6)}] + [ a r:Fact; r:gives {((3 4 5 6) ">=") list:sort (6 5 4 3)}] + skolem:lemma6122 + skolem:lemma6123 + [ a r:Fact; r:gives {(6543 3456) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3455 a r:Inference; + r:gives { + 3457 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3457 math:notEqualTo 0}] + skolem:lemma6124 + [ a r:Fact; r:gives {((3 4 5 7) "=<") list:sort (3 4 5 7)}] + [ a r:Fact; r:gives {((3 4 5 7) ">=") list:sort (7 5 4 3)}] + skolem:lemma6125 + skolem:lemma6126 + [ a r:Fact; r:gives {(7543 3457) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3457]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3457]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3456 a r:Inference; + r:gives { + 3458 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3458 math:notEqualTo 0}] + skolem:lemma6127 + [ a r:Fact; r:gives {((3 4 5 8) "=<") list:sort (3 4 5 8)}] + [ a r:Fact; r:gives {((3 4 5 8) ">=") list:sort (8 5 4 3)}] + skolem:lemma6128 + skolem:lemma6129 + [ a r:Fact; r:gives {(8543 3458) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3458]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3458]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3457 a r:Inference; + r:gives { + 3459 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3459 math:notEqualTo 0}] + skolem:lemma6130 + [ a r:Fact; r:gives {((3 4 5 9) "=<") list:sort (3 4 5 9)}] + [ a r:Fact; r:gives {((3 4 5 9) ">=") list:sort (9 5 4 3)}] + skolem:lemma6131 + skolem:lemma6132 + [ a r:Fact; r:gives {(9543 3459) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3459]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3459]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3458 a r:Inference; + r:gives { + 3460 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3460 math:notEqualTo 0}] + skolem:lemma6133 + [ a r:Fact; r:gives {((3 4 6 0) "=<") list:sort (0 3 4 6)}] + [ a r:Fact; r:gives {((3 4 6 0) ">=") list:sort (6 4 3 0)}] + skolem:lemma5535 + skolem:lemma5536 + [ a r:Fact; r:gives {(6430 346) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3460]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 6 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3459 a r:Inference; + r:gives { + 3461 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3461 math:notEqualTo 0}] + skolem:lemma6134 + [ a r:Fact; r:gives {((3 4 6 1) "=<") list:sort (1 3 4 6)}] + [ a r:Fact; r:gives {((3 4 6 1) ">=") list:sort (6 4 3 1)}] + skolem:lemma5707 + skolem:lemma5708 + [ a r:Fact; r:gives {(6431 1346) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3461]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 6 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3460 a r:Inference; + r:gives { + 3462 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3462 math:notEqualTo 0}] + skolem:lemma6135 + [ a r:Fact; r:gives {((3 4 6 2) "=<") list:sort (2 3 4 6)}] + [ a r:Fact; r:gives {((3 4 6 2) ">=") list:sort (6 4 3 2)}] + skolem:lemma4633 + skolem:lemma4634 + [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3462]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3461 a r:Inference; + r:gives { + 3463 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3463 math:notEqualTo 0}] + skolem:lemma6136 + [ a r:Fact; r:gives {((3 4 6 3) "=<") list:sort (3 3 4 6)}] + [ a r:Fact; r:gives {((3 4 6 3) ">=") list:sort (6 4 3 3)}] + skolem:lemma5960 + skolem:lemma5961 + [ a r:Fact; r:gives {(6433 3346) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3463]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3462 a r:Inference; + r:gives { + 3464 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3464 math:notEqualTo 0}] + skolem:lemma6137 + [ a r:Fact; r:gives {((3 4 6 4) "=<") list:sort (3 4 4 6)}] + [ a r:Fact; r:gives {((3 4 6 4) ">=") list:sort (6 4 4 3)}] + skolem:lemma6102 + skolem:lemma6103 + [ a r:Fact; r:gives {(6443 3446) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3464]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 6 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3446]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3463 a r:Inference; + r:gives { + 3465 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3465 math:notEqualTo 0}] + skolem:lemma6138 + [ a r:Fact; r:gives {((3 4 6 5) "=<") list:sort (3 4 5 6)}] + [ a r:Fact; r:gives {((3 4 6 5) ">=") list:sort (6 5 4 3)}] + skolem:lemma6122 + skolem:lemma6123 + [ a r:Fact; r:gives {(6543 3456) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3465]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 6 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3464 a r:Inference; + r:gives { + 3466 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3466 math:notEqualTo 0}] + skolem:lemma6139 + [ a r:Fact; r:gives {((3 4 6 6) "=<") list:sort (3 4 6 6)}] + [ a r:Fact; r:gives {((3 4 6 6) ">=") list:sort (6 6 4 3)}] + skolem:lemma6140 + skolem:lemma6141 + [ a r:Fact; r:gives {(6643 3466) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3466]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3466]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3465 a r:Inference; + r:gives { + 3467 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3467 math:notEqualTo 0}] + skolem:lemma6142 + [ a r:Fact; r:gives {((3 4 6 7) "=<") list:sort (3 4 6 7)}] + [ a r:Fact; r:gives {((3 4 6 7) ">=") list:sort (7 6 4 3)}] + skolem:lemma6143 + skolem:lemma6144 + [ a r:Fact; r:gives {(7643 3467) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3467]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3467]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3466 a r:Inference; + r:gives { + 3468 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3468 math:notEqualTo 0}] + skolem:lemma6145 + [ a r:Fact; r:gives {((3 4 6 8) "=<") list:sort (3 4 6 8)}] + [ a r:Fact; r:gives {((3 4 6 8) ">=") list:sort (8 6 4 3)}] + skolem:lemma6146 + skolem:lemma6147 + [ a r:Fact; r:gives {(8643 3468) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3468]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3468]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3467 a r:Inference; + r:gives { + 3469 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3469 math:notEqualTo 0}] + skolem:lemma6148 + [ a r:Fact; r:gives {((3 4 6 9) "=<") list:sort (3 4 6 9)}] + [ a r:Fact; r:gives {((3 4 6 9) ">=") list:sort (9 6 4 3)}] + skolem:lemma6149 + skolem:lemma6150 + [ a r:Fact; r:gives {(9643 3469) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3469]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3469]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3468 a r:Inference; + r:gives { + 3470 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3470 math:notEqualTo 0}] + skolem:lemma6151 + [ a r:Fact; r:gives {((3 4 7 0) "=<") list:sort (0 3 4 7)}] + [ a r:Fact; r:gives {((3 4 7 0) ">=") list:sort (7 4 3 0)}] + skolem:lemma5538 + skolem:lemma5539 + [ a r:Fact; r:gives {(7430 347) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3470]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 7 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3469 a r:Inference; + r:gives { + 3471 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3471 math:notEqualTo 0}] + skolem:lemma6152 + [ a r:Fact; r:gives {((3 4 7 1) "=<") list:sort (1 3 4 7)}] + [ a r:Fact; r:gives {((3 4 7 1) ">=") list:sort (7 4 3 1)}] + skolem:lemma5710 + skolem:lemma5711 + [ a r:Fact; r:gives {(7431 1347) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3471]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 7 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3470 a r:Inference; + r:gives { + 3472 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3472 math:notEqualTo 0}] + skolem:lemma6153 + [ a r:Fact; r:gives {((3 4 7 2) "=<") list:sort (2 3 4 7)}] + [ a r:Fact; r:gives {((3 4 7 2) ">=") list:sort (7 4 3 2)}] + skolem:lemma4636 + skolem:lemma4637 + [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3472]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3471 a r:Inference; + r:gives { + 3473 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3473 math:notEqualTo 0}] + skolem:lemma6154 + [ a r:Fact; r:gives {((3 4 7 3) "=<") list:sort (3 3 4 7)}] + [ a r:Fact; r:gives {((3 4 7 3) ">=") list:sort (7 4 3 3)}] + skolem:lemma5963 + skolem:lemma5964 + [ a r:Fact; r:gives {(7433 3347) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3473]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3472 a r:Inference; + r:gives { + 3474 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3474 math:notEqualTo 0}] + skolem:lemma6155 + [ a r:Fact; r:gives {((3 4 7 4) "=<") list:sort (3 4 4 7)}] + [ a r:Fact; r:gives {((3 4 7 4) ">=") list:sort (7 4 4 3)}] + skolem:lemma6105 + skolem:lemma6106 + [ a r:Fact; r:gives {(7443 3447) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3474]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 7 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3447]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3473 a r:Inference; + r:gives { + 3475 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3475 math:notEqualTo 0}] + skolem:lemma6156 + [ a r:Fact; r:gives {((3 4 7 5) "=<") list:sort (3 4 5 7)}] + [ a r:Fact; r:gives {((3 4 7 5) ">=") list:sort (7 5 4 3)}] + skolem:lemma6125 + skolem:lemma6126 + [ a r:Fact; r:gives {(7543 3457) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3475]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 7 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3457]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3474 a r:Inference; + r:gives { + 3476 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3476 math:notEqualTo 0}] + skolem:lemma6157 + [ a r:Fact; r:gives {((3 4 7 6) "=<") list:sort (3 4 6 7)}] + [ a r:Fact; r:gives {((3 4 7 6) ">=") list:sort (7 6 4 3)}] + skolem:lemma6143 + skolem:lemma6144 + [ a r:Fact; r:gives {(7643 3467) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3476]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 7 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3467]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3475 a r:Inference; + r:gives { + 3477 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3477 math:notEqualTo 0}] + skolem:lemma6158 + [ a r:Fact; r:gives {((3 4 7 7) "=<") list:sort (3 4 7 7)}] + [ a r:Fact; r:gives {((3 4 7 7) ">=") list:sort (7 7 4 3)}] + skolem:lemma6159 + skolem:lemma6160 + [ a r:Fact; r:gives {(7743 3477) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3477]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3477]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3476 a r:Inference; + r:gives { + 3478 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3478 math:notEqualTo 0}] + skolem:lemma6161 + [ a r:Fact; r:gives {((3 4 7 8) "=<") list:sort (3 4 7 8)}] + [ a r:Fact; r:gives {((3 4 7 8) ">=") list:sort (8 7 4 3)}] + skolem:lemma6162 + skolem:lemma6163 + [ a r:Fact; r:gives {(8743 3478) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3478]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3478]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3477 a r:Inference; + r:gives { + 3479 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3479 math:notEqualTo 0}] + skolem:lemma6164 + [ a r:Fact; r:gives {((3 4 7 9) "=<") list:sort (3 4 7 9)}] + [ a r:Fact; r:gives {((3 4 7 9) ">=") list:sort (9 7 4 3)}] + skolem:lemma6165 + skolem:lemma6166 + [ a r:Fact; r:gives {(9743 3479) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3479]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3479]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3478 a r:Inference; + r:gives { + 3480 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3480 math:notEqualTo 0}] + skolem:lemma6167 + [ a r:Fact; r:gives {((3 4 8 0) "=<") list:sort (0 3 4 8)}] + [ a r:Fact; r:gives {((3 4 8 0) ">=") list:sort (8 4 3 0)}] + skolem:lemma5541 + skolem:lemma5542 + [ a r:Fact; r:gives {(8430 348) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3480]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 8 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3479 a r:Inference; + r:gives { + 3481 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3481 math:notEqualTo 0}] + skolem:lemma6168 + [ a r:Fact; r:gives {((3 4 8 1) "=<") list:sort (1 3 4 8)}] + [ a r:Fact; r:gives {((3 4 8 1) ">=") list:sort (8 4 3 1)}] + skolem:lemma5713 + skolem:lemma5714 + [ a r:Fact; r:gives {(8431 1348) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3481]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 8 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3480 a r:Inference; + r:gives { + 3482 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3482 math:notEqualTo 0}] + skolem:lemma6169 + [ a r:Fact; r:gives {((3 4 8 2) "=<") list:sort (2 3 4 8)}] + [ a r:Fact; r:gives {((3 4 8 2) ">=") list:sort (8 4 3 2)}] + skolem:lemma4639 + skolem:lemma4640 + [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3482]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3481 a r:Inference; + r:gives { + 3483 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3483 math:notEqualTo 0}] + skolem:lemma6170 + [ a r:Fact; r:gives {((3 4 8 3) "=<") list:sort (3 3 4 8)}] + [ a r:Fact; r:gives {((3 4 8 3) ">=") list:sort (8 4 3 3)}] + skolem:lemma5966 + skolem:lemma5967 + [ a r:Fact; r:gives {(8433 3348) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3483]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3482 a r:Inference; + r:gives { + 3484 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3484 math:notEqualTo 0}] + skolem:lemma6171 + [ a r:Fact; r:gives {((3 4 8 4) "=<") list:sort (3 4 4 8)}] + [ a r:Fact; r:gives {((3 4 8 4) ">=") list:sort (8 4 4 3)}] + skolem:lemma6108 + skolem:lemma6109 + [ a r:Fact; r:gives {(8443 3448) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3484]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 8 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3448]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3483 a r:Inference; + r:gives { + 3485 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3485 math:notEqualTo 0}] + skolem:lemma6172 + [ a r:Fact; r:gives {((3 4 8 5) "=<") list:sort (3 4 5 8)}] + [ a r:Fact; r:gives {((3 4 8 5) ">=") list:sort (8 5 4 3)}] + skolem:lemma6128 + skolem:lemma6129 + [ a r:Fact; r:gives {(8543 3458) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3485]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 8 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3458]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3484 a r:Inference; + r:gives { + 3486 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3486 math:notEqualTo 0}] + skolem:lemma6173 + [ a r:Fact; r:gives {((3 4 8 6) "=<") list:sort (3 4 6 8)}] + [ a r:Fact; r:gives {((3 4 8 6) ">=") list:sort (8 6 4 3)}] + skolem:lemma6146 + skolem:lemma6147 + [ a r:Fact; r:gives {(8643 3468) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3486]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 8 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3468]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3485 a r:Inference; + r:gives { + 3487 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3487 math:notEqualTo 0}] + skolem:lemma6174 + [ a r:Fact; r:gives {((3 4 8 7) "=<") list:sort (3 4 7 8)}] + [ a r:Fact; r:gives {((3 4 8 7) ">=") list:sort (8 7 4 3)}] + skolem:lemma6162 + skolem:lemma6163 + [ a r:Fact; r:gives {(8743 3478) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3487]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 8 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3478]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3486 a r:Inference; + r:gives { + 3488 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3488 math:notEqualTo 0}] + skolem:lemma6175 + [ a r:Fact; r:gives {((3 4 8 8) "=<") list:sort (3 4 8 8)}] + [ a r:Fact; r:gives {((3 4 8 8) ">=") list:sort (8 8 4 3)}] + skolem:lemma6176 + skolem:lemma6177 + [ a r:Fact; r:gives {(8843 3488) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3488]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3488]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8843]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3487 a r:Inference; + r:gives { + 3489 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3489 math:notEqualTo 0}] + skolem:lemma6178 + [ a r:Fact; r:gives {((3 4 8 9) "=<") list:sort (3 4 8 9)}] + [ a r:Fact; r:gives {((3 4 8 9) ">=") list:sort (9 8 4 3)}] + skolem:lemma6179 + skolem:lemma6180 + [ a r:Fact; r:gives {(9843 3489) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3489]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3489]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9843]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3488 a r:Inference; + r:gives { + 3490 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3490 math:notEqualTo 0}] + skolem:lemma6181 + [ a r:Fact; r:gives {((3 4 9 0) "=<") list:sort (0 3 4 9)}] + [ a r:Fact; r:gives {((3 4 9 0) ">=") list:sort (9 4 3 0)}] + skolem:lemma5544 + skolem:lemma5545 + [ a r:Fact; r:gives {(9430 349) math:difference 9081}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9081 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 9081 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3490]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 9 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3489 a r:Inference; + r:gives { + 3491 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3491 math:notEqualTo 0}] + skolem:lemma6182 + [ a r:Fact; r:gives {((3 4 9 1) "=<") list:sort (1 3 4 9)}] + [ a r:Fact; r:gives {((3 4 9 1) ">=") list:sort (9 4 3 1)}] + skolem:lemma5716 + skolem:lemma5717 + [ a r:Fact; r:gives {(9431 1349) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3491]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 9 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3490 a r:Inference; + r:gives { + 3492 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3492 math:notEqualTo 0}] + skolem:lemma6183 + [ a r:Fact; r:gives {((3 4 9 2) "=<") list:sort (2 3 4 9)}] + [ a r:Fact; r:gives {((3 4 9 2) ">=") list:sort (9 4 3 2)}] + skolem:lemma4642 + skolem:lemma4643 + [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3492]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 9 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3491 a r:Inference; + r:gives { + 3493 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3493 math:notEqualTo 0}] + skolem:lemma6184 + [ a r:Fact; r:gives {((3 4 9 3) "=<") list:sort (3 3 4 9)}] + [ a r:Fact; r:gives {((3 4 9 3) ">=") list:sort (9 4 3 3)}] + skolem:lemma5969 + skolem:lemma5970 + [ a r:Fact; r:gives {(9433 3349) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3493]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 9 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3492 a r:Inference; + r:gives { + 3494 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3494 math:notEqualTo 0}] + skolem:lemma6185 + [ a r:Fact; r:gives {((3 4 9 4) "=<") list:sort (3 4 4 9)}] + [ a r:Fact; r:gives {((3 4 9 4) ">=") list:sort (9 4 4 3)}] + skolem:lemma6111 + skolem:lemma6112 + [ a r:Fact; r:gives {(9443 3449) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3494]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 9 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3449]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3493 a r:Inference; + r:gives { + 3495 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3495 math:notEqualTo 0}] + skolem:lemma6186 + [ a r:Fact; r:gives {((3 4 9 5) "=<") list:sort (3 4 5 9)}] + [ a r:Fact; r:gives {((3 4 9 5) ">=") list:sort (9 5 4 3)}] + skolem:lemma6131 + skolem:lemma6132 + [ a r:Fact; r:gives {(9543 3459) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3495]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 9 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3459]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3494 a r:Inference; + r:gives { + 3496 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3496 math:notEqualTo 0}] + skolem:lemma6187 + [ a r:Fact; r:gives {((3 4 9 6) "=<") list:sort (3 4 6 9)}] + [ a r:Fact; r:gives {((3 4 9 6) ">=") list:sort (9 6 4 3)}] + skolem:lemma6149 + skolem:lemma6150 + [ a r:Fact; r:gives {(9643 3469) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3496]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 9 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3469]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3495 a r:Inference; + r:gives { + 3497 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3497 math:notEqualTo 0}] + skolem:lemma6188 + [ a r:Fact; r:gives {((3 4 9 7) "=<") list:sort (3 4 7 9)}] + [ a r:Fact; r:gives {((3 4 9 7) ">=") list:sort (9 7 4 3)}] + skolem:lemma6165 + skolem:lemma6166 + [ a r:Fact; r:gives {(9743 3479) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3497]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 9 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3479]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3496 a r:Inference; + r:gives { + 3498 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3498 math:notEqualTo 0}] + skolem:lemma6189 + [ a r:Fact; r:gives {((3 4 9 8) "=<") list:sort (3 4 8 9)}] + [ a r:Fact; r:gives {((3 4 9 8) ">=") list:sort (9 8 4 3)}] + skolem:lemma6179 + skolem:lemma6180 + [ a r:Fact; r:gives {(9843 3489) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3498]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 9 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3489]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9843]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3497 a r:Inference; + r:gives { + 3499 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3499 math:notEqualTo 0}] + skolem:lemma6190 + [ a r:Fact; r:gives {((3 4 9 9) "=<") list:sort (3 4 9 9)}] + [ a r:Fact; r:gives {((3 4 9 9) ">=") list:sort (9 9 4 3)}] + skolem:lemma6191 + skolem:lemma6192 + [ a r:Fact; r:gives {(9943 3499) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3499]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 4 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3499]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9943]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3498 a r:Inference; + r:gives { + 3500 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3500 math:notEqualTo 0}] + skolem:lemma6193 + [ a r:Fact; r:gives {((3 5 0 0) "=<") list:sort (0 0 3 5)}] + [ a r:Fact; r:gives {((3 5 0 0) ">=") list:sort (5 3 0 0)}] + skolem:lemma5450 + skolem:lemma5451 + [ a r:Fact; r:gives {(5300 35) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 35]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3499 a r:Inference; + r:gives { + 3501 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3501 math:notEqualTo 0}] + skolem:lemma6194 + [ a r:Fact; r:gives {((3 5 0 1) "=<") list:sort (0 1 3 5)}] + [ a r:Fact; r:gives {((3 5 0 1) ">=") list:sort (5 3 1 0)}] + skolem:lemma5476 + skolem:lemma5477 + [ a r:Fact; r:gives {(5310 135) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3501]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 0 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 135]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3500 a r:Inference; + r:gives { + 3502 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3502 math:notEqualTo 0}] + skolem:lemma6195 + [ a r:Fact; r:gives {((3 5 0 2) "=<") list:sort (0 2 3 5)}] + [ a r:Fact; r:gives {((3 5 0 2) ">=") list:sort (5 3 2 0)}] + skolem:lemma4093 + skolem:lemma4094 + [ a r:Fact; r:gives {(5320 235) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3502]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 0 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3501 a r:Inference; + r:gives { + 3503 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3503 math:notEqualTo 0}] + skolem:lemma6196 + [ a r:Fact; r:gives {((3 5 0 3) "=<") list:sort (0 3 3 5)}] + [ a r:Fact; r:gives {((3 5 0 3) ">=") list:sort (5 3 3 0)}] + skolem:lemma5510 + skolem:lemma5511 + [ a r:Fact; r:gives {(5330 335) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3503]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 0 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3502 a r:Inference; + r:gives { + 3504 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3504 math:notEqualTo 0}] + skolem:lemma6197 + [ a r:Fact; r:gives {((3 5 0 4) "=<") list:sort (0 3 4 5)}] + [ a r:Fact; r:gives {((3 5 0 4) ">=") list:sort (5 4 3 0)}] + skolem:lemma5532 + skolem:lemma5533 + [ a r:Fact; r:gives {(5430 345) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3504]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 0 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3503 a r:Inference; + r:gives { + 3505 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3505 math:notEqualTo 0}] + skolem:lemma6198 + [ a r:Fact; r:gives {((3 5 0 5) "=<") list:sort (0 3 5 5)}] + [ a r:Fact; r:gives {((3 5 0 5) ">=") list:sort (5 5 3 0)}] + skolem:lemma5552 + skolem:lemma5553 + [ a r:Fact; r:gives {(5530 355) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3505]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 0 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3504 a r:Inference; + r:gives { + 3506 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3506 math:notEqualTo 0}] + skolem:lemma6199 + [ a r:Fact; r:gives {((3 5 0 6) "=<") list:sort (0 3 5 6)}] + [ a r:Fact; r:gives {((3 5 0 6) ">=") list:sort (6 5 3 0)}] + skolem:lemma5555 + skolem:lemma5556 + [ a r:Fact; r:gives {(6530 356) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3506]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 0 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3505 a r:Inference; + r:gives { + 3507 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3507 math:notEqualTo 0}] + skolem:lemma6200 + [ a r:Fact; r:gives {((3 5 0 7) "=<") list:sort (0 3 5 7)}] + [ a r:Fact; r:gives {((3 5 0 7) ">=") list:sort (7 5 3 0)}] + skolem:lemma5558 + skolem:lemma5559 + [ a r:Fact; r:gives {(7530 357) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3507]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 0 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3506 a r:Inference; + r:gives { + 3508 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3508 math:notEqualTo 0}] + skolem:lemma6201 + [ a r:Fact; r:gives {((3 5 0 8) "=<") list:sort (0 3 5 8)}] + [ a r:Fact; r:gives {((3 5 0 8) ">=") list:sort (8 5 3 0)}] + skolem:lemma5561 + skolem:lemma5562 + [ a r:Fact; r:gives {(8530 358) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3508]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 0 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3507 a r:Inference; + r:gives { + 3509 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3509 math:notEqualTo 0}] + skolem:lemma6202 + [ a r:Fact; r:gives {((3 5 0 9) "=<") list:sort (0 3 5 9)}] + [ a r:Fact; r:gives {((3 5 0 9) ">=") list:sort (9 5 3 0)}] + skolem:lemma5564 + skolem:lemma5565 + [ a r:Fact; r:gives {(9530 359) math:difference 9171}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9171 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9171 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3509]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 0 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3508 a r:Inference; + r:gives { + 3510 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3510 math:notEqualTo 0}] + skolem:lemma6203 + [ a r:Fact; r:gives {((3 5 1 0) "=<") list:sort (0 1 3 5)}] + [ a r:Fact; r:gives {((3 5 1 0) ">=") list:sort (5 3 1 0)}] + skolem:lemma5476 + skolem:lemma5477 + [ a r:Fact; r:gives {(5310 135) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3510]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 135]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3509 a r:Inference; + r:gives { + 3511 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3511 math:notEqualTo 0}] + skolem:lemma6204 + [ a r:Fact; r:gives {((3 5 1 1) "=<") list:sort (1 1 3 5)}] + [ a r:Fact; r:gives {((3 5 1 1) ">=") list:sort (5 3 1 1)}] + skolem:lemma5648 + skolem:lemma5649 + [ a r:Fact; r:gives {(5311 1135) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3511]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1135]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3510 a r:Inference; + r:gives { + 3512 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3512 math:notEqualTo 0}] + skolem:lemma6205 + [ a r:Fact; r:gives {((3 5 1 2) "=<") list:sort (1 2 3 5)}] + [ a r:Fact; r:gives {((3 5 1 2) ">=") list:sort (5 3 2 1)}] + skolem:lemma4283 + skolem:lemma4284 + [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3512]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3511 a r:Inference; + r:gives { + 3513 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3513 math:notEqualTo 0}] + skolem:lemma6206 + [ a r:Fact; r:gives {((3 5 1 3) "=<") list:sort (1 3 3 5)}] + [ a r:Fact; r:gives {((3 5 1 3) ">=") list:sort (5 3 3 1)}] + skolem:lemma5682 + skolem:lemma5683 + [ a r:Fact; r:gives {(5331 1335) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3513]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3512 a r:Inference; + r:gives { + 3514 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3514 math:notEqualTo 0}] + skolem:lemma6207 + [ a r:Fact; r:gives {((3 5 1 4) "=<") list:sort (1 3 4 5)}] + [ a r:Fact; r:gives {((3 5 1 4) ">=") list:sort (5 4 3 1)}] + skolem:lemma5704 + skolem:lemma5705 + [ a r:Fact; r:gives {(5431 1345) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3514]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 1 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3513 a r:Inference; + r:gives { + 3515 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3515 math:notEqualTo 0}] + skolem:lemma6208 + [ a r:Fact; r:gives {((3 5 1 5) "=<") list:sort (1 3 5 5)}] + [ a r:Fact; r:gives {((3 5 1 5) ">=") list:sort (5 5 3 1)}] + skolem:lemma5724 + skolem:lemma5725 + [ a r:Fact; r:gives {(5531 1355) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3515]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 1 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3514 a r:Inference; + r:gives { + 3516 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3516 math:notEqualTo 0}] + skolem:lemma6209 + [ a r:Fact; r:gives {((3 5 1 6) "=<") list:sort (1 3 5 6)}] + [ a r:Fact; r:gives {((3 5 1 6) ">=") list:sort (6 5 3 1)}] + skolem:lemma5727 + skolem:lemma5728 + [ a r:Fact; r:gives {(6531 1356) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3516]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 1 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3515 a r:Inference; + r:gives { + 3517 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3517 math:notEqualTo 0}] + skolem:lemma6210 + [ a r:Fact; r:gives {((3 5 1 7) "=<") list:sort (1 3 5 7)}] + [ a r:Fact; r:gives {((3 5 1 7) ">=") list:sort (7 5 3 1)}] + skolem:lemma5730 + skolem:lemma5731 + [ a r:Fact; r:gives {(7531 1357) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3517]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 1 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3516 a r:Inference; + r:gives { + 3518 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3518 math:notEqualTo 0}] + skolem:lemma6211 + [ a r:Fact; r:gives {((3 5 1 8) "=<") list:sort (1 3 5 8)}] + [ a r:Fact; r:gives {((3 5 1 8) ">=") list:sort (8 5 3 1)}] + skolem:lemma5733 + skolem:lemma5734 + [ a r:Fact; r:gives {(8531 1358) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3518]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 1 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3517 a r:Inference; + r:gives { + 3519 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3519 math:notEqualTo 0}] + skolem:lemma6212 + [ a r:Fact; r:gives {((3 5 1 9) "=<") list:sort (1 3 5 9)}] + [ a r:Fact; r:gives {((3 5 1 9) ">=") list:sort (9 5 3 1)}] + skolem:lemma5736 + skolem:lemma5737 + [ a r:Fact; r:gives {(9531 1359) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3519]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 1 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3518 a r:Inference; + r:gives { + 3520 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3520 math:notEqualTo 0}] + skolem:lemma6213 + [ a r:Fact; r:gives {((3 5 2 0) "=<") list:sort (0 2 3 5)}] + [ a r:Fact; r:gives {((3 5 2 0) ">=") list:sort (5 3 2 0)}] + skolem:lemma4093 + skolem:lemma4094 + [ a r:Fact; r:gives {(5320 235) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3519 a r:Inference; + r:gives { + 3521 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3521 math:notEqualTo 0}] + skolem:lemma6214 + [ a r:Fact; r:gives {((3 5 2 1) "=<") list:sort (1 2 3 5)}] + [ a r:Fact; r:gives {((3 5 2 1) ">=") list:sort (5 3 2 1)}] + skolem:lemma4283 + skolem:lemma4284 + [ a r:Fact; r:gives {(5321 1235) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3520 a r:Inference; + r:gives { + 3522 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3522 math:notEqualTo 0}] + skolem:lemma6215 + [ a r:Fact; r:gives {((3 5 2 2) "=<") list:sort (2 2 3 5)}] + [ a r:Fact; r:gives {((3 5 2 2) ">=") list:sort (5 3 2 2)}] + skolem:lemma4452 + skolem:lemma4453 + [ a r:Fact; r:gives {(5322 2235) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3521 a r:Inference; + r:gives { + 3523 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3523 math:notEqualTo 0}] + skolem:lemma6216 + [ a r:Fact; r:gives {((3 5 2 3) "=<") list:sort (2 3 3 5)}] + [ a r:Fact; r:gives {((3 5 2 3) ">=") list:sort (5 3 3 2)}] + skolem:lemma4608 + skolem:lemma4609 + [ a r:Fact; r:gives {(5332 2335) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3523]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3522 a r:Inference; + r:gives { + 3524 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3524 math:notEqualTo 0}] + skolem:lemma6217 + [ a r:Fact; r:gives {((3 5 2 4) "=<") list:sort (2 3 4 5)}] + [ a r:Fact; r:gives {((3 5 2 4) ">=") list:sort (5 4 3 2)}] + skolem:lemma4630 + skolem:lemma4631 + [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3524]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3523 a r:Inference; + r:gives { + 3525 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3525 math:notEqualTo 0}] + skolem:lemma6218 + [ a r:Fact; r:gives {((3 5 2 5) "=<") list:sort (2 3 5 5)}] + [ a r:Fact; r:gives {((3 5 2 5) ">=") list:sort (5 5 3 2)}] + skolem:lemma4650 + skolem:lemma4651 + [ a r:Fact; r:gives {(5532 2355) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3525]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3524 a r:Inference; + r:gives { + 3526 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3526 math:notEqualTo 0}] + skolem:lemma6219 + [ a r:Fact; r:gives {((3 5 2 6) "=<") list:sort (2 3 5 6)}] + [ a r:Fact; r:gives {((3 5 2 6) ">=") list:sort (6 5 3 2)}] + skolem:lemma4653 + skolem:lemma4654 + [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3526]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3525 a r:Inference; + r:gives { + 3527 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3527 math:notEqualTo 0}] + skolem:lemma6220 + [ a r:Fact; r:gives {((3 5 2 7) "=<") list:sort (2 3 5 7)}] + [ a r:Fact; r:gives {((3 5 2 7) ">=") list:sort (7 5 3 2)}] + skolem:lemma4656 + skolem:lemma4657 + [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3527]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3526 a r:Inference; + r:gives { + 3528 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3528 math:notEqualTo 0}] + skolem:lemma6221 + [ a r:Fact; r:gives {((3 5 2 8) "=<") list:sort (2 3 5 8)}] + [ a r:Fact; r:gives {((3 5 2 8) ">=") list:sort (8 5 3 2)}] + skolem:lemma4659 + skolem:lemma4660 + [ a r:Fact; r:gives {(8532 2358) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3528]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3527 a r:Inference; + r:gives { + 3529 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3529 math:notEqualTo 0}] + skolem:lemma6222 + [ a r:Fact; r:gives {((3 5 2 9) "=<") list:sort (2 3 5 9)}] + [ a r:Fact; r:gives {((3 5 2 9) ">=") list:sort (9 5 3 2)}] + skolem:lemma4662 + skolem:lemma4663 + [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3529]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3528 a r:Inference; + r:gives { + 3530 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3530 math:notEqualTo 0}] + skolem:lemma6223 + [ a r:Fact; r:gives {((3 5 3 0) "=<") list:sort (0 3 3 5)}] + [ a r:Fact; r:gives {((3 5 3 0) ">=") list:sort (5 3 3 0)}] + skolem:lemma5510 + skolem:lemma5511 + [ a r:Fact; r:gives {(5330 335) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3529 a r:Inference; + r:gives { + 3531 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3531 math:notEqualTo 0}] + skolem:lemma6224 + [ a r:Fact; r:gives {((3 5 3 1) "=<") list:sort (1 3 3 5)}] + [ a r:Fact; r:gives {((3 5 3 1) ">=") list:sort (5 3 3 1)}] + skolem:lemma5682 + skolem:lemma5683 + [ a r:Fact; r:gives {(5331 1335) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3530 a r:Inference; + r:gives { + 3532 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3532 math:notEqualTo 0}] + skolem:lemma6225 + [ a r:Fact; r:gives {((3 5 3 2) "=<") list:sort (2 3 3 5)}] + [ a r:Fact; r:gives {((3 5 3 2) ">=") list:sort (5 3 3 2)}] + skolem:lemma4608 + skolem:lemma4609 + [ a r:Fact; r:gives {(5332 2335) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3531 a r:Inference; + r:gives { + 3533 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3533 math:notEqualTo 0}] + skolem:lemma6226 + [ a r:Fact; r:gives {((3 5 3 3) "=<") list:sort (3 3 3 5)}] + [ a r:Fact; r:gives {((3 5 3 3) ">=") list:sort (5 3 3 3)}] + skolem:lemma5935 + skolem:lemma5936 + [ a r:Fact; r:gives {(5333 3335) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3532 a r:Inference; + r:gives { + 3534 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3534 math:notEqualTo 0}] + skolem:lemma6227 + [ a r:Fact; r:gives {((3 5 3 4) "=<") list:sort (3 3 4 5)}] + [ a r:Fact; r:gives {((3 5 3 4) ">=") list:sort (5 4 3 3)}] + skolem:lemma5957 + skolem:lemma5958 + [ a r:Fact; r:gives {(5433 3345) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3534]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3533 a r:Inference; + r:gives { + 3535 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3535 math:notEqualTo 0}] + skolem:lemma6228 + [ a r:Fact; r:gives {((3 5 3 5) "=<") list:sort (3 3 5 5)}] + [ a r:Fact; r:gives {((3 5 3 5) ">=") list:sort (5 5 3 3)}] + skolem:lemma5977 + skolem:lemma5978 + [ a r:Fact; r:gives {(5533 3355) math:difference 2178}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2178 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2178 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3535]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2178]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3534 a r:Inference; + r:gives { + 3536 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3536 math:notEqualTo 0}] + skolem:lemma6229 + [ a r:Fact; r:gives {((3 5 3 6) "=<") list:sort (3 3 5 6)}] + [ a r:Fact; r:gives {((3 5 3 6) ">=") list:sort (6 5 3 3)}] + skolem:lemma5980 + skolem:lemma5981 + [ a r:Fact; r:gives {(6533 3356) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3536]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3535 a r:Inference; + r:gives { + 3537 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3537 math:notEqualTo 0}] + skolem:lemma6230 + [ a r:Fact; r:gives {((3 5 3 7) "=<") list:sort (3 3 5 7)}] + [ a r:Fact; r:gives {((3 5 3 7) ">=") list:sort (7 5 3 3)}] + skolem:lemma5983 + skolem:lemma5984 + [ a r:Fact; r:gives {(7533 3357) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3537]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3536 a r:Inference; + r:gives { + 3538 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3538 math:notEqualTo 0}] + skolem:lemma6231 + [ a r:Fact; r:gives {((3 5 3 8) "=<") list:sort (3 3 5 8)}] + [ a r:Fact; r:gives {((3 5 3 8) ">=") list:sort (8 5 3 3)}] + skolem:lemma5986 + skolem:lemma5987 + [ a r:Fact; r:gives {(8533 3358) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3538]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3537 a r:Inference; + r:gives { + 3539 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3539 math:notEqualTo 0}] + skolem:lemma6232 + [ a r:Fact; r:gives {((3 5 3 9) "=<") list:sort (3 3 5 9)}] + [ a r:Fact; r:gives {((3 5 3 9) ">=") list:sort (9 5 3 3)}] + skolem:lemma5989 + skolem:lemma5990 + [ a r:Fact; r:gives {(9533 3359) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3539]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3538 a r:Inference; + r:gives { + 3540 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3540 math:notEqualTo 0}] + skolem:lemma6233 + [ a r:Fact; r:gives {((3 5 4 0) "=<") list:sort (0 3 4 5)}] + [ a r:Fact; r:gives {((3 5 4 0) ">=") list:sort (5 4 3 0)}] + skolem:lemma5532 + skolem:lemma5533 + [ a r:Fact; r:gives {(5430 345) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3540]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 4 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3539 a r:Inference; + r:gives { + 3541 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3541 math:notEqualTo 0}] + skolem:lemma6234 + [ a r:Fact; r:gives {((3 5 4 1) "=<") list:sort (1 3 4 5)}] + [ a r:Fact; r:gives {((3 5 4 1) ">=") list:sort (5 4 3 1)}] + skolem:lemma5704 + skolem:lemma5705 + [ a r:Fact; r:gives {(5431 1345) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3541]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 4 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3540 a r:Inference; + r:gives { + 3542 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3542 math:notEqualTo 0}] + skolem:lemma6235 + [ a r:Fact; r:gives {((3 5 4 2) "=<") list:sort (2 3 4 5)}] + [ a r:Fact; r:gives {((3 5 4 2) ">=") list:sort (5 4 3 2)}] + skolem:lemma4630 + skolem:lemma4631 + [ a r:Fact; r:gives {(5432 2345) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3541 a r:Inference; + r:gives { + 3543 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3543 math:notEqualTo 0}] + skolem:lemma6236 + [ a r:Fact; r:gives {((3 5 4 3) "=<") list:sort (3 3 4 5)}] + [ a r:Fact; r:gives {((3 5 4 3) ">=") list:sort (5 4 3 3)}] + skolem:lemma5957 + skolem:lemma5958 + [ a r:Fact; r:gives {(5433 3345) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3542 a r:Inference; + r:gives { + 3544 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3544 math:notEqualTo 0}] + skolem:lemma6237 + [ a r:Fact; r:gives {((3 5 4 4) "=<") list:sort (3 4 4 5)}] + [ a r:Fact; r:gives {((3 5 4 4) ">=") list:sort (5 4 4 3)}] + skolem:lemma6099 + skolem:lemma6100 + [ a r:Fact; r:gives {(5443 3445) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3544]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 4 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3445]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3543 a r:Inference; + r:gives { + 3545 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3545 math:notEqualTo 0}] + skolem:lemma6238 + [ a r:Fact; r:gives {((3 5 4 5) "=<") list:sort (3 4 5 5)}] + [ a r:Fact; r:gives {((3 5 4 5) ">=") list:sort (5 5 4 3)}] + skolem:lemma6119 + skolem:lemma6120 + [ a r:Fact; r:gives {(5543 3455) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3545]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3455]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3544 a r:Inference; + r:gives { + 3546 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3546 math:notEqualTo 0}] + skolem:lemma6239 + [ a r:Fact; r:gives {((3 5 4 6) "=<") list:sort (3 4 5 6)}] + [ a r:Fact; r:gives {((3 5 4 6) ">=") list:sort (6 5 4 3)}] + skolem:lemma6122 + skolem:lemma6123 + [ a r:Fact; r:gives {(6543 3456) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3546]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3545 a r:Inference; + r:gives { + 3547 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3547 math:notEqualTo 0}] + skolem:lemma6240 + [ a r:Fact; r:gives {((3 5 4 7) "=<") list:sort (3 4 5 7)}] + [ a r:Fact; r:gives {((3 5 4 7) ">=") list:sort (7 5 4 3)}] + skolem:lemma6125 + skolem:lemma6126 + [ a r:Fact; r:gives {(7543 3457) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3547]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3457]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3546 a r:Inference; + r:gives { + 3548 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3548 math:notEqualTo 0}] + skolem:lemma6241 + [ a r:Fact; r:gives {((3 5 4 8) "=<") list:sort (3 4 5 8)}] + [ a r:Fact; r:gives {((3 5 4 8) ">=") list:sort (8 5 4 3)}] + skolem:lemma6128 + skolem:lemma6129 + [ a r:Fact; r:gives {(8543 3458) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3548]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3458]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3547 a r:Inference; + r:gives { + 3549 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3549 math:notEqualTo 0}] + skolem:lemma6242 + [ a r:Fact; r:gives {((3 5 4 9) "=<") list:sort (3 4 5 9)}] + [ a r:Fact; r:gives {((3 5 4 9) ">=") list:sort (9 5 4 3)}] + skolem:lemma6131 + skolem:lemma6132 + [ a r:Fact; r:gives {(9543 3459) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3549]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3459]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3548 a r:Inference; + r:gives { + 3550 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3550 math:notEqualTo 0}] + skolem:lemma6243 + [ a r:Fact; r:gives {((3 5 5 0) "=<") list:sort (0 3 5 5)}] + [ a r:Fact; r:gives {((3 5 5 0) ">=") list:sort (5 5 3 0)}] + skolem:lemma5552 + skolem:lemma5553 + [ a r:Fact; r:gives {(5530 355) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3550]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 5 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3549 a r:Inference; + r:gives { + 3551 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3551 math:notEqualTo 0}] + skolem:lemma6244 + [ a r:Fact; r:gives {((3 5 5 1) "=<") list:sort (1 3 5 5)}] + [ a r:Fact; r:gives {((3 5 5 1) ">=") list:sort (5 5 3 1)}] + skolem:lemma5724 + skolem:lemma5725 + [ a r:Fact; r:gives {(5531 1355) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3551]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 5 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3550 a r:Inference; + r:gives { + 3552 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3552 math:notEqualTo 0}] + skolem:lemma6245 + [ a r:Fact; r:gives {((3 5 5 2) "=<") list:sort (2 3 5 5)}] + [ a r:Fact; r:gives {((3 5 5 2) ">=") list:sort (5 5 3 2)}] + skolem:lemma4650 + skolem:lemma4651 + [ a r:Fact; r:gives {(5532 2355) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3551 a r:Inference; + r:gives { + 3553 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3553 math:notEqualTo 0}] + skolem:lemma6246 + [ a r:Fact; r:gives {((3 5 5 3) "=<") list:sort (3 3 5 5)}] + [ a r:Fact; r:gives {((3 5 5 3) ">=") list:sort (5 5 3 3)}] + skolem:lemma5977 + skolem:lemma5978 + [ a r:Fact; r:gives {(5533 3355) math:difference 2178}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2178 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2178 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2178]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3552 a r:Inference; + r:gives { + 3554 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3554 math:notEqualTo 0}] + skolem:lemma6247 + [ a r:Fact; r:gives {((3 5 5 4) "=<") list:sort (3 4 5 5)}] + [ a r:Fact; r:gives {((3 5 5 4) ">=") list:sort (5 5 4 3)}] + skolem:lemma6119 + skolem:lemma6120 + [ a r:Fact; r:gives {(5543 3455) math:difference 2088}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2088 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 2088 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3554]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 5 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3455]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3553 a r:Inference; + r:gives { + 3555 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3555 math:notEqualTo 0}] + skolem:lemma6248 + [ a r:Fact; r:gives {((3 5 5 5) "=<") list:sort (3 5 5 5)}] + [ a r:Fact; r:gives {((3 5 5 5) ">=") list:sort (5 5 5 3)}] + skolem:lemma6249 + skolem:lemma6250 + [ a r:Fact; r:gives {(5553 3555) math:difference 1998}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 1998 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 1998 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3555]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (5 5 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3555]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3554 a r:Inference; + r:gives { + 3556 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3556 math:notEqualTo 0}] + skolem:lemma6251 + [ a r:Fact; r:gives {((3 5 5 6) "=<") list:sort (3 5 5 6)}] + [ a r:Fact; r:gives {((3 5 5 6) ">=") list:sort (6 5 5 3)}] + skolem:lemma6252 + skolem:lemma6253 + [ a r:Fact; r:gives {(6553 3556) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3556]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3556]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3555 a r:Inference; + r:gives { + 3557 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3557 math:notEqualTo 0}] + skolem:lemma6254 + [ a r:Fact; r:gives {((3 5 5 7) "=<") list:sort (3 5 5 7)}] + [ a r:Fact; r:gives {((3 5 5 7) ">=") list:sort (7 5 5 3)}] + skolem:lemma6255 + skolem:lemma6256 + [ a r:Fact; r:gives {(7553 3557) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3557]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3557]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3556 a r:Inference; + r:gives { + 3558 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3558 math:notEqualTo 0}] + skolem:lemma6257 + [ a r:Fact; r:gives {((3 5 5 8) "=<") list:sort (3 5 5 8)}] + [ a r:Fact; r:gives {((3 5 5 8) ">=") list:sort (8 5 5 3)}] + skolem:lemma6258 + skolem:lemma6259 + [ a r:Fact; r:gives {(8553 3558) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3558]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3558]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3557 a r:Inference; + r:gives { + 3559 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3559 math:notEqualTo 0}] + skolem:lemma6260 + [ a r:Fact; r:gives {((3 5 5 9) "=<") list:sort (3 5 5 9)}] + [ a r:Fact; r:gives {((3 5 5 9) ">=") list:sort (9 5 5 3)}] + skolem:lemma6261 + skolem:lemma6262 + [ a r:Fact; r:gives {(9553 3559) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3559]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3559]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3558 a r:Inference; + r:gives { + 3560 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3560 math:notEqualTo 0}] + skolem:lemma6263 + [ a r:Fact; r:gives {((3 5 6 0) "=<") list:sort (0 3 5 6)}] + [ a r:Fact; r:gives {((3 5 6 0) ">=") list:sort (6 5 3 0)}] + skolem:lemma5555 + skolem:lemma5556 + [ a r:Fact; r:gives {(6530 356) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3560]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 6 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3559 a r:Inference; + r:gives { + 3561 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3561 math:notEqualTo 0}] + skolem:lemma6264 + [ a r:Fact; r:gives {((3 5 6 1) "=<") list:sort (1 3 5 6)}] + [ a r:Fact; r:gives {((3 5 6 1) ">=") list:sort (6 5 3 1)}] + skolem:lemma5727 + skolem:lemma5728 + [ a r:Fact; r:gives {(6531 1356) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3561]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 6 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3560 a r:Inference; + r:gives { + 3562 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3562 math:notEqualTo 0}] + skolem:lemma6265 + [ a r:Fact; r:gives {((3 5 6 2) "=<") list:sort (2 3 5 6)}] + [ a r:Fact; r:gives {((3 5 6 2) ">=") list:sort (6 5 3 2)}] + skolem:lemma4653 + skolem:lemma4654 + [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3562]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3561 a r:Inference; + r:gives { + 3563 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3563 math:notEqualTo 0}] + skolem:lemma6266 + [ a r:Fact; r:gives {((3 5 6 3) "=<") list:sort (3 3 5 6)}] + [ a r:Fact; r:gives {((3 5 6 3) ">=") list:sort (6 5 3 3)}] + skolem:lemma5980 + skolem:lemma5981 + [ a r:Fact; r:gives {(6533 3356) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3563]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3562 a r:Inference; + r:gives { + 3564 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3564 math:notEqualTo 0}] + skolem:lemma6267 + [ a r:Fact; r:gives {((3 5 6 4) "=<") list:sort (3 4 5 6)}] + [ a r:Fact; r:gives {((3 5 6 4) ">=") list:sort (6 5 4 3)}] + skolem:lemma6122 + skolem:lemma6123 + [ a r:Fact; r:gives {(6543 3456) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3564]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 6 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3563 a r:Inference; + r:gives { + 3565 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3565 math:notEqualTo 0}] + skolem:lemma6268 + [ a r:Fact; r:gives {((3 5 6 5) "=<") list:sort (3 5 5 6)}] + [ a r:Fact; r:gives {((3 5 6 5) ">=") list:sort (6 5 5 3)}] + skolem:lemma6252 + skolem:lemma6253 + [ a r:Fact; r:gives {(6553 3556) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3565]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 6 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3556]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3564 a r:Inference; + r:gives { + 3566 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3566 math:notEqualTo 0}] + skolem:lemma6269 + [ a r:Fact; r:gives {((3 5 6 6) "=<") list:sort (3 5 6 6)}] + [ a r:Fact; r:gives {((3 5 6 6) ">=") list:sort (6 6 5 3)}] + skolem:lemma6270 + skolem:lemma6271 + [ a r:Fact; r:gives {(6653 3566) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3566]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3566]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3565 a r:Inference; + r:gives { + 3567 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3567 math:notEqualTo 0}] + skolem:lemma6272 + [ a r:Fact; r:gives {((3 5 6 7) "=<") list:sort (3 5 6 7)}] + [ a r:Fact; r:gives {((3 5 6 7) ">=") list:sort (7 6 5 3)}] + skolem:lemma6273 + skolem:lemma6274 + [ a r:Fact; r:gives {(7653 3567) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3567]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3567]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3566 a r:Inference; + r:gives { + 3568 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3568 math:notEqualTo 0}] + skolem:lemma6275 + [ a r:Fact; r:gives {((3 5 6 8) "=<") list:sort (3 5 6 8)}] + [ a r:Fact; r:gives {((3 5 6 8) ">=") list:sort (8 6 5 3)}] + skolem:lemma6276 + skolem:lemma6277 + [ a r:Fact; r:gives {(8653 3568) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3568]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3568]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3567 a r:Inference; + r:gives { + 3569 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3569 math:notEqualTo 0}] + skolem:lemma6278 + [ a r:Fact; r:gives {((3 5 6 9) "=<") list:sort (3 5 6 9)}] + [ a r:Fact; r:gives {((3 5 6 9) ">=") list:sort (9 6 5 3)}] + skolem:lemma6279 + skolem:lemma6280 + [ a r:Fact; r:gives {(9653 3569) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3569]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3569]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3568 a r:Inference; + r:gives { + 3570 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3570 math:notEqualTo 0}] + skolem:lemma6281 + [ a r:Fact; r:gives {((3 5 7 0) "=<") list:sort (0 3 5 7)}] + [ a r:Fact; r:gives {((3 5 7 0) ">=") list:sort (7 5 3 0)}] + skolem:lemma5558 + skolem:lemma5559 + [ a r:Fact; r:gives {(7530 357) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3570]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 7 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3569 a r:Inference; + r:gives { + 3571 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3571 math:notEqualTo 0}] + skolem:lemma6282 + [ a r:Fact; r:gives {((3 5 7 1) "=<") list:sort (1 3 5 7)}] + [ a r:Fact; r:gives {((3 5 7 1) ">=") list:sort (7 5 3 1)}] + skolem:lemma5730 + skolem:lemma5731 + [ a r:Fact; r:gives {(7531 1357) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3571]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 7 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3570 a r:Inference; + r:gives { + 3572 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3572 math:notEqualTo 0}] + skolem:lemma6283 + [ a r:Fact; r:gives {((3 5 7 2) "=<") list:sort (2 3 5 7)}] + [ a r:Fact; r:gives {((3 5 7 2) ">=") list:sort (7 5 3 2)}] + skolem:lemma4656 + skolem:lemma4657 + [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3572]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3571 a r:Inference; + r:gives { + 3573 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3573 math:notEqualTo 0}] + skolem:lemma6284 + [ a r:Fact; r:gives {((3 5 7 3) "=<") list:sort (3 3 5 7)}] + [ a r:Fact; r:gives {((3 5 7 3) ">=") list:sort (7 5 3 3)}] + skolem:lemma5983 + skolem:lemma5984 + [ a r:Fact; r:gives {(7533 3357) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3573]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3572 a r:Inference; + r:gives { + 3574 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3574 math:notEqualTo 0}] + skolem:lemma6285 + [ a r:Fact; r:gives {((3 5 7 4) "=<") list:sort (3 4 5 7)}] + [ a r:Fact; r:gives {((3 5 7 4) ">=") list:sort (7 5 4 3)}] + skolem:lemma6125 + skolem:lemma6126 + [ a r:Fact; r:gives {(7543 3457) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3574]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 7 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3457]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3573 a r:Inference; + r:gives { + 3575 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3575 math:notEqualTo 0}] + skolem:lemma6286 + [ a r:Fact; r:gives {((3 5 7 5) "=<") list:sort (3 5 5 7)}] + [ a r:Fact; r:gives {((3 5 7 5) ">=") list:sort (7 5 5 3)}] + skolem:lemma6255 + skolem:lemma6256 + [ a r:Fact; r:gives {(7553 3557) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3575]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 7 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3557]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3574 a r:Inference; + r:gives { + 3576 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3576 math:notEqualTo 0}] + skolem:lemma6287 + [ a r:Fact; r:gives {((3 5 7 6) "=<") list:sort (3 5 6 7)}] + [ a r:Fact; r:gives {((3 5 7 6) ">=") list:sort (7 6 5 3)}] + skolem:lemma6273 + skolem:lemma6274 + [ a r:Fact; r:gives {(7653 3567) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3576]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 7 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3567]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3575 a r:Inference; + r:gives { + 3577 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3577 math:notEqualTo 0}] + skolem:lemma6288 + [ a r:Fact; r:gives {((3 5 7 7) "=<") list:sort (3 5 7 7)}] + [ a r:Fact; r:gives {((3 5 7 7) ">=") list:sort (7 7 5 3)}] + skolem:lemma6289 + skolem:lemma6290 + [ a r:Fact; r:gives {(7753 3577) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3577]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3577]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3576 a r:Inference; + r:gives { + 3578 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3578 math:notEqualTo 0}] + skolem:lemma6291 + [ a r:Fact; r:gives {((3 5 7 8) "=<") list:sort (3 5 7 8)}] + [ a r:Fact; r:gives {((3 5 7 8) ">=") list:sort (8 7 5 3)}] + skolem:lemma6292 + skolem:lemma6293 + [ a r:Fact; r:gives {(8753 3578) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3578]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3578]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3577 a r:Inference; + r:gives { + 3579 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3579 math:notEqualTo 0}] + skolem:lemma6294 + [ a r:Fact; r:gives {((3 5 7 9) "=<") list:sort (3 5 7 9)}] + [ a r:Fact; r:gives {((3 5 7 9) ">=") list:sort (9 7 5 3)}] + skolem:lemma6295 + skolem:lemma6296 + [ a r:Fact; r:gives {(9753 3579) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3579]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3579]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3578 a r:Inference; + r:gives { + 3580 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3580 math:notEqualTo 0}] + skolem:lemma6297 + [ a r:Fact; r:gives {((3 5 8 0) "=<") list:sort (0 3 5 8)}] + [ a r:Fact; r:gives {((3 5 8 0) ">=") list:sort (8 5 3 0)}] + skolem:lemma5561 + skolem:lemma5562 + [ a r:Fact; r:gives {(8530 358) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3580]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 8 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3579 a r:Inference; + r:gives { + 3581 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3581 math:notEqualTo 0}] + skolem:lemma6298 + [ a r:Fact; r:gives {((3 5 8 1) "=<") list:sort (1 3 5 8)}] + [ a r:Fact; r:gives {((3 5 8 1) ">=") list:sort (8 5 3 1)}] + skolem:lemma5733 + skolem:lemma5734 + [ a r:Fact; r:gives {(8531 1358) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3581]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 8 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3580 a r:Inference; + r:gives { + 3582 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3582 math:notEqualTo 0}] + skolem:lemma6299 + [ a r:Fact; r:gives {((3 5 8 2) "=<") list:sort (2 3 5 8)}] + [ a r:Fact; r:gives {((3 5 8 2) ">=") list:sort (8 5 3 2)}] + skolem:lemma4659 + skolem:lemma4660 + [ a r:Fact; r:gives {(8532 2358) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3582]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3581 a r:Inference; + r:gives { + 3583 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3583 math:notEqualTo 0}] + skolem:lemma6300 + [ a r:Fact; r:gives {((3 5 8 3) "=<") list:sort (3 3 5 8)}] + [ a r:Fact; r:gives {((3 5 8 3) ">=") list:sort (8 5 3 3)}] + skolem:lemma5986 + skolem:lemma5987 + [ a r:Fact; r:gives {(8533 3358) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3583]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3582 a r:Inference; + r:gives { + 3584 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3584 math:notEqualTo 0}] + skolem:lemma6301 + [ a r:Fact; r:gives {((3 5 8 4) "=<") list:sort (3 4 5 8)}] + [ a r:Fact; r:gives {((3 5 8 4) ">=") list:sort (8 5 4 3)}] + skolem:lemma6128 + skolem:lemma6129 + [ a r:Fact; r:gives {(8543 3458) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3584]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 8 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3458]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3583 a r:Inference; + r:gives { + 3585 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3585 math:notEqualTo 0}] + skolem:lemma6302 + [ a r:Fact; r:gives {((3 5 8 5) "=<") list:sort (3 5 5 8)}] + [ a r:Fact; r:gives {((3 5 8 5) ">=") list:sort (8 5 5 3)}] + skolem:lemma6258 + skolem:lemma6259 + [ a r:Fact; r:gives {(8553 3558) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3585]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 8 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3558]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3584 a r:Inference; + r:gives { + 3586 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3586 math:notEqualTo 0}] + skolem:lemma6303 + [ a r:Fact; r:gives {((3 5 8 6) "=<") list:sort (3 5 6 8)}] + [ a r:Fact; r:gives {((3 5 8 6) ">=") list:sort (8 6 5 3)}] + skolem:lemma6276 + skolem:lemma6277 + [ a r:Fact; r:gives {(8653 3568) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3586]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 8 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3568]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3585 a r:Inference; + r:gives { + 3587 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3587 math:notEqualTo 0}] + skolem:lemma6304 + [ a r:Fact; r:gives {((3 5 8 7) "=<") list:sort (3 5 7 8)}] + [ a r:Fact; r:gives {((3 5 8 7) ">=") list:sort (8 7 5 3)}] + skolem:lemma6292 + skolem:lemma6293 + [ a r:Fact; r:gives {(8753 3578) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3587]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 8 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3578]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3586 a r:Inference; + r:gives { + 3588 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3588 math:notEqualTo 0}] + skolem:lemma6305 + [ a r:Fact; r:gives {((3 5 8 8) "=<") list:sort (3 5 8 8)}] + [ a r:Fact; r:gives {((3 5 8 8) ">=") list:sort (8 8 5 3)}] + skolem:lemma6306 + skolem:lemma6307 + [ a r:Fact; r:gives {(8853 3588) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3588]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3588]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8853]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3587 a r:Inference; + r:gives { + 3589 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3589 math:notEqualTo 0}] + skolem:lemma6308 + [ a r:Fact; r:gives {((3 5 8 9) "=<") list:sort (3 5 8 9)}] + [ a r:Fact; r:gives {((3 5 8 9) ">=") list:sort (9 8 5 3)}] + skolem:lemma6309 + skolem:lemma6310 + [ a r:Fact; r:gives {(9853 3589) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3589]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3589]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9853]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3588 a r:Inference; + r:gives { + 3590 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3590 math:notEqualTo 0}] + skolem:lemma6311 + [ a r:Fact; r:gives {((3 5 9 0) "=<") list:sort (0 3 5 9)}] + [ a r:Fact; r:gives {((3 5 9 0) ">=") list:sort (9 5 3 0)}] + skolem:lemma5564 + skolem:lemma5565 + [ a r:Fact; r:gives {(9530 359) math:difference 9171}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9171 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9171 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3590]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 9 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3589 a r:Inference; + r:gives { + 3591 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3591 math:notEqualTo 0}] + skolem:lemma6312 + [ a r:Fact; r:gives {((3 5 9 1) "=<") list:sort (1 3 5 9)}] + [ a r:Fact; r:gives {((3 5 9 1) ">=") list:sort (9 5 3 1)}] + skolem:lemma5736 + skolem:lemma5737 + [ a r:Fact; r:gives {(9531 1359) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3591]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 9 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3590 a r:Inference; + r:gives { + 3592 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3592 math:notEqualTo 0}] + skolem:lemma6313 + [ a r:Fact; r:gives {((3 5 9 2) "=<") list:sort (2 3 5 9)}] + [ a r:Fact; r:gives {((3 5 9 2) ">=") list:sort (9 5 3 2)}] + skolem:lemma4662 + skolem:lemma4663 + [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3592]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 9 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3591 a r:Inference; + r:gives { + 3593 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3593 math:notEqualTo 0}] + skolem:lemma6314 + [ a r:Fact; r:gives {((3 5 9 3) "=<") list:sort (3 3 5 9)}] + [ a r:Fact; r:gives {((3 5 9 3) ">=") list:sort (9 5 3 3)}] + skolem:lemma5989 + skolem:lemma5990 + [ a r:Fact; r:gives {(9533 3359) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3593]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 9 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3592 a r:Inference; + r:gives { + 3594 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3594 math:notEqualTo 0}] + skolem:lemma6315 + [ a r:Fact; r:gives {((3 5 9 4) "=<") list:sort (3 4 5 9)}] + [ a r:Fact; r:gives {((3 5 9 4) ">=") list:sort (9 5 4 3)}] + skolem:lemma6131 + skolem:lemma6132 + [ a r:Fact; r:gives {(9543 3459) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3594]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 9 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3459]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3593 a r:Inference; + r:gives { + 3595 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3595 math:notEqualTo 0}] + skolem:lemma6316 + [ a r:Fact; r:gives {((3 5 9 5) "=<") list:sort (3 5 5 9)}] + [ a r:Fact; r:gives {((3 5 9 5) ">=") list:sort (9 5 5 3)}] + skolem:lemma6261 + skolem:lemma6262 + [ a r:Fact; r:gives {(9553 3559) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3595]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 9 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3559]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3594 a r:Inference; + r:gives { + 3596 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3596 math:notEqualTo 0}] + skolem:lemma6317 + [ a r:Fact; r:gives {((3 5 9 6) "=<") list:sort (3 5 6 9)}] + [ a r:Fact; r:gives {((3 5 9 6) ">=") list:sort (9 6 5 3)}] + skolem:lemma6279 + skolem:lemma6280 + [ a r:Fact; r:gives {(9653 3569) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3596]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 9 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3569]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3595 a r:Inference; + r:gives { + 3597 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3597 math:notEqualTo 0}] + skolem:lemma6318 + [ a r:Fact; r:gives {((3 5 9 7) "=<") list:sort (3 5 7 9)}] + [ a r:Fact; r:gives {((3 5 9 7) ">=") list:sort (9 7 5 3)}] + skolem:lemma6295 + skolem:lemma6296 + [ a r:Fact; r:gives {(9753 3579) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3597]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 9 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3579]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3596 a r:Inference; + r:gives { + 3598 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3598 math:notEqualTo 0}] + skolem:lemma6319 + [ a r:Fact; r:gives {((3 5 9 8) "=<") list:sort (3 5 8 9)}] + [ a r:Fact; r:gives {((3 5 9 8) ">=") list:sort (9 8 5 3)}] + skolem:lemma6309 + skolem:lemma6310 + [ a r:Fact; r:gives {(9853 3589) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3598]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 9 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3589]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9853]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3597 a r:Inference; + r:gives { + 3599 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3599 math:notEqualTo 0}] + skolem:lemma6320 + [ a r:Fact; r:gives {((3 5 9 9) "=<") list:sort (3 5 9 9)}] + [ a r:Fact; r:gives {((3 5 9 9) ">=") list:sort (9 9 5 3)}] + skolem:lemma6321 + skolem:lemma6322 + [ a r:Fact; r:gives {(9953 3599) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3599]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 5 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3599]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9953]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3598 a r:Inference; + r:gives { + 3600 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3600 math:notEqualTo 0}] + skolem:lemma6323 + [ a r:Fact; r:gives {((3 6 0 0) "=<") list:sort (0 0 3 6)}] + [ a r:Fact; r:gives {((3 6 0 0) ">=") list:sort (6 3 0 0)}] + skolem:lemma5453 + skolem:lemma5454 + [ a r:Fact; r:gives {(6300 36) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 36]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3599 a r:Inference; + r:gives { + 3601 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3601 math:notEqualTo 0}] + skolem:lemma6324 + [ a r:Fact; r:gives {((3 6 0 1) "=<") list:sort (0 1 3 6)}] + [ a r:Fact; r:gives {((3 6 0 1) ">=") list:sort (6 3 1 0)}] + skolem:lemma5479 + skolem:lemma5480 + [ a r:Fact; r:gives {(6310 136) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3601]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 0 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 136]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3600 a r:Inference; + r:gives { + 3602 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3602 math:notEqualTo 0}] + skolem:lemma6325 + [ a r:Fact; r:gives {((3 6 0 2) "=<") list:sort (0 2 3 6)}] + [ a r:Fact; r:gives {((3 6 0 2) ">=") list:sort (6 3 2 0)}] + skolem:lemma4096 + skolem:lemma4097 + [ a r:Fact; r:gives {(6320 236) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3602]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 0 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3601 a r:Inference; + r:gives { + 3603 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3603 math:notEqualTo 0}] + skolem:lemma6326 + [ a r:Fact; r:gives {((3 6 0 3) "=<") list:sort (0 3 3 6)}] + [ a r:Fact; r:gives {((3 6 0 3) ">=") list:sort (6 3 3 0)}] + skolem:lemma5513 + skolem:lemma5514 + [ a r:Fact; r:gives {(6330 336) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3603]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 0 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3602 a r:Inference; + r:gives { + 3604 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3604 math:notEqualTo 0}] + skolem:lemma6327 + [ a r:Fact; r:gives {((3 6 0 4) "=<") list:sort (0 3 4 6)}] + [ a r:Fact; r:gives {((3 6 0 4) ">=") list:sort (6 4 3 0)}] + skolem:lemma5535 + skolem:lemma5536 + [ a r:Fact; r:gives {(6430 346) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3604]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 0 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3603 a r:Inference; + r:gives { + 3605 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3605 math:notEqualTo 0}] + skolem:lemma6328 + [ a r:Fact; r:gives {((3 6 0 5) "=<") list:sort (0 3 5 6)}] + [ a r:Fact; r:gives {((3 6 0 5) ">=") list:sort (6 5 3 0)}] + skolem:lemma5555 + skolem:lemma5556 + [ a r:Fact; r:gives {(6530 356) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3605]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 0 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3604 a r:Inference; + r:gives { + 3606 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3606 math:notEqualTo 0}] + skolem:lemma6329 + [ a r:Fact; r:gives {((3 6 0 6) "=<") list:sort (0 3 6 6)}] + [ a r:Fact; r:gives {((3 6 0 6) ">=") list:sort (6 6 3 0)}] + skolem:lemma5573 + skolem:lemma5574 + [ a r:Fact; r:gives {(6630 366) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3606]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 0 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3605 a r:Inference; + r:gives { + 3607 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3607 math:notEqualTo 0}] + skolem:lemma6330 + [ a r:Fact; r:gives {((3 6 0 7) "=<") list:sort (0 3 6 7)}] + [ a r:Fact; r:gives {((3 6 0 7) ">=") list:sort (7 6 3 0)}] + skolem:lemma5576 + skolem:lemma5577 + [ a r:Fact; r:gives {(7630 367) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3607]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 0 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3606 a r:Inference; + r:gives { + 3608 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3608 math:notEqualTo 0}] + skolem:lemma6331 + [ a r:Fact; r:gives {((3 6 0 8) "=<") list:sort (0 3 6 8)}] + [ a r:Fact; r:gives {((3 6 0 8) ">=") list:sort (8 6 3 0)}] + skolem:lemma5579 + skolem:lemma5580 + [ a r:Fact; r:gives {(8630 368) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3608]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 0 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3607 a r:Inference; + r:gives { + 3609 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3609 math:notEqualTo 0}] + skolem:lemma6332 + [ a r:Fact; r:gives {((3 6 0 9) "=<") list:sort (0 3 6 9)}] + [ a r:Fact; r:gives {((3 6 0 9) ">=") list:sort (9 6 3 0)}] + skolem:lemma5582 + skolem:lemma5583 + [ a r:Fact; r:gives {(9630 369) math:difference 9261}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9261 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9261 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3609]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 0 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9261]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3608 a r:Inference; + r:gives { + 3610 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3610 math:notEqualTo 0}] + skolem:lemma6333 + [ a r:Fact; r:gives {((3 6 1 0) "=<") list:sort (0 1 3 6)}] + [ a r:Fact; r:gives {((3 6 1 0) ">=") list:sort (6 3 1 0)}] + skolem:lemma5479 + skolem:lemma5480 + [ a r:Fact; r:gives {(6310 136) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3610]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 136]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3609 a r:Inference; + r:gives { + 3611 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3611 math:notEqualTo 0}] + skolem:lemma6334 + [ a r:Fact; r:gives {((3 6 1 1) "=<") list:sort (1 1 3 6)}] + [ a r:Fact; r:gives {((3 6 1 1) ">=") list:sort (6 3 1 1)}] + skolem:lemma5651 + skolem:lemma5652 + [ a r:Fact; r:gives {(6311 1136) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3611]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1136]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3610 a r:Inference; + r:gives { + 3612 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3612 math:notEqualTo 0}] + skolem:lemma6335 + [ a r:Fact; r:gives {((3 6 1 2) "=<") list:sort (1 2 3 6)}] + [ a r:Fact; r:gives {((3 6 1 2) ">=") list:sort (6 3 2 1)}] + skolem:lemma4286 + skolem:lemma4287 + [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3612]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3611 a r:Inference; + r:gives { + 3613 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3613 math:notEqualTo 0}] + skolem:lemma6336 + [ a r:Fact; r:gives {((3 6 1 3) "=<") list:sort (1 3 3 6)}] + [ a r:Fact; r:gives {((3 6 1 3) ">=") list:sort (6 3 3 1)}] + skolem:lemma5685 + skolem:lemma5686 + [ a r:Fact; r:gives {(6331 1336) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3613]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3612 a r:Inference; + r:gives { + 3614 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3614 math:notEqualTo 0}] + skolem:lemma6337 + [ a r:Fact; r:gives {((3 6 1 4) "=<") list:sort (1 3 4 6)}] + [ a r:Fact; r:gives {((3 6 1 4) ">=") list:sort (6 4 3 1)}] + skolem:lemma5707 + skolem:lemma5708 + [ a r:Fact; r:gives {(6431 1346) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3614]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 1 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3613 a r:Inference; + r:gives { + 3615 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3615 math:notEqualTo 0}] + skolem:lemma6338 + [ a r:Fact; r:gives {((3 6 1 5) "=<") list:sort (1 3 5 6)}] + [ a r:Fact; r:gives {((3 6 1 5) ">=") list:sort (6 5 3 1)}] + skolem:lemma5727 + skolem:lemma5728 + [ a r:Fact; r:gives {(6531 1356) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3615]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 1 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3614 a r:Inference; + r:gives { + 3616 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3616 math:notEqualTo 0}] + skolem:lemma6339 + [ a r:Fact; r:gives {((3 6 1 6) "=<") list:sort (1 3 6 6)}] + [ a r:Fact; r:gives {((3 6 1 6) ">=") list:sort (6 6 3 1)}] + skolem:lemma5745 + skolem:lemma5746 + [ a r:Fact; r:gives {(6631 1366) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3616]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 1 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3615 a r:Inference; + r:gives { + 3617 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3617 math:notEqualTo 0}] + skolem:lemma6340 + [ a r:Fact; r:gives {((3 6 1 7) "=<") list:sort (1 3 6 7)}] + [ a r:Fact; r:gives {((3 6 1 7) ">=") list:sort (7 6 3 1)}] + skolem:lemma5748 + skolem:lemma5749 + [ a r:Fact; r:gives {(7631 1367) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3617]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 1 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3616 a r:Inference; + r:gives { + 3618 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3618 math:notEqualTo 0}] + skolem:lemma6341 + [ a r:Fact; r:gives {((3 6 1 8) "=<") list:sort (1 3 6 8)}] + [ a r:Fact; r:gives {((3 6 1 8) ">=") list:sort (8 6 3 1)}] + skolem:lemma5751 + skolem:lemma5752 + [ a r:Fact; r:gives {(8631 1368) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3618]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 1 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3617 a r:Inference; + r:gives { + 3619 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3619 math:notEqualTo 0}] + skolem:lemma6342 + [ a r:Fact; r:gives {((3 6 1 9) "=<") list:sort (1 3 6 9)}] + [ a r:Fact; r:gives {((3 6 1 9) ">=") list:sort (9 6 3 1)}] + skolem:lemma5754 + skolem:lemma5755 + [ a r:Fact; r:gives {(9631 1369) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3619]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 1 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3618 a r:Inference; + r:gives { + 3620 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3620 math:notEqualTo 0}] + skolem:lemma6343 + [ a r:Fact; r:gives {((3 6 2 0) "=<") list:sort (0 2 3 6)}] + [ a r:Fact; r:gives {((3 6 2 0) ">=") list:sort (6 3 2 0)}] + skolem:lemma4096 + skolem:lemma4097 + [ a r:Fact; r:gives {(6320 236) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3619 a r:Inference; + r:gives { + 3621 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3621 math:notEqualTo 0}] + skolem:lemma6344 + [ a r:Fact; r:gives {((3 6 2 1) "=<") list:sort (1 2 3 6)}] + [ a r:Fact; r:gives {((3 6 2 1) ">=") list:sort (6 3 2 1)}] + skolem:lemma4286 + skolem:lemma4287 + [ a r:Fact; r:gives {(6321 1236) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3620 a r:Inference; + r:gives { + 3622 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3622 math:notEqualTo 0}] + skolem:lemma6345 + [ a r:Fact; r:gives {((3 6 2 2) "=<") list:sort (2 2 3 6)}] + [ a r:Fact; r:gives {((3 6 2 2) ">=") list:sort (6 3 2 2)}] + skolem:lemma4455 + skolem:lemma4456 + [ a r:Fact; r:gives {(6322 2236) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3621 a r:Inference; + r:gives { + 3623 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3623 math:notEqualTo 0}] + skolem:lemma6346 + [ a r:Fact; r:gives {((3 6 2 3) "=<") list:sort (2 3 3 6)}] + [ a r:Fact; r:gives {((3 6 2 3) ">=") list:sort (6 3 3 2)}] + skolem:lemma4611 + skolem:lemma4612 + [ a r:Fact; r:gives {(6332 2336) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3623]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3622 a r:Inference; + r:gives { + 3624 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3624 math:notEqualTo 0}] + skolem:lemma6347 + [ a r:Fact; r:gives {((3 6 2 4) "=<") list:sort (2 3 4 6)}] + [ a r:Fact; r:gives {((3 6 2 4) ">=") list:sort (6 4 3 2)}] + skolem:lemma4633 + skolem:lemma4634 + [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3624]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3623 a r:Inference; + r:gives { + 3625 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3625 math:notEqualTo 0}] + skolem:lemma6348 + [ a r:Fact; r:gives {((3 6 2 5) "=<") list:sort (2 3 5 6)}] + [ a r:Fact; r:gives {((3 6 2 5) ">=") list:sort (6 5 3 2)}] + skolem:lemma4653 + skolem:lemma4654 + [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3625]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3624 a r:Inference; + r:gives { + 3626 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3626 math:notEqualTo 0}] + skolem:lemma6349 + [ a r:Fact; r:gives {((3 6 2 6) "=<") list:sort (2 3 6 6)}] + [ a r:Fact; r:gives {((3 6 2 6) ">=") list:sort (6 6 3 2)}] + skolem:lemma4671 + skolem:lemma4672 + [ a r:Fact; r:gives {(6632 2366) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3626]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3625 a r:Inference; + r:gives { + 3627 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3627 math:notEqualTo 0}] + skolem:lemma6350 + [ a r:Fact; r:gives {((3 6 2 7) "=<") list:sort (2 3 6 7)}] + [ a r:Fact; r:gives {((3 6 2 7) ">=") list:sort (7 6 3 2)}] + skolem:lemma4674 + skolem:lemma4675 + [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3627]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3626 a r:Inference; + r:gives { + 3628 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3628 math:notEqualTo 0}] + skolem:lemma6351 + [ a r:Fact; r:gives {((3 6 2 8) "=<") list:sort (2 3 6 8)}] + [ a r:Fact; r:gives {((3 6 2 8) ">=") list:sort (8 6 3 2)}] + skolem:lemma4677 + skolem:lemma4678 + [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3628]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3627 a r:Inference; + r:gives { + 3629 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3629 math:notEqualTo 0}] + skolem:lemma6352 + [ a r:Fact; r:gives {((3 6 2 9) "=<") list:sort (2 3 6 9)}] + [ a r:Fact; r:gives {((3 6 2 9) ">=") list:sort (9 6 3 2)}] + skolem:lemma4680 + skolem:lemma4681 + [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3629]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3628 a r:Inference; + r:gives { + 3630 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3630 math:notEqualTo 0}] + skolem:lemma6353 + [ a r:Fact; r:gives {((3 6 3 0) "=<") list:sort (0 3 3 6)}] + [ a r:Fact; r:gives {((3 6 3 0) ">=") list:sort (6 3 3 0)}] + skolem:lemma5513 + skolem:lemma5514 + [ a r:Fact; r:gives {(6330 336) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3629 a r:Inference; + r:gives { + 3631 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3631 math:notEqualTo 0}] + skolem:lemma6354 + [ a r:Fact; r:gives {((3 6 3 1) "=<") list:sort (1 3 3 6)}] + [ a r:Fact; r:gives {((3 6 3 1) ">=") list:sort (6 3 3 1)}] + skolem:lemma5685 + skolem:lemma5686 + [ a r:Fact; r:gives {(6331 1336) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3630 a r:Inference; + r:gives { + 3632 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3632 math:notEqualTo 0}] + skolem:lemma6355 + [ a r:Fact; r:gives {((3 6 3 2) "=<") list:sort (2 3 3 6)}] + [ a r:Fact; r:gives {((3 6 3 2) ">=") list:sort (6 3 3 2)}] + skolem:lemma4611 + skolem:lemma4612 + [ a r:Fact; r:gives {(6332 2336) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3631 a r:Inference; + r:gives { + 3633 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3633 math:notEqualTo 0}] + skolem:lemma6356 + [ a r:Fact; r:gives {((3 6 3 3) "=<") list:sort (3 3 3 6)}] + [ a r:Fact; r:gives {((3 6 3 3) ">=") list:sort (6 3 3 3)}] + skolem:lemma5938 + skolem:lemma5939 + [ a r:Fact; r:gives {(6333 3336) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3632 a r:Inference; + r:gives { + 3634 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3634 math:notEqualTo 0}] + skolem:lemma6357 + [ a r:Fact; r:gives {((3 6 3 4) "=<") list:sort (3 3 4 6)}] + [ a r:Fact; r:gives {((3 6 3 4) ">=") list:sort (6 4 3 3)}] + skolem:lemma5960 + skolem:lemma5961 + [ a r:Fact; r:gives {(6433 3346) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3634]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3633 a r:Inference; + r:gives { + 3635 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3635 math:notEqualTo 0}] + skolem:lemma6358 + [ a r:Fact; r:gives {((3 6 3 5) "=<") list:sort (3 3 5 6)}] + [ a r:Fact; r:gives {((3 6 3 5) ">=") list:sort (6 5 3 3)}] + skolem:lemma5980 + skolem:lemma5981 + [ a r:Fact; r:gives {(6533 3356) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3635]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3634 a r:Inference; + r:gives { + 3636 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3636 math:notEqualTo 0}] + skolem:lemma6359 + [ a r:Fact; r:gives {((3 6 3 6) "=<") list:sort (3 3 6 6)}] + [ a r:Fact; r:gives {((3 6 3 6) ">=") list:sort (6 6 3 3)}] + skolem:lemma5998 + skolem:lemma5999 + [ a r:Fact; r:gives {(6633 3366) math:difference 3267}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3267 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 3267 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3636]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3635 a r:Inference; + r:gives { + 3637 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3637 math:notEqualTo 0}] + skolem:lemma6360 + [ a r:Fact; r:gives {((3 6 3 7) "=<") list:sort (3 3 6 7)}] + [ a r:Fact; r:gives {((3 6 3 7) ">=") list:sort (7 6 3 3)}] + skolem:lemma6001 + skolem:lemma6002 + [ a r:Fact; r:gives {(7633 3367) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3637]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3636 a r:Inference; + r:gives { + 3638 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3638 math:notEqualTo 0}] + skolem:lemma6361 + [ a r:Fact; r:gives {((3 6 3 8) "=<") list:sort (3 3 6 8)}] + [ a r:Fact; r:gives {((3 6 3 8) ">=") list:sort (8 6 3 3)}] + skolem:lemma6004 + skolem:lemma6005 + [ a r:Fact; r:gives {(8633 3368) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3638]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3637 a r:Inference; + r:gives { + 3639 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3639 math:notEqualTo 0}] + skolem:lemma6362 + [ a r:Fact; r:gives {((3 6 3 9) "=<") list:sort (3 3 6 9)}] + [ a r:Fact; r:gives {((3 6 3 9) ">=") list:sort (9 6 3 3)}] + skolem:lemma6007 + skolem:lemma6008 + [ a r:Fact; r:gives {(9633 3369) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3639]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3638 a r:Inference; + r:gives { + 3640 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3640 math:notEqualTo 0}] + skolem:lemma6363 + [ a r:Fact; r:gives {((3 6 4 0) "=<") list:sort (0 3 4 6)}] + [ a r:Fact; r:gives {((3 6 4 0) ">=") list:sort (6 4 3 0)}] + skolem:lemma5535 + skolem:lemma5536 + [ a r:Fact; r:gives {(6430 346) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3640]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 4 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3639 a r:Inference; + r:gives { + 3641 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3641 math:notEqualTo 0}] + skolem:lemma6364 + [ a r:Fact; r:gives {((3 6 4 1) "=<") list:sort (1 3 4 6)}] + [ a r:Fact; r:gives {((3 6 4 1) ">=") list:sort (6 4 3 1)}] + skolem:lemma5707 + skolem:lemma5708 + [ a r:Fact; r:gives {(6431 1346) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3641]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 4 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3640 a r:Inference; + r:gives { + 3642 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3642 math:notEqualTo 0}] + skolem:lemma6365 + [ a r:Fact; r:gives {((3 6 4 2) "=<") list:sort (2 3 4 6)}] + [ a r:Fact; r:gives {((3 6 4 2) ">=") list:sort (6 4 3 2)}] + skolem:lemma4633 + skolem:lemma4634 + [ a r:Fact; r:gives {(6432 2346) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3641 a r:Inference; + r:gives { + 3643 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3643 math:notEqualTo 0}] + skolem:lemma6366 + [ a r:Fact; r:gives {((3 6 4 3) "=<") list:sort (3 3 4 6)}] + [ a r:Fact; r:gives {((3 6 4 3) ">=") list:sort (6 4 3 3)}] + skolem:lemma5960 + skolem:lemma5961 + [ a r:Fact; r:gives {(6433 3346) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3642 a r:Inference; + r:gives { + 3644 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3644 math:notEqualTo 0}] + skolem:lemma6367 + [ a r:Fact; r:gives {((3 6 4 4) "=<") list:sort (3 4 4 6)}] + [ a r:Fact; r:gives {((3 6 4 4) ">=") list:sort (6 4 4 3)}] + skolem:lemma6102 + skolem:lemma6103 + [ a r:Fact; r:gives {(6443 3446) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3644]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 4 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3446]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3643 a r:Inference; + r:gives { + 3645 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3645 math:notEqualTo 0}] + skolem:lemma6368 + [ a r:Fact; r:gives {((3 6 4 5) "=<") list:sort (3 4 5 6)}] + [ a r:Fact; r:gives {((3 6 4 5) ">=") list:sort (6 5 4 3)}] + skolem:lemma6122 + skolem:lemma6123 + [ a r:Fact; r:gives {(6543 3456) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3645]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3644 a r:Inference; + r:gives { + 3646 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3646 math:notEqualTo 0}] + skolem:lemma6369 + [ a r:Fact; r:gives {((3 6 4 6) "=<") list:sort (3 4 6 6)}] + [ a r:Fact; r:gives {((3 6 4 6) ">=") list:sort (6 6 4 3)}] + skolem:lemma6140 + skolem:lemma6141 + [ a r:Fact; r:gives {(6643 3466) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3646]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3466]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3645 a r:Inference; + r:gives { + 3647 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3647 math:notEqualTo 0}] + skolem:lemma6370 + [ a r:Fact; r:gives {((3 6 4 7) "=<") list:sort (3 4 6 7)}] + [ a r:Fact; r:gives {((3 6 4 7) ">=") list:sort (7 6 4 3)}] + skolem:lemma6143 + skolem:lemma6144 + [ a r:Fact; r:gives {(7643 3467) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3647]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3467]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3646 a r:Inference; + r:gives { + 3648 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3648 math:notEqualTo 0}] + skolem:lemma6371 + [ a r:Fact; r:gives {((3 6 4 8) "=<") list:sort (3 4 6 8)}] + [ a r:Fact; r:gives {((3 6 4 8) ">=") list:sort (8 6 4 3)}] + skolem:lemma6146 + skolem:lemma6147 + [ a r:Fact; r:gives {(8643 3468) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3648]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3468]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3647 a r:Inference; + r:gives { + 3649 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3649 math:notEqualTo 0}] + skolem:lemma6372 + [ a r:Fact; r:gives {((3 6 4 9) "=<") list:sort (3 4 6 9)}] + [ a r:Fact; r:gives {((3 6 4 9) ">=") list:sort (9 6 4 3)}] + skolem:lemma6149 + skolem:lemma6150 + [ a r:Fact; r:gives {(9643 3469) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3649]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3469]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3648 a r:Inference; + r:gives { + 3650 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3650 math:notEqualTo 0}] + skolem:lemma6373 + [ a r:Fact; r:gives {((3 6 5 0) "=<") list:sort (0 3 5 6)}] + [ a r:Fact; r:gives {((3 6 5 0) ">=") list:sort (6 5 3 0)}] + skolem:lemma5555 + skolem:lemma5556 + [ a r:Fact; r:gives {(6530 356) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3650]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 5 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3649 a r:Inference; + r:gives { + 3651 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3651 math:notEqualTo 0}] + skolem:lemma6374 + [ a r:Fact; r:gives {((3 6 5 1) "=<") list:sort (1 3 5 6)}] + [ a r:Fact; r:gives {((3 6 5 1) ">=") list:sort (6 5 3 1)}] + skolem:lemma5727 + skolem:lemma5728 + [ a r:Fact; r:gives {(6531 1356) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3651]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 5 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3650 a r:Inference; + r:gives { + 3652 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3652 math:notEqualTo 0}] + skolem:lemma6375 + [ a r:Fact; r:gives {((3 6 5 2) "=<") list:sort (2 3 5 6)}] + [ a r:Fact; r:gives {((3 6 5 2) ">=") list:sort (6 5 3 2)}] + skolem:lemma4653 + skolem:lemma4654 + [ a r:Fact; r:gives {(6532 2356) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3651 a r:Inference; + r:gives { + 3653 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3653 math:notEqualTo 0}] + skolem:lemma6376 + [ a r:Fact; r:gives {((3 6 5 3) "=<") list:sort (3 3 5 6)}] + [ a r:Fact; r:gives {((3 6 5 3) ">=") list:sort (6 5 3 3)}] + skolem:lemma5980 + skolem:lemma5981 + [ a r:Fact; r:gives {(6533 3356) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3652 a r:Inference; + r:gives { + 3654 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3654 math:notEqualTo 0}] + skolem:lemma6377 + [ a r:Fact; r:gives {((3 6 5 4) "=<") list:sort (3 4 5 6)}] + [ a r:Fact; r:gives {((3 6 5 4) ">=") list:sort (6 5 4 3)}] + skolem:lemma6122 + skolem:lemma6123 + [ a r:Fact; r:gives {(6543 3456) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3654]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 5 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3653 a r:Inference; + r:gives { + 3655 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3655 math:notEqualTo 0}] + skolem:lemma6378 + [ a r:Fact; r:gives {((3 6 5 5) "=<") list:sort (3 5 5 6)}] + [ a r:Fact; r:gives {((3 6 5 5) ">=") list:sort (6 5 5 3)}] + skolem:lemma6252 + skolem:lemma6253 + [ a r:Fact; r:gives {(6553 3556) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3655]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 5 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3556]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3654 a r:Inference; + r:gives { + 3656 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3656 math:notEqualTo 0}] + skolem:lemma6379 + [ a r:Fact; r:gives {((3 6 5 6) "=<") list:sort (3 5 6 6)}] + [ a r:Fact; r:gives {((3 6 5 6) ">=") list:sort (6 6 5 3)}] + skolem:lemma6270 + skolem:lemma6271 + [ a r:Fact; r:gives {(6653 3566) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3656]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3566]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3655 a r:Inference; + r:gives { + 3657 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3657 math:notEqualTo 0}] + skolem:lemma6380 + [ a r:Fact; r:gives {((3 6 5 7) "=<") list:sort (3 5 6 7)}] + [ a r:Fact; r:gives {((3 6 5 7) ">=") list:sort (7 6 5 3)}] + skolem:lemma6273 + skolem:lemma6274 + [ a r:Fact; r:gives {(7653 3567) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3657]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3567]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3656 a r:Inference; + r:gives { + 3658 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3658 math:notEqualTo 0}] + skolem:lemma6381 + [ a r:Fact; r:gives {((3 6 5 8) "=<") list:sort (3 5 6 8)}] + [ a r:Fact; r:gives {((3 6 5 8) ">=") list:sort (8 6 5 3)}] + skolem:lemma6276 + skolem:lemma6277 + [ a r:Fact; r:gives {(8653 3568) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3658]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3568]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3657 a r:Inference; + r:gives { + 3659 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3659 math:notEqualTo 0}] + skolem:lemma6382 + [ a r:Fact; r:gives {((3 6 5 9) "=<") list:sort (3 5 6 9)}] + [ a r:Fact; r:gives {((3 6 5 9) ">=") list:sort (9 6 5 3)}] + skolem:lemma6279 + skolem:lemma6280 + [ a r:Fact; r:gives {(9653 3569) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3659]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3569]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3658 a r:Inference; + r:gives { + 3660 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3660 math:notEqualTo 0}] + skolem:lemma6383 + [ a r:Fact; r:gives {((3 6 6 0) "=<") list:sort (0 3 6 6)}] + [ a r:Fact; r:gives {((3 6 6 0) ">=") list:sort (6 6 3 0)}] + skolem:lemma5573 + skolem:lemma5574 + [ a r:Fact; r:gives {(6630 366) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3660]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 6 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3659 a r:Inference; + r:gives { + 3661 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3661 math:notEqualTo 0}] + skolem:lemma6384 + [ a r:Fact; r:gives {((3 6 6 1) "=<") list:sort (1 3 6 6)}] + [ a r:Fact; r:gives {((3 6 6 1) ">=") list:sort (6 6 3 1)}] + skolem:lemma5745 + skolem:lemma5746 + [ a r:Fact; r:gives {(6631 1366) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3661]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 6 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3660 a r:Inference; + r:gives { + 3662 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3662 math:notEqualTo 0}] + skolem:lemma6385 + [ a r:Fact; r:gives {((3 6 6 2) "=<") list:sort (2 3 6 6)}] + [ a r:Fact; r:gives {((3 6 6 2) ">=") list:sort (6 6 3 2)}] + skolem:lemma4671 + skolem:lemma4672 + [ a r:Fact; r:gives {(6632 2366) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3662]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3661 a r:Inference; + r:gives { + 3663 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3663 math:notEqualTo 0}] + skolem:lemma6386 + [ a r:Fact; r:gives {((3 6 6 3) "=<") list:sort (3 3 6 6)}] + [ a r:Fact; r:gives {((3 6 6 3) ">=") list:sort (6 6 3 3)}] + skolem:lemma5998 + skolem:lemma5999 + [ a r:Fact; r:gives {(6633 3366) math:difference 3267}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3267 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 3267 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3663]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3662 a r:Inference; + r:gives { + 3664 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3664 math:notEqualTo 0}] + skolem:lemma6387 + [ a r:Fact; r:gives {((3 6 6 4) "=<") list:sort (3 4 6 6)}] + [ a r:Fact; r:gives {((3 6 6 4) ">=") list:sort (6 6 4 3)}] + skolem:lemma6140 + skolem:lemma6141 + [ a r:Fact; r:gives {(6643 3466) math:difference 3177}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3177 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 3177 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3664]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 6 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3466]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3663 a r:Inference; + r:gives { + 3665 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3665 math:notEqualTo 0}] + skolem:lemma6388 + [ a r:Fact; r:gives {((3 6 6 5) "=<") list:sort (3 5 6 6)}] + [ a r:Fact; r:gives {((3 6 6 5) ">=") list:sort (6 6 5 3)}] + skolem:lemma6270 + skolem:lemma6271 + [ a r:Fact; r:gives {(6653 3566) math:difference 3087}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3087 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 3087 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3665]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 6 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3566]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3664 a r:Inference; + r:gives { + 3666 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3666 math:notEqualTo 0}] + skolem:lemma6389 + [ a r:Fact; r:gives {((3 6 6 6) "=<") list:sort (3 6 6 6)}] + [ a r:Fact; r:gives {((3 6 6 6) ">=") list:sort (6 6 6 3)}] + skolem:lemma6390 + skolem:lemma6391 + [ a r:Fact; r:gives {(6663 3666) math:difference 2997}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 2997 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 2997 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3666]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (6 6 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3666]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6663]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3665 a r:Inference; + r:gives { + 3667 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3667 math:notEqualTo 0}] + skolem:lemma6392 + [ a r:Fact; r:gives {((3 6 6 7) "=<") list:sort (3 6 6 7)}] + [ a r:Fact; r:gives {((3 6 6 7) ">=") list:sort (7 6 6 3)}] + skolem:lemma6393 + skolem:lemma6394 + [ a r:Fact; r:gives {(7663 3667) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3667]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3667]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7663]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3666 a r:Inference; + r:gives { + 3668 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3668 math:notEqualTo 0}] + skolem:lemma6395 + [ a r:Fact; r:gives {((3 6 6 8) "=<") list:sort (3 6 6 8)}] + [ a r:Fact; r:gives {((3 6 6 8) ">=") list:sort (8 6 6 3)}] + skolem:lemma6396 + skolem:lemma6397 + [ a r:Fact; r:gives {(8663 3668) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3668]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3668]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8663]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3667 a r:Inference; + r:gives { + 3669 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3669 math:notEqualTo 0}] + skolem:lemma6398 + [ a r:Fact; r:gives {((3 6 6 9) "=<") list:sort (3 6 6 9)}] + [ a r:Fact; r:gives {((3 6 6 9) ">=") list:sort (9 6 6 3)}] + skolem:lemma6399 + skolem:lemma6400 + [ a r:Fact; r:gives {(9663 3669) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3669]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3669]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9663]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3668 a r:Inference; + r:gives { + 3670 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3670 math:notEqualTo 0}] + skolem:lemma6401 + [ a r:Fact; r:gives {((3 6 7 0) "=<") list:sort (0 3 6 7)}] + [ a r:Fact; r:gives {((3 6 7 0) ">=") list:sort (7 6 3 0)}] + skolem:lemma5576 + skolem:lemma5577 + [ a r:Fact; r:gives {(7630 367) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3670]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 7 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3669 a r:Inference; + r:gives { + 3671 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3671 math:notEqualTo 0}] + skolem:lemma6402 + [ a r:Fact; r:gives {((3 6 7 1) "=<") list:sort (1 3 6 7)}] + [ a r:Fact; r:gives {((3 6 7 1) ">=") list:sort (7 6 3 1)}] + skolem:lemma5748 + skolem:lemma5749 + [ a r:Fact; r:gives {(7631 1367) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3671]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 7 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3670 a r:Inference; + r:gives { + 3672 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3672 math:notEqualTo 0}] + skolem:lemma6403 + [ a r:Fact; r:gives {((3 6 7 2) "=<") list:sort (2 3 6 7)}] + [ a r:Fact; r:gives {((3 6 7 2) ">=") list:sort (7 6 3 2)}] + skolem:lemma4674 + skolem:lemma4675 + [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3672]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3671 a r:Inference; + r:gives { + 3673 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3673 math:notEqualTo 0}] + skolem:lemma6404 + [ a r:Fact; r:gives {((3 6 7 3) "=<") list:sort (3 3 6 7)}] + [ a r:Fact; r:gives {((3 6 7 3) ">=") list:sort (7 6 3 3)}] + skolem:lemma6001 + skolem:lemma6002 + [ a r:Fact; r:gives {(7633 3367) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3673]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3672 a r:Inference; + r:gives { + 3674 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3674 math:notEqualTo 0}] + skolem:lemma6405 + [ a r:Fact; r:gives {((3 6 7 4) "=<") list:sort (3 4 6 7)}] + [ a r:Fact; r:gives {((3 6 7 4) ">=") list:sort (7 6 4 3)}] + skolem:lemma6143 + skolem:lemma6144 + [ a r:Fact; r:gives {(7643 3467) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3674]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 7 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3467]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3673 a r:Inference; + r:gives { + 3675 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3675 math:notEqualTo 0}] + skolem:lemma6406 + [ a r:Fact; r:gives {((3 6 7 5) "=<") list:sort (3 5 6 7)}] + [ a r:Fact; r:gives {((3 6 7 5) ">=") list:sort (7 6 5 3)}] + skolem:lemma6273 + skolem:lemma6274 + [ a r:Fact; r:gives {(7653 3567) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3675]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 7 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3567]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3674 a r:Inference; + r:gives { + 3676 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3676 math:notEqualTo 0}] + skolem:lemma6407 + [ a r:Fact; r:gives {((3 6 7 6) "=<") list:sort (3 6 6 7)}] + [ a r:Fact; r:gives {((3 6 7 6) ">=") list:sort (7 6 6 3)}] + skolem:lemma6393 + skolem:lemma6394 + [ a r:Fact; r:gives {(7663 3667) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3676]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 7 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3667]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7663]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3675 a r:Inference; + r:gives { + 3677 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3677 math:notEqualTo 0}] + skolem:lemma6408 + [ a r:Fact; r:gives {((3 6 7 7) "=<") list:sort (3 6 7 7)}] + [ a r:Fact; r:gives {((3 6 7 7) ">=") list:sort (7 7 6 3)}] + skolem:lemma6409 + skolem:lemma6410 + [ a r:Fact; r:gives {(7763 3677) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3677]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3677]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3676 a r:Inference; + r:gives { + 3678 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3678 math:notEqualTo 0}] + skolem:lemma6411 + [ a r:Fact; r:gives {((3 6 7 8) "=<") list:sort (3 6 7 8)}] + [ a r:Fact; r:gives {((3 6 7 8) ">=") list:sort (8 7 6 3)}] + skolem:lemma6412 + skolem:lemma6413 + [ a r:Fact; r:gives {(8763 3678) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3678]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3678]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3677 a r:Inference; + r:gives { + 3679 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3679 math:notEqualTo 0}] + skolem:lemma6414 + [ a r:Fact; r:gives {((3 6 7 9) "=<") list:sort (3 6 7 9)}] + [ a r:Fact; r:gives {((3 6 7 9) ">=") list:sort (9 7 6 3)}] + skolem:lemma6415 + skolem:lemma6416 + [ a r:Fact; r:gives {(9763 3679) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3679]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3679]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3678 a r:Inference; + r:gives { + 3680 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3680 math:notEqualTo 0}] + skolem:lemma6417 + [ a r:Fact; r:gives {((3 6 8 0) "=<") list:sort (0 3 6 8)}] + [ a r:Fact; r:gives {((3 6 8 0) ">=") list:sort (8 6 3 0)}] + skolem:lemma5579 + skolem:lemma5580 + [ a r:Fact; r:gives {(8630 368) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3680]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 8 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3679 a r:Inference; + r:gives { + 3681 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3681 math:notEqualTo 0}] + skolem:lemma6418 + [ a r:Fact; r:gives {((3 6 8 1) "=<") list:sort (1 3 6 8)}] + [ a r:Fact; r:gives {((3 6 8 1) ">=") list:sort (8 6 3 1)}] + skolem:lemma5751 + skolem:lemma5752 + [ a r:Fact; r:gives {(8631 1368) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3681]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 8 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3680 a r:Inference; + r:gives { + 3682 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3682 math:notEqualTo 0}] + skolem:lemma6419 + [ a r:Fact; r:gives {((3 6 8 2) "=<") list:sort (2 3 6 8)}] + [ a r:Fact; r:gives {((3 6 8 2) ">=") list:sort (8 6 3 2)}] + skolem:lemma4677 + skolem:lemma4678 + [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3682]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3681 a r:Inference; + r:gives { + 3683 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3683 math:notEqualTo 0}] + skolem:lemma6420 + [ a r:Fact; r:gives {((3 6 8 3) "=<") list:sort (3 3 6 8)}] + [ a r:Fact; r:gives {((3 6 8 3) ">=") list:sort (8 6 3 3)}] + skolem:lemma6004 + skolem:lemma6005 + [ a r:Fact; r:gives {(8633 3368) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3683]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3682 a r:Inference; + r:gives { + 3684 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3684 math:notEqualTo 0}] + skolem:lemma6421 + [ a r:Fact; r:gives {((3 6 8 4) "=<") list:sort (3 4 6 8)}] + [ a r:Fact; r:gives {((3 6 8 4) ">=") list:sort (8 6 4 3)}] + skolem:lemma6146 + skolem:lemma6147 + [ a r:Fact; r:gives {(8643 3468) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3684]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 8 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3468]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3683 a r:Inference; + r:gives { + 3685 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3685 math:notEqualTo 0}] + skolem:lemma6422 + [ a r:Fact; r:gives {((3 6 8 5) "=<") list:sort (3 5 6 8)}] + [ a r:Fact; r:gives {((3 6 8 5) ">=") list:sort (8 6 5 3)}] + skolem:lemma6276 + skolem:lemma6277 + [ a r:Fact; r:gives {(8653 3568) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3685]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 8 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3568]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3684 a r:Inference; + r:gives { + 3686 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3686 math:notEqualTo 0}] + skolem:lemma6423 + [ a r:Fact; r:gives {((3 6 8 6) "=<") list:sort (3 6 6 8)}] + [ a r:Fact; r:gives {((3 6 8 6) ">=") list:sort (8 6 6 3)}] + skolem:lemma6396 + skolem:lemma6397 + [ a r:Fact; r:gives {(8663 3668) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3686]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 8 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3668]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8663]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3685 a r:Inference; + r:gives { + 3687 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3687 math:notEqualTo 0}] + skolem:lemma6424 + [ a r:Fact; r:gives {((3 6 8 7) "=<") list:sort (3 6 7 8)}] + [ a r:Fact; r:gives {((3 6 8 7) ">=") list:sort (8 7 6 3)}] + skolem:lemma6412 + skolem:lemma6413 + [ a r:Fact; r:gives {(8763 3678) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3687]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 8 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3678]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3686 a r:Inference; + r:gives { + 3688 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3688 math:notEqualTo 0}] + skolem:lemma6425 + [ a r:Fact; r:gives {((3 6 8 8) "=<") list:sort (3 6 8 8)}] + [ a r:Fact; r:gives {((3 6 8 8) ">=") list:sort (8 8 6 3)}] + skolem:lemma6426 + skolem:lemma6427 + [ a r:Fact; r:gives {(8863 3688) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3688]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3688]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8863]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3687 a r:Inference; + r:gives { + 3689 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3689 math:notEqualTo 0}] + skolem:lemma6428 + [ a r:Fact; r:gives {((3 6 8 9) "=<") list:sort (3 6 8 9)}] + [ a r:Fact; r:gives {((3 6 8 9) ">=") list:sort (9 8 6 3)}] + skolem:lemma6429 + skolem:lemma6430 + [ a r:Fact; r:gives {(9863 3689) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3689]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3689]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9863]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3688 a r:Inference; + r:gives { + 3690 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3690 math:notEqualTo 0}] + skolem:lemma6431 + [ a r:Fact; r:gives {((3 6 9 0) "=<") list:sort (0 3 6 9)}] + [ a r:Fact; r:gives {((3 6 9 0) ">=") list:sort (9 6 3 0)}] + skolem:lemma5582 + skolem:lemma5583 + [ a r:Fact; r:gives {(9630 369) math:difference 9261}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9261 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9261 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3690]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 9 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9261]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3689 a r:Inference; + r:gives { + 3691 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3691 math:notEqualTo 0}] + skolem:lemma6432 + [ a r:Fact; r:gives {((3 6 9 1) "=<") list:sort (1 3 6 9)}] + [ a r:Fact; r:gives {((3 6 9 1) ">=") list:sort (9 6 3 1)}] + skolem:lemma5754 + skolem:lemma5755 + [ a r:Fact; r:gives {(9631 1369) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3691]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 9 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3690 a r:Inference; + r:gives { + 3692 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3692 math:notEqualTo 0}] + skolem:lemma6433 + [ a r:Fact; r:gives {((3 6 9 2) "=<") list:sort (2 3 6 9)}] + [ a r:Fact; r:gives {((3 6 9 2) ">=") list:sort (9 6 3 2)}] + skolem:lemma4680 + skolem:lemma4681 + [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3692]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 9 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3691 a r:Inference; + r:gives { + 3693 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3693 math:notEqualTo 0}] + skolem:lemma6434 + [ a r:Fact; r:gives {((3 6 9 3) "=<") list:sort (3 3 6 9)}] + [ a r:Fact; r:gives {((3 6 9 3) ">=") list:sort (9 6 3 3)}] + skolem:lemma6007 + skolem:lemma6008 + [ a r:Fact; r:gives {(9633 3369) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3693]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 9 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3692 a r:Inference; + r:gives { + 3694 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3694 math:notEqualTo 0}] + skolem:lemma6435 + [ a r:Fact; r:gives {((3 6 9 4) "=<") list:sort (3 4 6 9)}] + [ a r:Fact; r:gives {((3 6 9 4) ">=") list:sort (9 6 4 3)}] + skolem:lemma6149 + skolem:lemma6150 + [ a r:Fact; r:gives {(9643 3469) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3694]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 9 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3469]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3693 a r:Inference; + r:gives { + 3695 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3695 math:notEqualTo 0}] + skolem:lemma6436 + [ a r:Fact; r:gives {((3 6 9 5) "=<") list:sort (3 5 6 9)}] + [ a r:Fact; r:gives {((3 6 9 5) ">=") list:sort (9 6 5 3)}] + skolem:lemma6279 + skolem:lemma6280 + [ a r:Fact; r:gives {(9653 3569) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3695]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 9 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3569]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3694 a r:Inference; + r:gives { + 3696 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3696 math:notEqualTo 0}] + skolem:lemma6437 + [ a r:Fact; r:gives {((3 6 9 6) "=<") list:sort (3 6 6 9)}] + [ a r:Fact; r:gives {((3 6 9 6) ">=") list:sort (9 6 6 3)}] + skolem:lemma6399 + skolem:lemma6400 + [ a r:Fact; r:gives {(9663 3669) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3696]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 9 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3669]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9663]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3695 a r:Inference; + r:gives { + 3697 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3697 math:notEqualTo 0}] + skolem:lemma6438 + [ a r:Fact; r:gives {((3 6 9 7) "=<") list:sort (3 6 7 9)}] + [ a r:Fact; r:gives {((3 6 9 7) ">=") list:sort (9 7 6 3)}] + skolem:lemma6415 + skolem:lemma6416 + [ a r:Fact; r:gives {(9763 3679) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3697]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 9 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3679]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3696 a r:Inference; + r:gives { + 3698 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3698 math:notEqualTo 0}] + skolem:lemma6439 + [ a r:Fact; r:gives {((3 6 9 8) "=<") list:sort (3 6 8 9)}] + [ a r:Fact; r:gives {((3 6 9 8) ">=") list:sort (9 8 6 3)}] + skolem:lemma6429 + skolem:lemma6430 + [ a r:Fact; r:gives {(9863 3689) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3698]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 9 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3689]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9863]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3697 a r:Inference; + r:gives { + 3699 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3699 math:notEqualTo 0}] + skolem:lemma6440 + [ a r:Fact; r:gives {((3 6 9 9) "=<") list:sort (3 6 9 9)}] + [ a r:Fact; r:gives {((3 6 9 9) ">=") list:sort (9 9 6 3)}] + skolem:lemma6441 + skolem:lemma6442 + [ a r:Fact; r:gives {(9963 3699) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3699]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 6 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3699]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9963]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3698 a r:Inference; + r:gives { + 3700 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3700 math:notEqualTo 0}] + skolem:lemma6443 + [ a r:Fact; r:gives {((3 7 0 0) "=<") list:sort (0 0 3 7)}] + [ a r:Fact; r:gives {((3 7 0 0) ">=") list:sort (7 3 0 0)}] + skolem:lemma5456 + skolem:lemma5457 + [ a r:Fact; r:gives {(7300 37) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 37]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3699 a r:Inference; + r:gives { + 3701 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3701 math:notEqualTo 0}] + skolem:lemma6444 + [ a r:Fact; r:gives {((3 7 0 1) "=<") list:sort (0 1 3 7)}] + [ a r:Fact; r:gives {((3 7 0 1) ">=") list:sort (7 3 1 0)}] + skolem:lemma5482 + skolem:lemma5483 + [ a r:Fact; r:gives {(7310 137) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3701]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 0 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 137]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3700 a r:Inference; + r:gives { + 3702 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3702 math:notEqualTo 0}] + skolem:lemma6445 + [ a r:Fact; r:gives {((3 7 0 2) "=<") list:sort (0 2 3 7)}] + [ a r:Fact; r:gives {((3 7 0 2) ">=") list:sort (7 3 2 0)}] + skolem:lemma4099 + skolem:lemma4100 + [ a r:Fact; r:gives {(7320 237) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3702]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 0 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3701 a r:Inference; + r:gives { + 3703 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3703 math:notEqualTo 0}] + skolem:lemma6446 + [ a r:Fact; r:gives {((3 7 0 3) "=<") list:sort (0 3 3 7)}] + [ a r:Fact; r:gives {((3 7 0 3) ">=") list:sort (7 3 3 0)}] + skolem:lemma5516 + skolem:lemma5517 + [ a r:Fact; r:gives {(7330 337) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3703]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 0 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3702 a r:Inference; + r:gives { + 3704 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3704 math:notEqualTo 0}] + skolem:lemma6447 + [ a r:Fact; r:gives {((3 7 0 4) "=<") list:sort (0 3 4 7)}] + [ a r:Fact; r:gives {((3 7 0 4) ">=") list:sort (7 4 3 0)}] + skolem:lemma5538 + skolem:lemma5539 + [ a r:Fact; r:gives {(7430 347) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3704]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 0 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3703 a r:Inference; + r:gives { + 3705 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3705 math:notEqualTo 0}] + skolem:lemma6448 + [ a r:Fact; r:gives {((3 7 0 5) "=<") list:sort (0 3 5 7)}] + [ a r:Fact; r:gives {((3 7 0 5) ">=") list:sort (7 5 3 0)}] + skolem:lemma5558 + skolem:lemma5559 + [ a r:Fact; r:gives {(7530 357) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3705]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 0 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3704 a r:Inference; + r:gives { + 3706 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3706 math:notEqualTo 0}] + skolem:lemma6449 + [ a r:Fact; r:gives {((3 7 0 6) "=<") list:sort (0 3 6 7)}] + [ a r:Fact; r:gives {((3 7 0 6) ">=") list:sort (7 6 3 0)}] + skolem:lemma5576 + skolem:lemma5577 + [ a r:Fact; r:gives {(7630 367) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3706]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 0 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3705 a r:Inference; + r:gives { + 3707 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3707 math:notEqualTo 0}] + skolem:lemma6450 + [ a r:Fact; r:gives {((3 7 0 7) "=<") list:sort (0 3 7 7)}] + [ a r:Fact; r:gives {((3 7 0 7) ">=") list:sort (7 7 3 0)}] + skolem:lemma5592 + skolem:lemma5593 + [ a r:Fact; r:gives {(7730 377) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3707]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 0 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3706 a r:Inference; + r:gives { + 3708 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3708 math:notEqualTo 0}] + skolem:lemma6451 + [ a r:Fact; r:gives {((3 7 0 8) "=<") list:sort (0 3 7 8)}] + [ a r:Fact; r:gives {((3 7 0 8) ">=") list:sort (8 7 3 0)}] + skolem:lemma5595 + skolem:lemma5596 + [ a r:Fact; r:gives {(8730 378) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3708]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 0 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3707 a r:Inference; + r:gives { + 3709 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3709 math:notEqualTo 0}] + skolem:lemma6452 + [ a r:Fact; r:gives {((3 7 0 9) "=<") list:sort (0 3 7 9)}] + [ a r:Fact; r:gives {((3 7 0 9) ">=") list:sort (9 7 3 0)}] + skolem:lemma5598 + skolem:lemma5599 + [ a r:Fact; r:gives {(9730 379) math:difference 9351}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9351 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9351 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3709]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 0 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9351]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3708 a r:Inference; + r:gives { + 3710 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3710 math:notEqualTo 0}] + skolem:lemma6453 + [ a r:Fact; r:gives {((3 7 1 0) "=<") list:sort (0 1 3 7)}] + [ a r:Fact; r:gives {((3 7 1 0) ">=") list:sort (7 3 1 0)}] + skolem:lemma5482 + skolem:lemma5483 + [ a r:Fact; r:gives {(7310 137) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3710]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 137]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3709 a r:Inference; + r:gives { + 3711 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3711 math:notEqualTo 0}] + skolem:lemma6454 + [ a r:Fact; r:gives {((3 7 1 1) "=<") list:sort (1 1 3 7)}] + [ a r:Fact; r:gives {((3 7 1 1) ">=") list:sort (7 3 1 1)}] + skolem:lemma5654 + skolem:lemma5655 + [ a r:Fact; r:gives {(7311 1137) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3711]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1137]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3710 a r:Inference; + r:gives { + 3712 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3712 math:notEqualTo 0}] + skolem:lemma6455 + [ a r:Fact; r:gives {((3 7 1 2) "=<") list:sort (1 2 3 7)}] + [ a r:Fact; r:gives {((3 7 1 2) ">=") list:sort (7 3 2 1)}] + skolem:lemma4289 + skolem:lemma4290 + [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3712]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3711 a r:Inference; + r:gives { + 3713 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3713 math:notEqualTo 0}] + skolem:lemma6456 + [ a r:Fact; r:gives {((3 7 1 3) "=<") list:sort (1 3 3 7)}] + [ a r:Fact; r:gives {((3 7 1 3) ">=") list:sort (7 3 3 1)}] + skolem:lemma5688 + skolem:lemma5689 + [ a r:Fact; r:gives {(7331 1337) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3713]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3712 a r:Inference; + r:gives { + 3714 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3714 math:notEqualTo 0}] + skolem:lemma6457 + [ a r:Fact; r:gives {((3 7 1 4) "=<") list:sort (1 3 4 7)}] + [ a r:Fact; r:gives {((3 7 1 4) ">=") list:sort (7 4 3 1)}] + skolem:lemma5710 + skolem:lemma5711 + [ a r:Fact; r:gives {(7431 1347) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3714]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 1 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3713 a r:Inference; + r:gives { + 3715 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3715 math:notEqualTo 0}] + skolem:lemma6458 + [ a r:Fact; r:gives {((3 7 1 5) "=<") list:sort (1 3 5 7)}] + [ a r:Fact; r:gives {((3 7 1 5) ">=") list:sort (7 5 3 1)}] + skolem:lemma5730 + skolem:lemma5731 + [ a r:Fact; r:gives {(7531 1357) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3715]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 1 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3714 a r:Inference; + r:gives { + 3716 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3716 math:notEqualTo 0}] + skolem:lemma6459 + [ a r:Fact; r:gives {((3 7 1 6) "=<") list:sort (1 3 6 7)}] + [ a r:Fact; r:gives {((3 7 1 6) ">=") list:sort (7 6 3 1)}] + skolem:lemma5748 + skolem:lemma5749 + [ a r:Fact; r:gives {(7631 1367) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3716]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 1 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3715 a r:Inference; + r:gives { + 3717 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3717 math:notEqualTo 0}] + skolem:lemma6460 + [ a r:Fact; r:gives {((3 7 1 7) "=<") list:sort (1 3 7 7)}] + [ a r:Fact; r:gives {((3 7 1 7) ">=") list:sort (7 7 3 1)}] + skolem:lemma5764 + skolem:lemma5765 + [ a r:Fact; r:gives {(7731 1377) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3717]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 1 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7731]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3716 a r:Inference; + r:gives { + 3718 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3718 math:notEqualTo 0}] + skolem:lemma6461 + [ a r:Fact; r:gives {((3 7 1 8) "=<") list:sort (1 3 7 8)}] + [ a r:Fact; r:gives {((3 7 1 8) ">=") list:sort (8 7 3 1)}] + skolem:lemma5767 + skolem:lemma5768 + [ a r:Fact; r:gives {(8731 1378) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3718]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 1 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8731]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3717 a r:Inference; + r:gives { + 3719 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3719 math:notEqualTo 0}] + skolem:lemma6462 + [ a r:Fact; r:gives {((3 7 1 9) "=<") list:sort (1 3 7 9)}] + [ a r:Fact; r:gives {((3 7 1 9) ">=") list:sort (9 7 3 1)}] + skolem:lemma5770 + skolem:lemma5771 + [ a r:Fact; r:gives {(9731 1379) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3719]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 1 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9731]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3718 a r:Inference; + r:gives { + 3720 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3720 math:notEqualTo 0}] + skolem:lemma6463 + [ a r:Fact; r:gives {((3 7 2 0) "=<") list:sort (0 2 3 7)}] + [ a r:Fact; r:gives {((3 7 2 0) ">=") list:sort (7 3 2 0)}] + skolem:lemma4099 + skolem:lemma4100 + [ a r:Fact; r:gives {(7320 237) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3719 a r:Inference; + r:gives { + 3721 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3721 math:notEqualTo 0}] + skolem:lemma6464 + [ a r:Fact; r:gives {((3 7 2 1) "=<") list:sort (1 2 3 7)}] + [ a r:Fact; r:gives {((3 7 2 1) ">=") list:sort (7 3 2 1)}] + skolem:lemma4289 + skolem:lemma4290 + [ a r:Fact; r:gives {(7321 1237) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3720 a r:Inference; + r:gives { + 3722 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3722 math:notEqualTo 0}] + skolem:lemma6465 + [ a r:Fact; r:gives {((3 7 2 2) "=<") list:sort (2 2 3 7)}] + [ a r:Fact; r:gives {((3 7 2 2) ">=") list:sort (7 3 2 2)}] + skolem:lemma4458 + skolem:lemma4459 + [ a r:Fact; r:gives {(7322 2237) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3721 a r:Inference; + r:gives { + 3723 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3723 math:notEqualTo 0}] + skolem:lemma6466 + [ a r:Fact; r:gives {((3 7 2 3) "=<") list:sort (2 3 3 7)}] + [ a r:Fact; r:gives {((3 7 2 3) ">=") list:sort (7 3 3 2)}] + skolem:lemma4614 + skolem:lemma4615 + [ a r:Fact; r:gives {(7332 2337) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3723]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3722 a r:Inference; + r:gives { + 3724 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3724 math:notEqualTo 0}] + skolem:lemma6467 + [ a r:Fact; r:gives {((3 7 2 4) "=<") list:sort (2 3 4 7)}] + [ a r:Fact; r:gives {((3 7 2 4) ">=") list:sort (7 4 3 2)}] + skolem:lemma4636 + skolem:lemma4637 + [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3724]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3723 a r:Inference; + r:gives { + 3725 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3725 math:notEqualTo 0}] + skolem:lemma6468 + [ a r:Fact; r:gives {((3 7 2 5) "=<") list:sort (2 3 5 7)}] + [ a r:Fact; r:gives {((3 7 2 5) ">=") list:sort (7 5 3 2)}] + skolem:lemma4656 + skolem:lemma4657 + [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3725]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3724 a r:Inference; + r:gives { + 3726 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3726 math:notEqualTo 0}] + skolem:lemma6469 + [ a r:Fact; r:gives {((3 7 2 6) "=<") list:sort (2 3 6 7)}] + [ a r:Fact; r:gives {((3 7 2 6) ">=") list:sort (7 6 3 2)}] + skolem:lemma4674 + skolem:lemma4675 + [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3726]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3725 a r:Inference; + r:gives { + 3727 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3727 math:notEqualTo 0}] + skolem:lemma6470 + [ a r:Fact; r:gives {((3 7 2 7) "=<") list:sort (2 3 7 7)}] + [ a r:Fact; r:gives {((3 7 2 7) ">=") list:sort (7 7 3 2)}] + skolem:lemma4690 + skolem:lemma4691 + [ a r:Fact; r:gives {(7732 2377) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3727]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3726 a r:Inference; + r:gives { + 3728 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3728 math:notEqualTo 0}] + skolem:lemma6471 + [ a r:Fact; r:gives {((3 7 2 8) "=<") list:sort (2 3 7 8)}] + [ a r:Fact; r:gives {((3 7 2 8) ">=") list:sort (8 7 3 2)}] + skolem:lemma4693 + skolem:lemma4694 + [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3728]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3727 a r:Inference; + r:gives { + 3729 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3729 math:notEqualTo 0}] + skolem:lemma6472 + [ a r:Fact; r:gives {((3 7 2 9) "=<") list:sort (2 3 7 9)}] + [ a r:Fact; r:gives {((3 7 2 9) ">=") list:sort (9 7 3 2)}] + skolem:lemma4696 + skolem:lemma4697 + [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3729]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3728 a r:Inference; + r:gives { + 3730 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3730 math:notEqualTo 0}] + skolem:lemma6473 + [ a r:Fact; r:gives {((3 7 3 0) "=<") list:sort (0 3 3 7)}] + [ a r:Fact; r:gives {((3 7 3 0) ">=") list:sort (7 3 3 0)}] + skolem:lemma5516 + skolem:lemma5517 + [ a r:Fact; r:gives {(7330 337) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3729 a r:Inference; + r:gives { + 3731 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3731 math:notEqualTo 0}] + skolem:lemma6474 + [ a r:Fact; r:gives {((3 7 3 1) "=<") list:sort (1 3 3 7)}] + [ a r:Fact; r:gives {((3 7 3 1) ">=") list:sort (7 3 3 1)}] + skolem:lemma5688 + skolem:lemma5689 + [ a r:Fact; r:gives {(7331 1337) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3731]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3730 a r:Inference; + r:gives { + 3732 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3732 math:notEqualTo 0}] + skolem:lemma6475 + [ a r:Fact; r:gives {((3 7 3 2) "=<") list:sort (2 3 3 7)}] + [ a r:Fact; r:gives {((3 7 3 2) ">=") list:sort (7 3 3 2)}] + skolem:lemma4614 + skolem:lemma4615 + [ a r:Fact; r:gives {(7332 2337) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3731 a r:Inference; + r:gives { + 3733 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3733 math:notEqualTo 0}] + skolem:lemma6476 + [ a r:Fact; r:gives {((3 7 3 3) "=<") list:sort (3 3 3 7)}] + [ a r:Fact; r:gives {((3 7 3 3) ">=") list:sort (7 3 3 3)}] + skolem:lemma5941 + skolem:lemma5942 + [ a r:Fact; r:gives {(7333 3337) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3732 a r:Inference; + r:gives { + 3734 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3734 math:notEqualTo 0}] + skolem:lemma6477 + [ a r:Fact; r:gives {((3 7 3 4) "=<") list:sort (3 3 4 7)}] + [ a r:Fact; r:gives {((3 7 3 4) ">=") list:sort (7 4 3 3)}] + skolem:lemma5963 + skolem:lemma5964 + [ a r:Fact; r:gives {(7433 3347) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3734]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3733 a r:Inference; + r:gives { + 3735 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3735 math:notEqualTo 0}] + skolem:lemma6478 + [ a r:Fact; r:gives {((3 7 3 5) "=<") list:sort (3 3 5 7)}] + [ a r:Fact; r:gives {((3 7 3 5) ">=") list:sort (7 5 3 3)}] + skolem:lemma5983 + skolem:lemma5984 + [ a r:Fact; r:gives {(7533 3357) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3735]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3734 a r:Inference; + r:gives { + 3736 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3736 math:notEqualTo 0}] + skolem:lemma6479 + [ a r:Fact; r:gives {((3 7 3 6) "=<") list:sort (3 3 6 7)}] + [ a r:Fact; r:gives {((3 7 3 6) ">=") list:sort (7 6 3 3)}] + skolem:lemma6001 + skolem:lemma6002 + [ a r:Fact; r:gives {(7633 3367) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3736]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3735 a r:Inference; + r:gives { + 3737 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3737 math:notEqualTo 0}] + skolem:lemma6480 + [ a r:Fact; r:gives {((3 7 3 7) "=<") list:sort (3 3 7 7)}] + [ a r:Fact; r:gives {((3 7 3 7) ">=") list:sort (7 7 3 3)}] + skolem:lemma6017 + skolem:lemma6018 + [ a r:Fact; r:gives {(7733 3377) math:difference 4356}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4356 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 4356 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3737]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3736 a r:Inference; + r:gives { + 3738 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3738 math:notEqualTo 0}] + skolem:lemma6481 + [ a r:Fact; r:gives {((3 7 3 8) "=<") list:sort (3 3 7 8)}] + [ a r:Fact; r:gives {((3 7 3 8) ">=") list:sort (8 7 3 3)}] + skolem:lemma6020 + skolem:lemma6021 + [ a r:Fact; r:gives {(8733 3378) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3738]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3737 a r:Inference; + r:gives { + 3739 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3739 math:notEqualTo 0}] + skolem:lemma6482 + [ a r:Fact; r:gives {((3 7 3 9) "=<") list:sort (3 3 7 9)}] + [ a r:Fact; r:gives {((3 7 3 9) ">=") list:sort (9 7 3 3)}] + skolem:lemma6023 + skolem:lemma6024 + [ a r:Fact; r:gives {(9733 3379) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3739]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3738 a r:Inference; + r:gives { + 3740 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3740 math:notEqualTo 0}] + skolem:lemma6483 + [ a r:Fact; r:gives {((3 7 4 0) "=<") list:sort (0 3 4 7)}] + [ a r:Fact; r:gives {((3 7 4 0) ">=") list:sort (7 4 3 0)}] + skolem:lemma5538 + skolem:lemma5539 + [ a r:Fact; r:gives {(7430 347) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3740]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 4 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3739 a r:Inference; + r:gives { + 3741 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3741 math:notEqualTo 0}] + skolem:lemma6484 + [ a r:Fact; r:gives {((3 7 4 1) "=<") list:sort (1 3 4 7)}] + [ a r:Fact; r:gives {((3 7 4 1) ">=") list:sort (7 4 3 1)}] + skolem:lemma5710 + skolem:lemma5711 + [ a r:Fact; r:gives {(7431 1347) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3741]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 4 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3740 a r:Inference; + r:gives { + 3742 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3742 math:notEqualTo 0}] + skolem:lemma6485 + [ a r:Fact; r:gives {((3 7 4 2) "=<") list:sort (2 3 4 7)}] + [ a r:Fact; r:gives {((3 7 4 2) ">=") list:sort (7 4 3 2)}] + skolem:lemma4636 + skolem:lemma4637 + [ a r:Fact; r:gives {(7432 2347) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3741 a r:Inference; + r:gives { + 3743 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3743 math:notEqualTo 0}] + skolem:lemma6486 + [ a r:Fact; r:gives {((3 7 4 3) "=<") list:sort (3 3 4 7)}] + [ a r:Fact; r:gives {((3 7 4 3) ">=") list:sort (7 4 3 3)}] + skolem:lemma5963 + skolem:lemma5964 + [ a r:Fact; r:gives {(7433 3347) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3742 a r:Inference; + r:gives { + 3744 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3744 math:notEqualTo 0}] + skolem:lemma6487 + [ a r:Fact; r:gives {((3 7 4 4) "=<") list:sort (3 4 4 7)}] + [ a r:Fact; r:gives {((3 7 4 4) ">=") list:sort (7 4 4 3)}] + skolem:lemma6105 + skolem:lemma6106 + [ a r:Fact; r:gives {(7443 3447) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3744]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 4 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3447]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3743 a r:Inference; + r:gives { + 3745 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3745 math:notEqualTo 0}] + skolem:lemma6488 + [ a r:Fact; r:gives {((3 7 4 5) "=<") list:sort (3 4 5 7)}] + [ a r:Fact; r:gives {((3 7 4 5) ">=") list:sort (7 5 4 3)}] + skolem:lemma6125 + skolem:lemma6126 + [ a r:Fact; r:gives {(7543 3457) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3745]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3457]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3744 a r:Inference; + r:gives { + 3746 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3746 math:notEqualTo 0}] + skolem:lemma6489 + [ a r:Fact; r:gives {((3 7 4 6) "=<") list:sort (3 4 6 7)}] + [ a r:Fact; r:gives {((3 7 4 6) ">=") list:sort (7 6 4 3)}] + skolem:lemma6143 + skolem:lemma6144 + [ a r:Fact; r:gives {(7643 3467) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3746]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3467]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3745 a r:Inference; + r:gives { + 3747 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3747 math:notEqualTo 0}] + skolem:lemma6490 + [ a r:Fact; r:gives {((3 7 4 7) "=<") list:sort (3 4 7 7)}] + [ a r:Fact; r:gives {((3 7 4 7) ">=") list:sort (7 7 4 3)}] + skolem:lemma6159 + skolem:lemma6160 + [ a r:Fact; r:gives {(7743 3477) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3747]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3477]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3746 a r:Inference; + r:gives { + 3748 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3748 math:notEqualTo 0}] + skolem:lemma6491 + [ a r:Fact; r:gives {((3 7 4 8) "=<") list:sort (3 4 7 8)}] + [ a r:Fact; r:gives {((3 7 4 8) ">=") list:sort (8 7 4 3)}] + skolem:lemma6162 + skolem:lemma6163 + [ a r:Fact; r:gives {(8743 3478) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3748]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3478]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3747 a r:Inference; + r:gives { + 3749 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3749 math:notEqualTo 0}] + skolem:lemma6492 + [ a r:Fact; r:gives {((3 7 4 9) "=<") list:sort (3 4 7 9)}] + [ a r:Fact; r:gives {((3 7 4 9) ">=") list:sort (9 7 4 3)}] + skolem:lemma6165 + skolem:lemma6166 + [ a r:Fact; r:gives {(9743 3479) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3749]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3479]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3748 a r:Inference; + r:gives { + 3750 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3750 math:notEqualTo 0}] + skolem:lemma6493 + [ a r:Fact; r:gives {((3 7 5 0) "=<") list:sort (0 3 5 7)}] + [ a r:Fact; r:gives {((3 7 5 0) ">=") list:sort (7 5 3 0)}] + skolem:lemma5558 + skolem:lemma5559 + [ a r:Fact; r:gives {(7530 357) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3750]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 5 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3749 a r:Inference; + r:gives { + 3751 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3751 math:notEqualTo 0}] + skolem:lemma6494 + [ a r:Fact; r:gives {((3 7 5 1) "=<") list:sort (1 3 5 7)}] + [ a r:Fact; r:gives {((3 7 5 1) ">=") list:sort (7 5 3 1)}] + skolem:lemma5730 + skolem:lemma5731 + [ a r:Fact; r:gives {(7531 1357) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3751]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 5 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3750 a r:Inference; + r:gives { + 3752 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3752 math:notEqualTo 0}] + skolem:lemma6495 + [ a r:Fact; r:gives {((3 7 5 2) "=<") list:sort (2 3 5 7)}] + [ a r:Fact; r:gives {((3 7 5 2) ">=") list:sort (7 5 3 2)}] + skolem:lemma4656 + skolem:lemma4657 + [ a r:Fact; r:gives {(7532 2357) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3751 a r:Inference; + r:gives { + 3753 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3753 math:notEqualTo 0}] + skolem:lemma6496 + [ a r:Fact; r:gives {((3 7 5 3) "=<") list:sort (3 3 5 7)}] + [ a r:Fact; r:gives {((3 7 5 3) ">=") list:sort (7 5 3 3)}] + skolem:lemma5983 + skolem:lemma5984 + [ a r:Fact; r:gives {(7533 3357) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3752 a r:Inference; + r:gives { + 3754 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3754 math:notEqualTo 0}] + skolem:lemma6497 + [ a r:Fact; r:gives {((3 7 5 4) "=<") list:sort (3 4 5 7)}] + [ a r:Fact; r:gives {((3 7 5 4) ">=") list:sort (7 5 4 3)}] + skolem:lemma6125 + skolem:lemma6126 + [ a r:Fact; r:gives {(7543 3457) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3754]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 5 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3457]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3753 a r:Inference; + r:gives { + 3755 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3755 math:notEqualTo 0}] + skolem:lemma6498 + [ a r:Fact; r:gives {((3 7 5 5) "=<") list:sort (3 5 5 7)}] + [ a r:Fact; r:gives {((3 7 5 5) ">=") list:sort (7 5 5 3)}] + skolem:lemma6255 + skolem:lemma6256 + [ a r:Fact; r:gives {(7553 3557) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3755]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 5 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3557]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3754 a r:Inference; + r:gives { + 3756 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3756 math:notEqualTo 0}] + skolem:lemma6499 + [ a r:Fact; r:gives {((3 7 5 6) "=<") list:sort (3 5 6 7)}] + [ a r:Fact; r:gives {((3 7 5 6) ">=") list:sort (7 6 5 3)}] + skolem:lemma6273 + skolem:lemma6274 + [ a r:Fact; r:gives {(7653 3567) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3756]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3567]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3755 a r:Inference; + r:gives { + 3757 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3757 math:notEqualTo 0}] + skolem:lemma6500 + [ a r:Fact; r:gives {((3 7 5 7) "=<") list:sort (3 5 7 7)}] + [ a r:Fact; r:gives {((3 7 5 7) ">=") list:sort (7 7 5 3)}] + skolem:lemma6289 + skolem:lemma6290 + [ a r:Fact; r:gives {(7753 3577) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3757]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3577]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3756 a r:Inference; + r:gives { + 3758 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3758 math:notEqualTo 0}] + skolem:lemma6501 + [ a r:Fact; r:gives {((3 7 5 8) "=<") list:sort (3 5 7 8)}] + [ a r:Fact; r:gives {((3 7 5 8) ">=") list:sort (8 7 5 3)}] + skolem:lemma6292 + skolem:lemma6293 + [ a r:Fact; r:gives {(8753 3578) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3758]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3578]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3757 a r:Inference; + r:gives { + 3759 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3759 math:notEqualTo 0}] + skolem:lemma6502 + [ a r:Fact; r:gives {((3 7 5 9) "=<") list:sort (3 5 7 9)}] + [ a r:Fact; r:gives {((3 7 5 9) ">=") list:sort (9 7 5 3)}] + skolem:lemma6295 + skolem:lemma6296 + [ a r:Fact; r:gives {(9753 3579) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3759]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3579]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3758 a r:Inference; + r:gives { + 3760 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3760 math:notEqualTo 0}] + skolem:lemma6503 + [ a r:Fact; r:gives {((3 7 6 0) "=<") list:sort (0 3 6 7)}] + [ a r:Fact; r:gives {((3 7 6 0) ">=") list:sort (7 6 3 0)}] + skolem:lemma5576 + skolem:lemma5577 + [ a r:Fact; r:gives {(7630 367) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3760]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 6 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3759 a r:Inference; + r:gives { + 3761 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3761 math:notEqualTo 0}] + skolem:lemma6504 + [ a r:Fact; r:gives {((3 7 6 1) "=<") list:sort (1 3 6 7)}] + [ a r:Fact; r:gives {((3 7 6 1) ">=") list:sort (7 6 3 1)}] + skolem:lemma5748 + skolem:lemma5749 + [ a r:Fact; r:gives {(7631 1367) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3761]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 6 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3760 a r:Inference; + r:gives { + 3762 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3762 math:notEqualTo 0}] + skolem:lemma6505 + [ a r:Fact; r:gives {((3 7 6 2) "=<") list:sort (2 3 6 7)}] + [ a r:Fact; r:gives {((3 7 6 2) ">=") list:sort (7 6 3 2)}] + skolem:lemma4674 + skolem:lemma4675 + [ a r:Fact; r:gives {(7632 2367) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3761 a r:Inference; + r:gives { + 3763 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3763 math:notEqualTo 0}] + skolem:lemma6506 + [ a r:Fact; r:gives {((3 7 6 3) "=<") list:sort (3 3 6 7)}] + [ a r:Fact; r:gives {((3 7 6 3) ">=") list:sort (7 6 3 3)}] + skolem:lemma6001 + skolem:lemma6002 + [ a r:Fact; r:gives {(7633 3367) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3762 a r:Inference; + r:gives { + 3764 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3764 math:notEqualTo 0}] + skolem:lemma6507 + [ a r:Fact; r:gives {((3 7 6 4) "=<") list:sort (3 4 6 7)}] + [ a r:Fact; r:gives {((3 7 6 4) ">=") list:sort (7 6 4 3)}] + skolem:lemma6143 + skolem:lemma6144 + [ a r:Fact; r:gives {(7643 3467) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3764]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 6 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3467]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3763 a r:Inference; + r:gives { + 3765 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3765 math:notEqualTo 0}] + skolem:lemma6508 + [ a r:Fact; r:gives {((3 7 6 5) "=<") list:sort (3 5 6 7)}] + [ a r:Fact; r:gives {((3 7 6 5) ">=") list:sort (7 6 5 3)}] + skolem:lemma6273 + skolem:lemma6274 + [ a r:Fact; r:gives {(7653 3567) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3765]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 6 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3567]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3764 a r:Inference; + r:gives { + 3766 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3766 math:notEqualTo 0}] + skolem:lemma6509 + [ a r:Fact; r:gives {((3 7 6 6) "=<") list:sort (3 6 6 7)}] + [ a r:Fact; r:gives {((3 7 6 6) ">=") list:sort (7 6 6 3)}] + skolem:lemma6393 + skolem:lemma6394 + [ a r:Fact; r:gives {(7663 3667) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3766]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 6 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3667]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7663]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3765 a r:Inference; + r:gives { + 3767 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3767 math:notEqualTo 0}] + skolem:lemma6510 + [ a r:Fact; r:gives {((3 7 6 7) "=<") list:sort (3 6 7 7)}] + [ a r:Fact; r:gives {((3 7 6 7) ">=") list:sort (7 7 6 3)}] + skolem:lemma6409 + skolem:lemma6410 + [ a r:Fact; r:gives {(7763 3677) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3767]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3677]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3766 a r:Inference; + r:gives { + 3768 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3768 math:notEqualTo 0}] + skolem:lemma6511 + [ a r:Fact; r:gives {((3 7 6 8) "=<") list:sort (3 6 7 8)}] + [ a r:Fact; r:gives {((3 7 6 8) ">=") list:sort (8 7 6 3)}] + skolem:lemma6412 + skolem:lemma6413 + [ a r:Fact; r:gives {(8763 3678) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3768]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3678]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3767 a r:Inference; + r:gives { + 3769 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3769 math:notEqualTo 0}] + skolem:lemma6512 + [ a r:Fact; r:gives {((3 7 6 9) "=<") list:sort (3 6 7 9)}] + [ a r:Fact; r:gives {((3 7 6 9) ">=") list:sort (9 7 6 3)}] + skolem:lemma6415 + skolem:lemma6416 + [ a r:Fact; r:gives {(9763 3679) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3769]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3679]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3768 a r:Inference; + r:gives { + 3770 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3770 math:notEqualTo 0}] + skolem:lemma6513 + [ a r:Fact; r:gives {((3 7 7 0) "=<") list:sort (0 3 7 7)}] + [ a r:Fact; r:gives {((3 7 7 0) ">=") list:sort (7 7 3 0)}] + skolem:lemma5592 + skolem:lemma5593 + [ a r:Fact; r:gives {(7730 377) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3770]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 7 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3769 a r:Inference; + r:gives { + 3771 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3771 math:notEqualTo 0}] + skolem:lemma6514 + [ a r:Fact; r:gives {((3 7 7 1) "=<") list:sort (1 3 7 7)}] + [ a r:Fact; r:gives {((3 7 7 1) ">=") list:sort (7 7 3 1)}] + skolem:lemma5764 + skolem:lemma5765 + [ a r:Fact; r:gives {(7731 1377) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3771]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 7 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7731]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3770 a r:Inference; + r:gives { + 3772 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3772 math:notEqualTo 0}] + skolem:lemma6515 + [ a r:Fact; r:gives {((3 7 7 2) "=<") list:sort (2 3 7 7)}] + [ a r:Fact; r:gives {((3 7 7 2) ">=") list:sort (7 7 3 2)}] + skolem:lemma4690 + skolem:lemma4691 + [ a r:Fact; r:gives {(7732 2377) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3772]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3771 a r:Inference; + r:gives { + 3773 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3773 math:notEqualTo 0}] + skolem:lemma6516 + [ a r:Fact; r:gives {((3 7 7 3) "=<") list:sort (3 3 7 7)}] + [ a r:Fact; r:gives {((3 7 7 3) ">=") list:sort (7 7 3 3)}] + skolem:lemma6017 + skolem:lemma6018 + [ a r:Fact; r:gives {(7733 3377) math:difference 4356}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4356 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 4356 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3773]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3772 a r:Inference; + r:gives { + 3774 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3774 math:notEqualTo 0}] + skolem:lemma6517 + [ a r:Fact; r:gives {((3 7 7 4) "=<") list:sort (3 4 7 7)}] + [ a r:Fact; r:gives {((3 7 7 4) ">=") list:sort (7 7 4 3)}] + skolem:lemma6159 + skolem:lemma6160 + [ a r:Fact; r:gives {(7743 3477) math:difference 4266}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4266 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 4266 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3774]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 7 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3477]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3773 a r:Inference; + r:gives { + 3775 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3775 math:notEqualTo 0}] + skolem:lemma6518 + [ a r:Fact; r:gives {((3 7 7 5) "=<") list:sort (3 5 7 7)}] + [ a r:Fact; r:gives {((3 7 7 5) ">=") list:sort (7 7 5 3)}] + skolem:lemma6289 + skolem:lemma6290 + [ a r:Fact; r:gives {(7753 3577) math:difference 4176}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4176 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 4176 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3775]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 7 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3577]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3774 a r:Inference; + r:gives { + 3776 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3776 math:notEqualTo 0}] + skolem:lemma6519 + [ a r:Fact; r:gives {((3 7 7 6) "=<") list:sort (3 6 7 7)}] + [ a r:Fact; r:gives {((3 7 7 6) ">=") list:sort (7 7 6 3)}] + skolem:lemma6409 + skolem:lemma6410 + [ a r:Fact; r:gives {(7763 3677) math:difference 4086}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4086 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 4086 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3776]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 7 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3677]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3775 a r:Inference; + r:gives { + 3777 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3777 math:notEqualTo 0}] + skolem:lemma6520 + [ a r:Fact; r:gives {((3 7 7 7) "=<") list:sort (3 7 7 7)}] + [ a r:Fact; r:gives {((3 7 7 7) ">=") list:sort (7 7 7 3)}] + skolem:lemma6521 + skolem:lemma6522 + [ a r:Fact; r:gives {(7773 3777) math:difference 3996}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 3996 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 3996 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3777]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (7 7 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3777]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7773]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3776 a r:Inference; + r:gives { + 3778 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3778 math:notEqualTo 0}] + skolem:lemma6523 + [ a r:Fact; r:gives {((3 7 7 8) "=<") list:sort (3 7 7 8)}] + [ a r:Fact; r:gives {((3 7 7 8) ">=") list:sort (8 7 7 3)}] + skolem:lemma6524 + skolem:lemma6525 + [ a r:Fact; r:gives {(8773 3778) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3778]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3778]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8773]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3777 a r:Inference; + r:gives { + 3779 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3779 math:notEqualTo 0}] + skolem:lemma6526 + [ a r:Fact; r:gives {((3 7 7 9) "=<") list:sort (3 7 7 9)}] + [ a r:Fact; r:gives {((3 7 7 9) ">=") list:sort (9 7 7 3)}] + skolem:lemma6527 + skolem:lemma6528 + [ a r:Fact; r:gives {(9773 3779) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3779]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3779]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9773]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3778 a r:Inference; + r:gives { + 3780 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3780 math:notEqualTo 0}] + skolem:lemma6529 + [ a r:Fact; r:gives {((3 7 8 0) "=<") list:sort (0 3 7 8)}] + [ a r:Fact; r:gives {((3 7 8 0) ">=") list:sort (8 7 3 0)}] + skolem:lemma5595 + skolem:lemma5596 + [ a r:Fact; r:gives {(8730 378) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3780]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 8 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3779 a r:Inference; + r:gives { + 3781 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3781 math:notEqualTo 0}] + skolem:lemma6530 + [ a r:Fact; r:gives {((3 7 8 1) "=<") list:sort (1 3 7 8)}] + [ a r:Fact; r:gives {((3 7 8 1) ">=") list:sort (8 7 3 1)}] + skolem:lemma5767 + skolem:lemma5768 + [ a r:Fact; r:gives {(8731 1378) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3781]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 8 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8731]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3780 a r:Inference; + r:gives { + 3782 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3782 math:notEqualTo 0}] + skolem:lemma6531 + [ a r:Fact; r:gives {((3 7 8 2) "=<") list:sort (2 3 7 8)}] + [ a r:Fact; r:gives {((3 7 8 2) ">=") list:sort (8 7 3 2)}] + skolem:lemma4693 + skolem:lemma4694 + [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3782]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3781 a r:Inference; + r:gives { + 3783 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3783 math:notEqualTo 0}] + skolem:lemma6532 + [ a r:Fact; r:gives {((3 7 8 3) "=<") list:sort (3 3 7 8)}] + [ a r:Fact; r:gives {((3 7 8 3) ">=") list:sort (8 7 3 3)}] + skolem:lemma6020 + skolem:lemma6021 + [ a r:Fact; r:gives {(8733 3378) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3783]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3782 a r:Inference; + r:gives { + 3784 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3784 math:notEqualTo 0}] + skolem:lemma6533 + [ a r:Fact; r:gives {((3 7 8 4) "=<") list:sort (3 4 7 8)}] + [ a r:Fact; r:gives {((3 7 8 4) ">=") list:sort (8 7 4 3)}] + skolem:lemma6162 + skolem:lemma6163 + [ a r:Fact; r:gives {(8743 3478) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3784]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 8 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3478]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3783 a r:Inference; + r:gives { + 3785 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3785 math:notEqualTo 0}] + skolem:lemma6534 + [ a r:Fact; r:gives {((3 7 8 5) "=<") list:sort (3 5 7 8)}] + [ a r:Fact; r:gives {((3 7 8 5) ">=") list:sort (8 7 5 3)}] + skolem:lemma6292 + skolem:lemma6293 + [ a r:Fact; r:gives {(8753 3578) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3785]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 8 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3578]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3784 a r:Inference; + r:gives { + 3786 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3786 math:notEqualTo 0}] + skolem:lemma6535 + [ a r:Fact; r:gives {((3 7 8 6) "=<") list:sort (3 6 7 8)}] + [ a r:Fact; r:gives {((3 7 8 6) ">=") list:sort (8 7 6 3)}] + skolem:lemma6412 + skolem:lemma6413 + [ a r:Fact; r:gives {(8763 3678) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3786]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 8 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3678]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3785 a r:Inference; + r:gives { + 3787 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3787 math:notEqualTo 0}] + skolem:lemma6536 + [ a r:Fact; r:gives {((3 7 8 7) "=<") list:sort (3 7 7 8)}] + [ a r:Fact; r:gives {((3 7 8 7) ">=") list:sort (8 7 7 3)}] + skolem:lemma6524 + skolem:lemma6525 + [ a r:Fact; r:gives {(8773 3778) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3787]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 8 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3778]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8773]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3786 a r:Inference; + r:gives { + 3788 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3788 math:notEqualTo 0}] + skolem:lemma6537 + [ a r:Fact; r:gives {((3 7 8 8) "=<") list:sort (3 7 8 8)}] + [ a r:Fact; r:gives {((3 7 8 8) ">=") list:sort (8 8 7 3)}] + skolem:lemma6538 + skolem:lemma6539 + [ a r:Fact; r:gives {(8873 3788) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3788]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3788]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8873]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3787 a r:Inference; + r:gives { + 3789 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3789 math:notEqualTo 0}] + skolem:lemma6540 + [ a r:Fact; r:gives {((3 7 8 9) "=<") list:sort (3 7 8 9)}] + [ a r:Fact; r:gives {((3 7 8 9) ">=") list:sort (9 8 7 3)}] + skolem:lemma6541 + skolem:lemma6542 + [ a r:Fact; r:gives {(9873 3789) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3789]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3789]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9873]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3788 a r:Inference; + r:gives { + 3790 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3790 math:notEqualTo 0}] + skolem:lemma6543 + [ a r:Fact; r:gives {((3 7 9 0) "=<") list:sort (0 3 7 9)}] + [ a r:Fact; r:gives {((3 7 9 0) ">=") list:sort (9 7 3 0)}] + skolem:lemma5598 + skolem:lemma5599 + [ a r:Fact; r:gives {(9730 379) math:difference 9351}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9351 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9351 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3790]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 9 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9351]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3789 a r:Inference; + r:gives { + 3791 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3791 math:notEqualTo 0}] + skolem:lemma6544 + [ a r:Fact; r:gives {((3 7 9 1) "=<") list:sort (1 3 7 9)}] + [ a r:Fact; r:gives {((3 7 9 1) ">=") list:sort (9 7 3 1)}] + skolem:lemma5770 + skolem:lemma5771 + [ a r:Fact; r:gives {(9731 1379) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3791]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 9 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9731]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3790 a r:Inference; + r:gives { + 3792 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3792 math:notEqualTo 0}] + skolem:lemma6545 + [ a r:Fact; r:gives {((3 7 9 2) "=<") list:sort (2 3 7 9)}] + [ a r:Fact; r:gives {((3 7 9 2) ">=") list:sort (9 7 3 2)}] + skolem:lemma4696 + skolem:lemma4697 + [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3792]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 9 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3791 a r:Inference; + r:gives { + 3793 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3793 math:notEqualTo 0}] + skolem:lemma6546 + [ a r:Fact; r:gives {((3 7 9 3) "=<") list:sort (3 3 7 9)}] + [ a r:Fact; r:gives {((3 7 9 3) ">=") list:sort (9 7 3 3)}] + skolem:lemma6023 + skolem:lemma6024 + [ a r:Fact; r:gives {(9733 3379) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3793]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 9 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3792 a r:Inference; + r:gives { + 3794 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3794 math:notEqualTo 0}] + skolem:lemma6547 + [ a r:Fact; r:gives {((3 7 9 4) "=<") list:sort (3 4 7 9)}] + [ a r:Fact; r:gives {((3 7 9 4) ">=") list:sort (9 7 4 3)}] + skolem:lemma6165 + skolem:lemma6166 + [ a r:Fact; r:gives {(9743 3479) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3794]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 9 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3479]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3793 a r:Inference; + r:gives { + 3795 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3795 math:notEqualTo 0}] + skolem:lemma6548 + [ a r:Fact; r:gives {((3 7 9 5) "=<") list:sort (3 5 7 9)}] + [ a r:Fact; r:gives {((3 7 9 5) ">=") list:sort (9 7 5 3)}] + skolem:lemma6295 + skolem:lemma6296 + [ a r:Fact; r:gives {(9753 3579) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3795]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 9 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3579]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3794 a r:Inference; + r:gives { + 3796 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3796 math:notEqualTo 0}] + skolem:lemma6549 + [ a r:Fact; r:gives {((3 7 9 6) "=<") list:sort (3 6 7 9)}] + [ a r:Fact; r:gives {((3 7 9 6) ">=") list:sort (9 7 6 3)}] + skolem:lemma6415 + skolem:lemma6416 + [ a r:Fact; r:gives {(9763 3679) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3796]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 9 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3679]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3795 a r:Inference; + r:gives { + 3797 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3797 math:notEqualTo 0}] + skolem:lemma6550 + [ a r:Fact; r:gives {((3 7 9 7) "=<") list:sort (3 7 7 9)}] + [ a r:Fact; r:gives {((3 7 9 7) ">=") list:sort (9 7 7 3)}] + skolem:lemma6527 + skolem:lemma6528 + [ a r:Fact; r:gives {(9773 3779) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3797]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 9 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3779]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9773]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3796 a r:Inference; + r:gives { + 3798 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3798 math:notEqualTo 0}] + skolem:lemma6551 + [ a r:Fact; r:gives {((3 7 9 8) "=<") list:sort (3 7 8 9)}] + [ a r:Fact; r:gives {((3 7 9 8) ">=") list:sort (9 8 7 3)}] + skolem:lemma6541 + skolem:lemma6542 + [ a r:Fact; r:gives {(9873 3789) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3798]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 9 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3789]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9873]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3797 a r:Inference; + r:gives { + 3799 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3799 math:notEqualTo 0}] + skolem:lemma6552 + [ a r:Fact; r:gives {((3 7 9 9) "=<") list:sort (3 7 9 9)}] + [ a r:Fact; r:gives {((3 7 9 9) ">=") list:sort (9 9 7 3)}] + skolem:lemma6553 + skolem:lemma6554 + [ a r:Fact; r:gives {(9973 3799) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3799]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 7 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3799]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9973]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3798 a r:Inference; + r:gives { + 3800 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3800 math:notEqualTo 0}] + skolem:lemma6555 + [ a r:Fact; r:gives {((3 8 0 0) "=<") list:sort (0 0 3 8)}] + [ a r:Fact; r:gives {((3 8 0 0) ">=") list:sort (8 3 0 0)}] + skolem:lemma5459 + skolem:lemma5460 + [ a r:Fact; r:gives {(8300 38) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 38]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3799 a r:Inference; + r:gives { + 3801 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3801 math:notEqualTo 0}] + skolem:lemma6556 + [ a r:Fact; r:gives {((3 8 0 1) "=<") list:sort (0 1 3 8)}] + [ a r:Fact; r:gives {((3 8 0 1) ">=") list:sort (8 3 1 0)}] + skolem:lemma5485 + skolem:lemma5486 + [ a r:Fact; r:gives {(8310 138) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3801]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 0 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 138]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3800 a r:Inference; + r:gives { + 3802 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3802 math:notEqualTo 0}] + skolem:lemma6557 + [ a r:Fact; r:gives {((3 8 0 2) "=<") list:sort (0 2 3 8)}] + [ a r:Fact; r:gives {((3 8 0 2) ">=") list:sort (8 3 2 0)}] + skolem:lemma4102 + skolem:lemma4103 + [ a r:Fact; r:gives {(8320 238) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3802]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 0 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3801 a r:Inference; + r:gives { + 3803 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3803 math:notEqualTo 0}] + skolem:lemma6558 + [ a r:Fact; r:gives {((3 8 0 3) "=<") list:sort (0 3 3 8)}] + [ a r:Fact; r:gives {((3 8 0 3) ">=") list:sort (8 3 3 0)}] + skolem:lemma5519 + skolem:lemma5520 + [ a r:Fact; r:gives {(8330 338) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3803]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 0 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3802 a r:Inference; + r:gives { + 3804 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3804 math:notEqualTo 0}] + skolem:lemma6559 + [ a r:Fact; r:gives {((3 8 0 4) "=<") list:sort (0 3 4 8)}] + [ a r:Fact; r:gives {((3 8 0 4) ">=") list:sort (8 4 3 0)}] + skolem:lemma5541 + skolem:lemma5542 + [ a r:Fact; r:gives {(8430 348) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3804]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 0 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3803 a r:Inference; + r:gives { + 3805 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3805 math:notEqualTo 0}] + skolem:lemma6560 + [ a r:Fact; r:gives {((3 8 0 5) "=<") list:sort (0 3 5 8)}] + [ a r:Fact; r:gives {((3 8 0 5) ">=") list:sort (8 5 3 0)}] + skolem:lemma5561 + skolem:lemma5562 + [ a r:Fact; r:gives {(8530 358) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3805]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 0 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3804 a r:Inference; + r:gives { + 3806 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3806 math:notEqualTo 0}] + skolem:lemma6561 + [ a r:Fact; r:gives {((3 8 0 6) "=<") list:sort (0 3 6 8)}] + [ a r:Fact; r:gives {((3 8 0 6) ">=") list:sort (8 6 3 0)}] + skolem:lemma5579 + skolem:lemma5580 + [ a r:Fact; r:gives {(8630 368) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3806]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 0 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3805 a r:Inference; + r:gives { + 3807 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3807 math:notEqualTo 0}] + skolem:lemma6562 + [ a r:Fact; r:gives {((3 8 0 7) "=<") list:sort (0 3 7 8)}] + [ a r:Fact; r:gives {((3 8 0 7) ">=") list:sort (8 7 3 0)}] + skolem:lemma5595 + skolem:lemma5596 + [ a r:Fact; r:gives {(8730 378) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3807]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 0 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3806 a r:Inference; + r:gives { + 3808 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3808 math:notEqualTo 0}] + skolem:lemma6563 + [ a r:Fact; r:gives {((3 8 0 8) "=<") list:sort (0 3 8 8)}] + [ a r:Fact; r:gives {((3 8 0 8) ">=") list:sort (8 8 3 0)}] + skolem:lemma5609 + skolem:lemma5610 + [ a r:Fact; r:gives {(8830 388) math:difference 8442}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8442 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 8442 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3808]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 0 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8830]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3807 a r:Inference; + r:gives { + 3809 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3809 math:notEqualTo 0}] + skolem:lemma6564 + [ a r:Fact; r:gives {((3 8 0 9) "=<") list:sort (0 3 8 9)}] + [ a r:Fact; r:gives {((3 8 0 9) ">=") list:sort (9 8 3 0)}] + skolem:lemma5612 + skolem:lemma5613 + [ a r:Fact; r:gives {(9830 389) math:difference 9441}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9441 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9441 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3809]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 0 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9830]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9441]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3808 a r:Inference; + r:gives { + 3810 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3810 math:notEqualTo 0}] + skolem:lemma6565 + [ a r:Fact; r:gives {((3 8 1 0) "=<") list:sort (0 1 3 8)}] + [ a r:Fact; r:gives {((3 8 1 0) ">=") list:sort (8 3 1 0)}] + skolem:lemma5485 + skolem:lemma5486 + [ a r:Fact; r:gives {(8310 138) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3810]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 138]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3809 a r:Inference; + r:gives { + 3811 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3811 math:notEqualTo 0}] + skolem:lemma6566 + [ a r:Fact; r:gives {((3 8 1 1) "=<") list:sort (1 1 3 8)}] + [ a r:Fact; r:gives {((3 8 1 1) ">=") list:sort (8 3 1 1)}] + skolem:lemma5657 + skolem:lemma5658 + [ a r:Fact; r:gives {(8311 1138) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3811]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1138]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3810 a r:Inference; + r:gives { + 3812 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3812 math:notEqualTo 0}] + skolem:lemma6567 + [ a r:Fact; r:gives {((3 8 1 2) "=<") list:sort (1 2 3 8)}] + [ a r:Fact; r:gives {((3 8 1 2) ">=") list:sort (8 3 2 1)}] + skolem:lemma4292 + skolem:lemma4293 + [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3812]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3811 a r:Inference; + r:gives { + 3813 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3813 math:notEqualTo 0}] + skolem:lemma6568 + [ a r:Fact; r:gives {((3 8 1 3) "=<") list:sort (1 3 3 8)}] + [ a r:Fact; r:gives {((3 8 1 3) ">=") list:sort (8 3 3 1)}] + skolem:lemma5691 + skolem:lemma5692 + [ a r:Fact; r:gives {(8331 1338) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3813]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3812 a r:Inference; + r:gives { + 3814 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3814 math:notEqualTo 0}] + skolem:lemma6569 + [ a r:Fact; r:gives {((3 8 1 4) "=<") list:sort (1 3 4 8)}] + [ a r:Fact; r:gives {((3 8 1 4) ">=") list:sort (8 4 3 1)}] + skolem:lemma5713 + skolem:lemma5714 + [ a r:Fact; r:gives {(8431 1348) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3814]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 1 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3813 a r:Inference; + r:gives { + 3815 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3815 math:notEqualTo 0}] + skolem:lemma6570 + [ a r:Fact; r:gives {((3 8 1 5) "=<") list:sort (1 3 5 8)}] + [ a r:Fact; r:gives {((3 8 1 5) ">=") list:sort (8 5 3 1)}] + skolem:lemma5733 + skolem:lemma5734 + [ a r:Fact; r:gives {(8531 1358) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3815]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 1 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3814 a r:Inference; + r:gives { + 3816 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3816 math:notEqualTo 0}] + skolem:lemma6571 + [ a r:Fact; r:gives {((3 8 1 6) "=<") list:sort (1 3 6 8)}] + [ a r:Fact; r:gives {((3 8 1 6) ">=") list:sort (8 6 3 1)}] + skolem:lemma5751 + skolem:lemma5752 + [ a r:Fact; r:gives {(8631 1368) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3816]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 1 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3815 a r:Inference; + r:gives { + 3817 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3817 math:notEqualTo 0}] + skolem:lemma6572 + [ a r:Fact; r:gives {((3 8 1 7) "=<") list:sort (1 3 7 8)}] + [ a r:Fact; r:gives {((3 8 1 7) ">=") list:sort (8 7 3 1)}] + skolem:lemma5767 + skolem:lemma5768 + [ a r:Fact; r:gives {(8731 1378) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3817]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 1 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8731]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3816 a r:Inference; + r:gives { + 3818 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3818 math:notEqualTo 0}] + skolem:lemma6573 + [ a r:Fact; r:gives {((3 8 1 8) "=<") list:sort (1 3 8 8)}] + [ a r:Fact; r:gives {((3 8 1 8) ">=") list:sort (8 8 3 1)}] + skolem:lemma5781 + skolem:lemma5782 + [ a r:Fact; r:gives {(8831 1388) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3818]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 1 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8831]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3817 a r:Inference; + r:gives { + 3819 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3819 math:notEqualTo 0}] + skolem:lemma6574 + [ a r:Fact; r:gives {((3 8 1 9) "=<") list:sort (1 3 8 9)}] + [ a r:Fact; r:gives {((3 8 1 9) ">=") list:sort (9 8 3 1)}] + skolem:lemma5784 + skolem:lemma5785 + [ a r:Fact; r:gives {(9831 1389) math:difference 8442}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8442 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 8442 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3819]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 1 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9831]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3818 a r:Inference; + r:gives { + 3820 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3820 math:notEqualTo 0}] + skolem:lemma6575 + [ a r:Fact; r:gives {((3 8 2 0) "=<") list:sort (0 2 3 8)}] + [ a r:Fact; r:gives {((3 8 2 0) ">=") list:sort (8 3 2 0)}] + skolem:lemma4102 + skolem:lemma4103 + [ a r:Fact; r:gives {(8320 238) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3820]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3819 a r:Inference; + r:gives { + 3821 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3821 math:notEqualTo 0}] + skolem:lemma6576 + [ a r:Fact; r:gives {((3 8 2 1) "=<") list:sort (1 2 3 8)}] + [ a r:Fact; r:gives {((3 8 2 1) ">=") list:sort (8 3 2 1)}] + skolem:lemma4292 + skolem:lemma4293 + [ a r:Fact; r:gives {(8321 1238) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3821]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3820 a r:Inference; + r:gives { + 3822 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3822 math:notEqualTo 0}] + skolem:lemma6577 + [ a r:Fact; r:gives {((3 8 2 2) "=<") list:sort (2 2 3 8)}] + [ a r:Fact; r:gives {((3 8 2 2) ">=") list:sort (8 3 2 2)}] + skolem:lemma4461 + skolem:lemma4462 + [ a r:Fact; r:gives {(8322 2238) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3822]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3821 a r:Inference; + r:gives { + 3823 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3823 math:notEqualTo 0}] + skolem:lemma6578 + [ a r:Fact; r:gives {((3 8 2 3) "=<") list:sort (2 3 3 8)}] + [ a r:Fact; r:gives {((3 8 2 3) ">=") list:sort (8 3 3 2)}] + skolem:lemma4617 + skolem:lemma4618 + [ a r:Fact; r:gives {(8332 2338) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3823]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3822 a r:Inference; + r:gives { + 3824 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3824 math:notEqualTo 0}] + skolem:lemma6579 + [ a r:Fact; r:gives {((3 8 2 4) "=<") list:sort (2 3 4 8)}] + [ a r:Fact; r:gives {((3 8 2 4) ">=") list:sort (8 4 3 2)}] + skolem:lemma4639 + skolem:lemma4640 + [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3824]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3823 a r:Inference; + r:gives { + 3825 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3825 math:notEqualTo 0}] + skolem:lemma6580 + [ a r:Fact; r:gives {((3 8 2 5) "=<") list:sort (2 3 5 8)}] + [ a r:Fact; r:gives {((3 8 2 5) ">=") list:sort (8 5 3 2)}] + skolem:lemma4659 + skolem:lemma4660 + [ a r:Fact; r:gives {(8532 2358) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3825]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3824 a r:Inference; + r:gives { + 3826 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3826 math:notEqualTo 0}] + skolem:lemma6581 + [ a r:Fact; r:gives {((3 8 2 6) "=<") list:sort (2 3 6 8)}] + [ a r:Fact; r:gives {((3 8 2 6) ">=") list:sort (8 6 3 2)}] + skolem:lemma4677 + skolem:lemma4678 + [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3826]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3825 a r:Inference; + r:gives { + 3827 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3827 math:notEqualTo 0}] + skolem:lemma6582 + [ a r:Fact; r:gives {((3 8 2 7) "=<") list:sort (2 3 7 8)}] + [ a r:Fact; r:gives {((3 8 2 7) ">=") list:sort (8 7 3 2)}] + skolem:lemma4693 + skolem:lemma4694 + [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3827]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3826 a r:Inference; + r:gives { + 3828 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3828 math:notEqualTo 0}] + skolem:lemma6583 + [ a r:Fact; r:gives {((3 8 2 8) "=<") list:sort (2 3 8 8)}] + [ a r:Fact; r:gives {((3 8 2 8) ">=") list:sort (8 8 3 2)}] + skolem:lemma4707 + skolem:lemma4708 + [ a r:Fact; r:gives {(8832 2388) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3828]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3827 a r:Inference; + r:gives { + 3829 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3829 math:notEqualTo 0}] + skolem:lemma6584 + [ a r:Fact; r:gives {((3 8 2 9) "=<") list:sort (2 3 8 9)}] + [ a r:Fact; r:gives {((3 8 2 9) ">=") list:sort (9 8 3 2)}] + skolem:lemma4710 + skolem:lemma4711 + [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3829]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3828 a r:Inference; + r:gives { + 3830 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3830 math:notEqualTo 0}] + skolem:lemma6585 + [ a r:Fact; r:gives {((3 8 3 0) "=<") list:sort (0 3 3 8)}] + [ a r:Fact; r:gives {((3 8 3 0) ">=") list:sort (8 3 3 0)}] + skolem:lemma5519 + skolem:lemma5520 + [ a r:Fact; r:gives {(8330 338) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3830]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3829 a r:Inference; + r:gives { + 3831 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3831 math:notEqualTo 0}] + skolem:lemma6586 + [ a r:Fact; r:gives {((3 8 3 1) "=<") list:sort (1 3 3 8)}] + [ a r:Fact; r:gives {((3 8 3 1) ">=") list:sort (8 3 3 1)}] + skolem:lemma5691 + skolem:lemma5692 + [ a r:Fact; r:gives {(8331 1338) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3831]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3830 a r:Inference; + r:gives { + 3832 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3832 math:notEqualTo 0}] + skolem:lemma6587 + [ a r:Fact; r:gives {((3 8 3 2) "=<") list:sort (2 3 3 8)}] + [ a r:Fact; r:gives {((3 8 3 2) ">=") list:sort (8 3 3 2)}] + skolem:lemma4617 + skolem:lemma4618 + [ a r:Fact; r:gives {(8332 2338) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3831 a r:Inference; + r:gives { + 3833 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3833 math:notEqualTo 0}] + skolem:lemma6588 + [ a r:Fact; r:gives {((3 8 3 3) "=<") list:sort (3 3 3 8)}] + [ a r:Fact; r:gives {((3 8 3 3) ">=") list:sort (8 3 3 3)}] + skolem:lemma5944 + skolem:lemma5945 + [ a r:Fact; r:gives {(8333 3338) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3833]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3832 a r:Inference; + r:gives { + 3834 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3834 math:notEqualTo 0}] + skolem:lemma6589 + [ a r:Fact; r:gives {((3 8 3 4) "=<") list:sort (3 3 4 8)}] + [ a r:Fact; r:gives {((3 8 3 4) ">=") list:sort (8 4 3 3)}] + skolem:lemma5966 + skolem:lemma5967 + [ a r:Fact; r:gives {(8433 3348) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3834]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3833 a r:Inference; + r:gives { + 3835 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3835 math:notEqualTo 0}] + skolem:lemma6590 + [ a r:Fact; r:gives {((3 8 3 5) "=<") list:sort (3 3 5 8)}] + [ a r:Fact; r:gives {((3 8 3 5) ">=") list:sort (8 5 3 3)}] + skolem:lemma5986 + skolem:lemma5987 + [ a r:Fact; r:gives {(8533 3358) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3835]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3834 a r:Inference; + r:gives { + 3836 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3836 math:notEqualTo 0}] + skolem:lemma6591 + [ a r:Fact; r:gives {((3 8 3 6) "=<") list:sort (3 3 6 8)}] + [ a r:Fact; r:gives {((3 8 3 6) ">=") list:sort (8 6 3 3)}] + skolem:lemma6004 + skolem:lemma6005 + [ a r:Fact; r:gives {(8633 3368) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3836]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3835 a r:Inference; + r:gives { + 3837 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3837 math:notEqualTo 0}] + skolem:lemma6592 + [ a r:Fact; r:gives {((3 8 3 7) "=<") list:sort (3 3 7 8)}] + [ a r:Fact; r:gives {((3 8 3 7) ">=") list:sort (8 7 3 3)}] + skolem:lemma6020 + skolem:lemma6021 + [ a r:Fact; r:gives {(8733 3378) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3837]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3836 a r:Inference; + r:gives { + 3838 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3838 math:notEqualTo 0}] + skolem:lemma6593 + [ a r:Fact; r:gives {((3 8 3 8) "=<") list:sort (3 3 8 8)}] + [ a r:Fact; r:gives {((3 8 3 8) ">=") list:sort (8 8 3 3)}] + skolem:lemma6034 + skolem:lemma6035 + [ a r:Fact; r:gives {(8833 3388) math:difference 5445}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5445 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5445 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3838]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8833]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5445]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3837 a r:Inference; + r:gives { + 3839 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3839 math:notEqualTo 0}] + skolem:lemma6594 + [ a r:Fact; r:gives {((3 8 3 9) "=<") list:sort (3 3 8 9)}] + [ a r:Fact; r:gives {((3 8 3 9) ">=") list:sort (9 8 3 3)}] + skolem:lemma6037 + skolem:lemma6038 + [ a r:Fact; r:gives {(9833 3389) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3839]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9833]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3838 a r:Inference; + r:gives { + 3840 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3840 math:notEqualTo 0}] + skolem:lemma6595 + [ a r:Fact; r:gives {((3 8 4 0) "=<") list:sort (0 3 4 8)}] + [ a r:Fact; r:gives {((3 8 4 0) ">=") list:sort (8 4 3 0)}] + skolem:lemma5541 + skolem:lemma5542 + [ a r:Fact; r:gives {(8430 348) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3840]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 4 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3839 a r:Inference; + r:gives { + 3841 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3841 math:notEqualTo 0}] + skolem:lemma6596 + [ a r:Fact; r:gives {((3 8 4 1) "=<") list:sort (1 3 4 8)}] + [ a r:Fact; r:gives {((3 8 4 1) ">=") list:sort (8 4 3 1)}] + skolem:lemma5713 + skolem:lemma5714 + [ a r:Fact; r:gives {(8431 1348) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3841]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 4 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3840 a r:Inference; + r:gives { + 3842 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3842 math:notEqualTo 0}] + skolem:lemma6597 + [ a r:Fact; r:gives {((3 8 4 2) "=<") list:sort (2 3 4 8)}] + [ a r:Fact; r:gives {((3 8 4 2) ">=") list:sort (8 4 3 2)}] + skolem:lemma4639 + skolem:lemma4640 + [ a r:Fact; r:gives {(8432 2348) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3842]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3841 a r:Inference; + r:gives { + 3843 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3843 math:notEqualTo 0}] + skolem:lemma6598 + [ a r:Fact; r:gives {((3 8 4 3) "=<") list:sort (3 3 4 8)}] + [ a r:Fact; r:gives {((3 8 4 3) ">=") list:sort (8 4 3 3)}] + skolem:lemma5966 + skolem:lemma5967 + [ a r:Fact; r:gives {(8433 3348) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3843]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3842 a r:Inference; + r:gives { + 3844 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3844 math:notEqualTo 0}] + skolem:lemma6599 + [ a r:Fact; r:gives {((3 8 4 4) "=<") list:sort (3 4 4 8)}] + [ a r:Fact; r:gives {((3 8 4 4) ">=") list:sort (8 4 4 3)}] + skolem:lemma6108 + skolem:lemma6109 + [ a r:Fact; r:gives {(8443 3448) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3844]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 4 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3448]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3843 a r:Inference; + r:gives { + 3845 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3845 math:notEqualTo 0}] + skolem:lemma6600 + [ a r:Fact; r:gives {((3 8 4 5) "=<") list:sort (3 4 5 8)}] + [ a r:Fact; r:gives {((3 8 4 5) ">=") list:sort (8 5 4 3)}] + skolem:lemma6128 + skolem:lemma6129 + [ a r:Fact; r:gives {(8543 3458) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3845]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3458]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3844 a r:Inference; + r:gives { + 3846 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3846 math:notEqualTo 0}] + skolem:lemma6601 + [ a r:Fact; r:gives {((3 8 4 6) "=<") list:sort (3 4 6 8)}] + [ a r:Fact; r:gives {((3 8 4 6) ">=") list:sort (8 6 4 3)}] + skolem:lemma6146 + skolem:lemma6147 + [ a r:Fact; r:gives {(8643 3468) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3846]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3468]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3845 a r:Inference; + r:gives { + 3847 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3847 math:notEqualTo 0}] + skolem:lemma6602 + [ a r:Fact; r:gives {((3 8 4 7) "=<") list:sort (3 4 7 8)}] + [ a r:Fact; r:gives {((3 8 4 7) ">=") list:sort (8 7 4 3)}] + skolem:lemma6162 + skolem:lemma6163 + [ a r:Fact; r:gives {(8743 3478) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3847]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3478]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3846 a r:Inference; + r:gives { + 3848 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3848 math:notEqualTo 0}] + skolem:lemma6603 + [ a r:Fact; r:gives {((3 8 4 8) "=<") list:sort (3 4 8 8)}] + [ a r:Fact; r:gives {((3 8 4 8) ">=") list:sort (8 8 4 3)}] + skolem:lemma6176 + skolem:lemma6177 + [ a r:Fact; r:gives {(8843 3488) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3848]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3488]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8843]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3847 a r:Inference; + r:gives { + 3849 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3849 math:notEqualTo 0}] + skolem:lemma6604 + [ a r:Fact; r:gives {((3 8 4 9) "=<") list:sort (3 4 8 9)}] + [ a r:Fact; r:gives {((3 8 4 9) ">=") list:sort (9 8 4 3)}] + skolem:lemma6179 + skolem:lemma6180 + [ a r:Fact; r:gives {(9843 3489) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3849]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3489]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9843]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3848 a r:Inference; + r:gives { + 3850 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3850 math:notEqualTo 0}] + skolem:lemma6605 + [ a r:Fact; r:gives {((3 8 5 0) "=<") list:sort (0 3 5 8)}] + [ a r:Fact; r:gives {((3 8 5 0) ">=") list:sort (8 5 3 0)}] + skolem:lemma5561 + skolem:lemma5562 + [ a r:Fact; r:gives {(8530 358) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3850]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 5 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3849 a r:Inference; + r:gives { + 3851 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3851 math:notEqualTo 0}] + skolem:lemma6606 + [ a r:Fact; r:gives {((3 8 5 1) "=<") list:sort (1 3 5 8)}] + [ a r:Fact; r:gives {((3 8 5 1) ">=") list:sort (8 5 3 1)}] + skolem:lemma5733 + skolem:lemma5734 + [ a r:Fact; r:gives {(8531 1358) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3851]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 5 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3850 a r:Inference; + r:gives { + 3852 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3852 math:notEqualTo 0}] + skolem:lemma6607 + [ a r:Fact; r:gives {((3 8 5 2) "=<") list:sort (2 3 5 8)}] + [ a r:Fact; r:gives {((3 8 5 2) ">=") list:sort (8 5 3 2)}] + skolem:lemma4659 + skolem:lemma4660 + [ a r:Fact; r:gives {(8532 2358) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3852]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3851 a r:Inference; + r:gives { + 3853 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3853 math:notEqualTo 0}] + skolem:lemma6608 + [ a r:Fact; r:gives {((3 8 5 3) "=<") list:sort (3 3 5 8)}] + [ a r:Fact; r:gives {((3 8 5 3) ">=") list:sort (8 5 3 3)}] + skolem:lemma5986 + skolem:lemma5987 + [ a r:Fact; r:gives {(8533 3358) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3853]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3852 a r:Inference; + r:gives { + 3854 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3854 math:notEqualTo 0}] + skolem:lemma6609 + [ a r:Fact; r:gives {((3 8 5 4) "=<") list:sort (3 4 5 8)}] + [ a r:Fact; r:gives {((3 8 5 4) ">=") list:sort (8 5 4 3)}] + skolem:lemma6128 + skolem:lemma6129 + [ a r:Fact; r:gives {(8543 3458) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3854]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 5 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3458]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3853 a r:Inference; + r:gives { + 3855 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3855 math:notEqualTo 0}] + skolem:lemma6610 + [ a r:Fact; r:gives {((3 8 5 5) "=<") list:sort (3 5 5 8)}] + [ a r:Fact; r:gives {((3 8 5 5) ">=") list:sort (8 5 5 3)}] + skolem:lemma6258 + skolem:lemma6259 + [ a r:Fact; r:gives {(8553 3558) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3855]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 5 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3558]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3854 a r:Inference; + r:gives { + 3856 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3856 math:notEqualTo 0}] + skolem:lemma6611 + [ a r:Fact; r:gives {((3 8 5 6) "=<") list:sort (3 5 6 8)}] + [ a r:Fact; r:gives {((3 8 5 6) ">=") list:sort (8 6 5 3)}] + skolem:lemma6276 + skolem:lemma6277 + [ a r:Fact; r:gives {(8653 3568) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3856]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3568]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3855 a r:Inference; + r:gives { + 3857 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3857 math:notEqualTo 0}] + skolem:lemma6612 + [ a r:Fact; r:gives {((3 8 5 7) "=<") list:sort (3 5 7 8)}] + [ a r:Fact; r:gives {((3 8 5 7) ">=") list:sort (8 7 5 3)}] + skolem:lemma6292 + skolem:lemma6293 + [ a r:Fact; r:gives {(8753 3578) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3857]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3578]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3856 a r:Inference; + r:gives { + 3858 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3858 math:notEqualTo 0}] + skolem:lemma6613 + [ a r:Fact; r:gives {((3 8 5 8) "=<") list:sort (3 5 8 8)}] + [ a r:Fact; r:gives {((3 8 5 8) ">=") list:sort (8 8 5 3)}] + skolem:lemma6306 + skolem:lemma6307 + [ a r:Fact; r:gives {(8853 3588) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3858]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3588]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8853]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3857 a r:Inference; + r:gives { + 3859 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3859 math:notEqualTo 0}] + skolem:lemma6614 + [ a r:Fact; r:gives {((3 8 5 9) "=<") list:sort (3 5 8 9)}] + [ a r:Fact; r:gives {((3 8 5 9) ">=") list:sort (9 8 5 3)}] + skolem:lemma6309 + skolem:lemma6310 + [ a r:Fact; r:gives {(9853 3589) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3859]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3589]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9853]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3858 a r:Inference; + r:gives { + 3860 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3860 math:notEqualTo 0}] + skolem:lemma6615 + [ a r:Fact; r:gives {((3 8 6 0) "=<") list:sort (0 3 6 8)}] + [ a r:Fact; r:gives {((3 8 6 0) ">=") list:sort (8 6 3 0)}] + skolem:lemma5579 + skolem:lemma5580 + [ a r:Fact; r:gives {(8630 368) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3860]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 6 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3859 a r:Inference; + r:gives { + 3861 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3861 math:notEqualTo 0}] + skolem:lemma6616 + [ a r:Fact; r:gives {((3 8 6 1) "=<") list:sort (1 3 6 8)}] + [ a r:Fact; r:gives {((3 8 6 1) ">=") list:sort (8 6 3 1)}] + skolem:lemma5751 + skolem:lemma5752 + [ a r:Fact; r:gives {(8631 1368) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3861]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 6 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3860 a r:Inference; + r:gives { + 3862 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3862 math:notEqualTo 0}] + skolem:lemma6617 + [ a r:Fact; r:gives {((3 8 6 2) "=<") list:sort (2 3 6 8)}] + [ a r:Fact; r:gives {((3 8 6 2) ">=") list:sort (8 6 3 2)}] + skolem:lemma4677 + skolem:lemma4678 + [ a r:Fact; r:gives {(8632 2368) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3862]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3861 a r:Inference; + r:gives { + 3863 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3863 math:notEqualTo 0}] + skolem:lemma6618 + [ a r:Fact; r:gives {((3 8 6 3) "=<") list:sort (3 3 6 8)}] + [ a r:Fact; r:gives {((3 8 6 3) ">=") list:sort (8 6 3 3)}] + skolem:lemma6004 + skolem:lemma6005 + [ a r:Fact; r:gives {(8633 3368) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3863]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3862 a r:Inference; + r:gives { + 3864 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3864 math:notEqualTo 0}] + skolem:lemma6619 + [ a r:Fact; r:gives {((3 8 6 4) "=<") list:sort (3 4 6 8)}] + [ a r:Fact; r:gives {((3 8 6 4) ">=") list:sort (8 6 4 3)}] + skolem:lemma6146 + skolem:lemma6147 + [ a r:Fact; r:gives {(8643 3468) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3864]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 6 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3468]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3863 a r:Inference; + r:gives { + 3865 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3865 math:notEqualTo 0}] + skolem:lemma6620 + [ a r:Fact; r:gives {((3 8 6 5) "=<") list:sort (3 5 6 8)}] + [ a r:Fact; r:gives {((3 8 6 5) ">=") list:sort (8 6 5 3)}] + skolem:lemma6276 + skolem:lemma6277 + [ a r:Fact; r:gives {(8653 3568) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3865]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 6 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3568]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3864 a r:Inference; + r:gives { + 3866 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3866 math:notEqualTo 0}] + skolem:lemma6621 + [ a r:Fact; r:gives {((3 8 6 6) "=<") list:sort (3 6 6 8)}] + [ a r:Fact; r:gives {((3 8 6 6) ">=") list:sort (8 6 6 3)}] + skolem:lemma6396 + skolem:lemma6397 + [ a r:Fact; r:gives {(8663 3668) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3866]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 6 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3668]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8663]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3865 a r:Inference; + r:gives { + 3867 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3867 math:notEqualTo 0}] + skolem:lemma6622 + [ a r:Fact; r:gives {((3 8 6 7) "=<") list:sort (3 6 7 8)}] + [ a r:Fact; r:gives {((3 8 6 7) ">=") list:sort (8 7 6 3)}] + skolem:lemma6412 + skolem:lemma6413 + [ a r:Fact; r:gives {(8763 3678) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3867]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3678]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3866 a r:Inference; + r:gives { + 3868 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3868 math:notEqualTo 0}] + skolem:lemma6623 + [ a r:Fact; r:gives {((3 8 6 8) "=<") list:sort (3 6 8 8)}] + [ a r:Fact; r:gives {((3 8 6 8) ">=") list:sort (8 8 6 3)}] + skolem:lemma6426 + skolem:lemma6427 + [ a r:Fact; r:gives {(8863 3688) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3868]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3688]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8863]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3867 a r:Inference; + r:gives { + 3869 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3869 math:notEqualTo 0}] + skolem:lemma6624 + [ a r:Fact; r:gives {((3 8 6 9) "=<") list:sort (3 6 8 9)}] + [ a r:Fact; r:gives {((3 8 6 9) ">=") list:sort (9 8 6 3)}] + skolem:lemma6429 + skolem:lemma6430 + [ a r:Fact; r:gives {(9863 3689) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3869]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3689]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9863]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3868 a r:Inference; + r:gives { + 3870 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3870 math:notEqualTo 0}] + skolem:lemma6625 + [ a r:Fact; r:gives {((3 8 7 0) "=<") list:sort (0 3 7 8)}] + [ a r:Fact; r:gives {((3 8 7 0) ">=") list:sort (8 7 3 0)}] + skolem:lemma5595 + skolem:lemma5596 + [ a r:Fact; r:gives {(8730 378) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3870]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 7 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3869 a r:Inference; + r:gives { + 3871 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3871 math:notEqualTo 0}] + skolem:lemma6626 + [ a r:Fact; r:gives {((3 8 7 1) "=<") list:sort (1 3 7 8)}] + [ a r:Fact; r:gives {((3 8 7 1) ">=") list:sort (8 7 3 1)}] + skolem:lemma5767 + skolem:lemma5768 + [ a r:Fact; r:gives {(8731 1378) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3871]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 7 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8731]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3870 a r:Inference; + r:gives { + 3872 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3872 math:notEqualTo 0}] + skolem:lemma6627 + [ a r:Fact; r:gives {((3 8 7 2) "=<") list:sort (2 3 7 8)}] + [ a r:Fact; r:gives {((3 8 7 2) ">=") list:sort (8 7 3 2)}] + skolem:lemma4693 + skolem:lemma4694 + [ a r:Fact; r:gives {(8732 2378) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3872]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3871 a r:Inference; + r:gives { + 3873 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3873 math:notEqualTo 0}] + skolem:lemma6628 + [ a r:Fact; r:gives {((3 8 7 3) "=<") list:sort (3 3 7 8)}] + [ a r:Fact; r:gives {((3 8 7 3) ">=") list:sort (8 7 3 3)}] + skolem:lemma6020 + skolem:lemma6021 + [ a r:Fact; r:gives {(8733 3378) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3873]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3872 a r:Inference; + r:gives { + 3874 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3874 math:notEqualTo 0}] + skolem:lemma6629 + [ a r:Fact; r:gives {((3 8 7 4) "=<") list:sort (3 4 7 8)}] + [ a r:Fact; r:gives {((3 8 7 4) ">=") list:sort (8 7 4 3)}] + skolem:lemma6162 + skolem:lemma6163 + [ a r:Fact; r:gives {(8743 3478) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3874]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 7 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3478]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3873 a r:Inference; + r:gives { + 3875 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3875 math:notEqualTo 0}] + skolem:lemma6630 + [ a r:Fact; r:gives {((3 8 7 5) "=<") list:sort (3 5 7 8)}] + [ a r:Fact; r:gives {((3 8 7 5) ">=") list:sort (8 7 5 3)}] + skolem:lemma6292 + skolem:lemma6293 + [ a r:Fact; r:gives {(8753 3578) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3875]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 7 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3578]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3874 a r:Inference; + r:gives { + 3876 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3876 math:notEqualTo 0}] + skolem:lemma6631 + [ a r:Fact; r:gives {((3 8 7 6) "=<") list:sort (3 6 7 8)}] + [ a r:Fact; r:gives {((3 8 7 6) ">=") list:sort (8 7 6 3)}] + skolem:lemma6412 + skolem:lemma6413 + [ a r:Fact; r:gives {(8763 3678) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3876]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 7 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3678]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3875 a r:Inference; + r:gives { + 3877 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3877 math:notEqualTo 0}] + skolem:lemma6632 + [ a r:Fact; r:gives {((3 8 7 7) "=<") list:sort (3 7 7 8)}] + [ a r:Fact; r:gives {((3 8 7 7) ">=") list:sort (8 7 7 3)}] + skolem:lemma6524 + skolem:lemma6525 + [ a r:Fact; r:gives {(8773 3778) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3877]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 7 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3778]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8773]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3876 a r:Inference; + r:gives { + 3878 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3878 math:notEqualTo 0}] + skolem:lemma6633 + [ a r:Fact; r:gives {((3 8 7 8) "=<") list:sort (3 7 8 8)}] + [ a r:Fact; r:gives {((3 8 7 8) ">=") list:sort (8 8 7 3)}] + skolem:lemma6538 + skolem:lemma6539 + [ a r:Fact; r:gives {(8873 3788) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3878]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3788]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8873]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3877 a r:Inference; + r:gives { + 3879 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3879 math:notEqualTo 0}] + skolem:lemma6634 + [ a r:Fact; r:gives {((3 8 7 9) "=<") list:sort (3 7 8 9)}] + [ a r:Fact; r:gives {((3 8 7 9) ">=") list:sort (9 8 7 3)}] + skolem:lemma6541 + skolem:lemma6542 + [ a r:Fact; r:gives {(9873 3789) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3879]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3789]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9873]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3878 a r:Inference; + r:gives { + 3880 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3880 math:notEqualTo 0}] + skolem:lemma6635 + [ a r:Fact; r:gives {((3 8 8 0) "=<") list:sort (0 3 8 8)}] + [ a r:Fact; r:gives {((3 8 8 0) ">=") list:sort (8 8 3 0)}] + skolem:lemma5609 + skolem:lemma5610 + [ a r:Fact; r:gives {(8830 388) math:difference 8442}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8442 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 8442 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3880]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 8 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8830]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3879 a r:Inference; + r:gives { + 3881 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3881 math:notEqualTo 0}] + skolem:lemma6636 + [ a r:Fact; r:gives {((3 8 8 1) "=<") list:sort (1 3 8 8)}] + [ a r:Fact; r:gives {((3 8 8 1) ">=") list:sort (8 8 3 1)}] + skolem:lemma5781 + skolem:lemma5782 + [ a r:Fact; r:gives {(8831 1388) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3881]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 8 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8831]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3880 a r:Inference; + r:gives { + 3882 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3882 math:notEqualTo 0}] + skolem:lemma6637 + [ a r:Fact; r:gives {((3 8 8 2) "=<") list:sort (2 3 8 8)}] + [ a r:Fact; r:gives {((3 8 8 2) ">=") list:sort (8 8 3 2)}] + skolem:lemma4707 + skolem:lemma4708 + [ a r:Fact; r:gives {(8832 2388) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3882]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3881 a r:Inference; + r:gives { + 3883 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3883 math:notEqualTo 0}] + skolem:lemma6638 + [ a r:Fact; r:gives {((3 8 8 3) "=<") list:sort (3 3 8 8)}] + [ a r:Fact; r:gives {((3 8 8 3) ">=") list:sort (8 8 3 3)}] + skolem:lemma6034 + skolem:lemma6035 + [ a r:Fact; r:gives {(8833 3388) math:difference 5445}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5445 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5445 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3883]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8833]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5445]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3882 a r:Inference; + r:gives { + 3884 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3884 math:notEqualTo 0}] + skolem:lemma6639 + [ a r:Fact; r:gives {((3 8 8 4) "=<") list:sort (3 4 8 8)}] + [ a r:Fact; r:gives {((3 8 8 4) ">=") list:sort (8 8 4 3)}] + skolem:lemma6176 + skolem:lemma6177 + [ a r:Fact; r:gives {(8843 3488) math:difference 5355}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5355 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5355 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3884]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 8 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3488]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8843]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3883 a r:Inference; + r:gives { + 3885 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3885 math:notEqualTo 0}] + skolem:lemma6640 + [ a r:Fact; r:gives {((3 8 8 5) "=<") list:sort (3 5 8 8)}] + [ a r:Fact; r:gives {((3 8 8 5) ">=") list:sort (8 8 5 3)}] + skolem:lemma6306 + skolem:lemma6307 + [ a r:Fact; r:gives {(8853 3588) math:difference 5265}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5265 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 5265 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3885]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 8 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3588]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8853]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3884 a r:Inference; + r:gives { + 3886 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3886 math:notEqualTo 0}] + skolem:lemma6641 + [ a r:Fact; r:gives {((3 8 8 6) "=<") list:sort (3 6 8 8)}] + [ a r:Fact; r:gives {((3 8 8 6) ">=") list:sort (8 8 6 3)}] + skolem:lemma6426 + skolem:lemma6427 + [ a r:Fact; r:gives {(8863 3688) math:difference 5175}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5175 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5175 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3886]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 8 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3688]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8863]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3885 a r:Inference; + r:gives { + 3887 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3887 math:notEqualTo 0}] + skolem:lemma6642 + [ a r:Fact; r:gives {((3 8 8 7) "=<") list:sort (3 7 8 8)}] + [ a r:Fact; r:gives {((3 8 8 7) ">=") list:sort (8 8 7 3)}] + skolem:lemma6538 + skolem:lemma6539 + [ a r:Fact; r:gives {(8873 3788) math:difference 5085}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5085 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 5085 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3887]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 8 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3788]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8873]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3886 a r:Inference; + r:gives { + 3888 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3888 math:notEqualTo 0}] + skolem:lemma6643 + [ a r:Fact; r:gives {((3 8 8 8) "=<") list:sort (3 8 8 8)}] + [ a r:Fact; r:gives {((3 8 8 8) ">=") list:sort (8 8 8 3)}] + skolem:lemma6644 + skolem:lemma6645 + [ a r:Fact; r:gives {(8883 3888) math:difference 4995}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 4995 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 4995 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3888]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 8 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (8 8 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3888]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8883]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3887 a r:Inference; + r:gives { + 3889 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3889 math:notEqualTo 0}] + skolem:lemma6646 + [ a r:Fact; r:gives {((3 8 8 9) "=<") list:sort (3 8 8 9)}] + [ a r:Fact; r:gives {((3 8 8 9) ">=") list:sort (9 8 8 3)}] + skolem:lemma6647 + skolem:lemma6648 + [ a r:Fact; r:gives {(9883 3889) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3889]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 8 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3889]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9883]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3888 a r:Inference; + r:gives { + 3890 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3890 math:notEqualTo 0}] + skolem:lemma6649 + [ a r:Fact; r:gives {((3 8 9 0) "=<") list:sort (0 3 8 9)}] + [ a r:Fact; r:gives {((3 8 9 0) ">=") list:sort (9 8 3 0)}] + skolem:lemma5612 + skolem:lemma5613 + [ a r:Fact; r:gives {(9830 389) math:difference 9441}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9441 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9441 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3890]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 9 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9830]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9441]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3889 a r:Inference; + r:gives { + 3891 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3891 math:notEqualTo 0}] + skolem:lemma6650 + [ a r:Fact; r:gives {((3 8 9 1) "=<") list:sort (1 3 8 9)}] + [ a r:Fact; r:gives {((3 8 9 1) ">=") list:sort (9 8 3 1)}] + skolem:lemma5784 + skolem:lemma5785 + [ a r:Fact; r:gives {(9831 1389) math:difference 8442}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8442 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 8442 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3891]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 9 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9831]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3890 a r:Inference; + r:gives { + 3892 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3892 math:notEqualTo 0}] + skolem:lemma6651 + [ a r:Fact; r:gives {((3 8 9 2) "=<") list:sort (2 3 8 9)}] + [ a r:Fact; r:gives {((3 8 9 2) ">=") list:sort (9 8 3 2)}] + skolem:lemma4710 + skolem:lemma4711 + [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3892]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 9 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3891 a r:Inference; + r:gives { + 3893 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3893 math:notEqualTo 0}] + skolem:lemma6652 + [ a r:Fact; r:gives {((3 8 9 3) "=<") list:sort (3 3 8 9)}] + [ a r:Fact; r:gives {((3 8 9 3) ">=") list:sort (9 8 3 3)}] + skolem:lemma6037 + skolem:lemma6038 + [ a r:Fact; r:gives {(9833 3389) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3893]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 9 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9833]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3892 a r:Inference; + r:gives { + 3894 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3894 math:notEqualTo 0}] + skolem:lemma6653 + [ a r:Fact; r:gives {((3 8 9 4) "=<") list:sort (3 4 8 9)}] + [ a r:Fact; r:gives {((3 8 9 4) ">=") list:sort (9 8 4 3)}] + skolem:lemma6179 + skolem:lemma6180 + [ a r:Fact; r:gives {(9843 3489) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3894]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 9 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3489]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9843]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3893 a r:Inference; + r:gives { + 3895 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3895 math:notEqualTo 0}] + skolem:lemma6654 + [ a r:Fact; r:gives {((3 8 9 5) "=<") list:sort (3 5 8 9)}] + [ a r:Fact; r:gives {((3 8 9 5) ">=") list:sort (9 8 5 3)}] + skolem:lemma6309 + skolem:lemma6310 + [ a r:Fact; r:gives {(9853 3589) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3895]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 9 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3589]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9853]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3894 a r:Inference; + r:gives { + 3896 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3896 math:notEqualTo 0}] + skolem:lemma6655 + [ a r:Fact; r:gives {((3 8 9 6) "=<") list:sort (3 6 8 9)}] + [ a r:Fact; r:gives {((3 8 9 6) ">=") list:sort (9 8 6 3)}] + skolem:lemma6429 + skolem:lemma6430 + [ a r:Fact; r:gives {(9863 3689) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3896]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 9 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3689]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9863]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3895 a r:Inference; + r:gives { + 3897 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3897 math:notEqualTo 0}] + skolem:lemma6656 + [ a r:Fact; r:gives {((3 8 9 7) "=<") list:sort (3 7 8 9)}] + [ a r:Fact; r:gives {((3 8 9 7) ">=") list:sort (9 8 7 3)}] + skolem:lemma6541 + skolem:lemma6542 + [ a r:Fact; r:gives {(9873 3789) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3897]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 9 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3789]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9873]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3896 a r:Inference; + r:gives { + 3898 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3898 math:notEqualTo 0}] + skolem:lemma6657 + [ a r:Fact; r:gives {((3 8 9 8) "=<") list:sort (3 8 8 9)}] + [ a r:Fact; r:gives {((3 8 9 8) ">=") list:sort (9 8 8 3)}] + skolem:lemma6647 + skolem:lemma6648 + [ a r:Fact; r:gives {(9883 3889) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3898]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 9 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 8 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3889]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9883]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3897 a r:Inference; + r:gives { + 3899 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3899 math:notEqualTo 0}] + skolem:lemma6658 + [ a r:Fact; r:gives {((3 8 9 9) "=<") list:sort (3 8 9 9)}] + [ a r:Fact; r:gives {((3 8 9 9) ">=") list:sort (9 9 8 3)}] + skolem:lemma6659 + skolem:lemma6660 + [ a r:Fact; r:gives {(9983 3899) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3899]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 8 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 8 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3899]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9983]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3898 a r:Inference; + r:gives { + 3900 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3900 math:notEqualTo 0}] + skolem:lemma6661 + [ a r:Fact; r:gives {((3 9 0 0) "=<") list:sort (0 0 3 9)}] + [ a r:Fact; r:gives {((3 9 0 0) ">=") list:sort (9 3 0 0)}] + skolem:lemma5462 + skolem:lemma5463 + [ a r:Fact; r:gives {(9300 39) math:difference 9261}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9261 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9261 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3900]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 0 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 0 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 39]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9261]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3899 a r:Inference; + r:gives { + 3901 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3901 math:notEqualTo 0}] + skolem:lemma6662 + [ a r:Fact; r:gives {((3 9 0 1) "=<") list:sort (0 1 3 9)}] + [ a r:Fact; r:gives {((3 9 0 1) ">=") list:sort (9 3 1 0)}] + skolem:lemma5488 + skolem:lemma5489 + [ a r:Fact; r:gives {(9310 139) math:difference 9171}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9171 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9171 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3901]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 0 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 139]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3900 a r:Inference; + r:gives { + 3902 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3902 math:notEqualTo 0}] + skolem:lemma6663 + [ a r:Fact; r:gives {((3 9 0 2) "=<") list:sort (0 2 3 9)}] + [ a r:Fact; r:gives {((3 9 0 2) ">=") list:sort (9 3 2 0)}] + skolem:lemma4105 + skolem:lemma4106 + [ a r:Fact; r:gives {(9320 239) math:difference 9081}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9081 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 9081 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3902]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 0 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3901 a r:Inference; + r:gives { + 3903 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3903 math:notEqualTo 0}] + skolem:lemma6664 + [ a r:Fact; r:gives {((3 9 0 3) "=<") list:sort (0 3 3 9)}] + [ a r:Fact; r:gives {((3 9 0 3) ">=") list:sort (9 3 3 0)}] + skolem:lemma5522 + skolem:lemma5523 + [ a r:Fact; r:gives {(9330 339) math:difference 8991}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8991 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 8991 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3903]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 0 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8991]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3902 a r:Inference; + r:gives { + 3904 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3904 math:notEqualTo 0}] + skolem:lemma6665 + [ a r:Fact; r:gives {((3 9 0 4) "=<") list:sort (0 3 4 9)}] + [ a r:Fact; r:gives {((3 9 0 4) ">=") list:sort (9 4 3 0)}] + skolem:lemma5544 + skolem:lemma5545 + [ a r:Fact; r:gives {(9430 349) math:difference 9081}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9081 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 9081 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3904]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 0 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3903 a r:Inference; + r:gives { + 3905 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3905 math:notEqualTo 0}] + skolem:lemma6666 + [ a r:Fact; r:gives {((3 9 0 5) "=<") list:sort (0 3 5 9)}] + [ a r:Fact; r:gives {((3 9 0 5) ">=") list:sort (9 5 3 0)}] + skolem:lemma5564 + skolem:lemma5565 + [ a r:Fact; r:gives {(9530 359) math:difference 9171}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9171 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9171 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3905]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 0 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3904 a r:Inference; + r:gives { + 3906 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3906 math:notEqualTo 0}] + skolem:lemma6667 + [ a r:Fact; r:gives {((3 9 0 6) "=<") list:sort (0 3 6 9)}] + [ a r:Fact; r:gives {((3 9 0 6) ">=") list:sort (9 6 3 0)}] + skolem:lemma5582 + skolem:lemma5583 + [ a r:Fact; r:gives {(9630 369) math:difference 9261}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9261 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9261 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3906]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 0 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9261]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3905 a r:Inference; + r:gives { + 3907 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3907 math:notEqualTo 0}] + skolem:lemma6668 + [ a r:Fact; r:gives {((3 9 0 7) "=<") list:sort (0 3 7 9)}] + [ a r:Fact; r:gives {((3 9 0 7) ">=") list:sort (9 7 3 0)}] + skolem:lemma5598 + skolem:lemma5599 + [ a r:Fact; r:gives {(9730 379) math:difference 9351}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9351 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9351 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3907]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 0 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9351]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3906 a r:Inference; + r:gives { + 3908 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3908 math:notEqualTo 0}] + skolem:lemma6669 + [ a r:Fact; r:gives {((3 9 0 8) "=<") list:sort (0 3 8 9)}] + [ a r:Fact; r:gives {((3 9 0 8) ">=") list:sort (9 8 3 0)}] + skolem:lemma5612 + skolem:lemma5613 + [ a r:Fact; r:gives {(9830 389) math:difference 9441}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9441 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9441 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3908]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 0 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9830]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9441]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3907 a r:Inference; + r:gives { + 3909 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3909 math:notEqualTo 0}] + skolem:lemma6670 + [ a r:Fact; r:gives {((3 9 0 9) "=<") list:sort (0 3 9 9)}] + [ a r:Fact; r:gives {((3 9 0 9) ">=") list:sort (9 9 3 0)}] + skolem:lemma5624 + skolem:lemma5625 + [ a r:Fact; r:gives {(9930 399) math:difference 9531}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9531 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9531 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3909]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 0 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9930]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3908 a r:Inference; + r:gives { + 3910 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3910 math:notEqualTo 0}] + skolem:lemma6671 + [ a r:Fact; r:gives {((3 9 1 0) "=<") list:sort (0 1 3 9)}] + [ a r:Fact; r:gives {((3 9 1 0) ">=") list:sort (9 3 1 0)}] + skolem:lemma5488 + skolem:lemma5489 + [ a r:Fact; r:gives {(9310 139) math:difference 9171}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9171 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9171 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3910]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 1 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 1 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 139]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3909 a r:Inference; + r:gives { + 3911 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3911 math:notEqualTo 0}] + skolem:lemma6672 + [ a r:Fact; r:gives {((3 9 1 1) "=<") list:sort (1 1 3 9)}] + [ a r:Fact; r:gives {((3 9 1 1) ">=") list:sort (9 3 1 1)}] + skolem:lemma5660 + skolem:lemma5661 + [ a r:Fact; r:gives {(9311 1139) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3911]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 1 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 1 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1139]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3910 a r:Inference; + r:gives { + 3912 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3912 math:notEqualTo 0}] + skolem:lemma6673 + [ a r:Fact; r:gives {((3 9 1 2) "=<") list:sort (1 2 3 9)}] + [ a r:Fact; r:gives {((3 9 1 2) ">=") list:sort (9 3 2 1)}] + skolem:lemma4295 + skolem:lemma4296 + [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3912]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 1 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3911 a r:Inference; + r:gives { + 3913 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3913 math:notEqualTo 0}] + skolem:lemma6674 + [ a r:Fact; r:gives {((3 9 1 3) "=<") list:sort (1 3 3 9)}] + [ a r:Fact; r:gives {((3 9 1 3) ">=") list:sort (9 3 3 1)}] + skolem:lemma5694 + skolem:lemma5695 + [ a r:Fact; r:gives {(9331 1339) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3913]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 1 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3912 a r:Inference; + r:gives { + 3914 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3914 math:notEqualTo 0}] + skolem:lemma6675 + [ a r:Fact; r:gives {((3 9 1 4) "=<") list:sort (1 3 4 9)}] + [ a r:Fact; r:gives {((3 9 1 4) ">=") list:sort (9 4 3 1)}] + skolem:lemma5716 + skolem:lemma5717 + [ a r:Fact; r:gives {(9431 1349) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3914]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 1 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3913 a r:Inference; + r:gives { + 3915 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3915 math:notEqualTo 0}] + skolem:lemma6676 + [ a r:Fact; r:gives {((3 9 1 5) "=<") list:sort (1 3 5 9)}] + [ a r:Fact; r:gives {((3 9 1 5) ">=") list:sort (9 5 3 1)}] + skolem:lemma5736 + skolem:lemma5737 + [ a r:Fact; r:gives {(9531 1359) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3915]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 1 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3914 a r:Inference; + r:gives { + 3916 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3916 math:notEqualTo 0}] + skolem:lemma6677 + [ a r:Fact; r:gives {((3 9 1 6) "=<") list:sort (1 3 6 9)}] + [ a r:Fact; r:gives {((3 9 1 6) ">=") list:sort (9 6 3 1)}] + skolem:lemma5754 + skolem:lemma5755 + [ a r:Fact; r:gives {(9631 1369) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3916]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 1 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3915 a r:Inference; + r:gives { + 3917 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3917 math:notEqualTo 0}] + skolem:lemma6678 + [ a r:Fact; r:gives {((3 9 1 7) "=<") list:sort (1 3 7 9)}] + [ a r:Fact; r:gives {((3 9 1 7) ">=") list:sort (9 7 3 1)}] + skolem:lemma5770 + skolem:lemma5771 + [ a r:Fact; r:gives {(9731 1379) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3917]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 1 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9731]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3916 a r:Inference; + r:gives { + 3918 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3918 math:notEqualTo 0}] + skolem:lemma6679 + [ a r:Fact; r:gives {((3 9 1 8) "=<") list:sort (1 3 8 9)}] + [ a r:Fact; r:gives {((3 9 1 8) ">=") list:sort (9 8 3 1)}] + skolem:lemma5784 + skolem:lemma5785 + [ a r:Fact; r:gives {(9831 1389) math:difference 8442}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8442 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 8442 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3918]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 1 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9831]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3917 a r:Inference; + r:gives { + 3919 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3919 math:notEqualTo 0}] + skolem:lemma6680 + [ a r:Fact; r:gives {((3 9 1 9) "=<") list:sort (1 3 9 9)}] + [ a r:Fact; r:gives {((3 9 1 9) ">=") list:sort (9 9 3 1)}] + skolem:lemma5796 + skolem:lemma5797 + [ a r:Fact; r:gives {(9931 1399) math:difference 8532}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8532 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8532 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3919]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 1 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9931]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3918 a r:Inference; + r:gives { + 3920 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3920 math:notEqualTo 0}] + skolem:lemma6681 + [ a r:Fact; r:gives {((3 9 2 0) "=<") list:sort (0 2 3 9)}] + [ a r:Fact; r:gives {((3 9 2 0) ">=") list:sort (9 3 2 0)}] + skolem:lemma4105 + skolem:lemma4106 + [ a r:Fact; r:gives {(9320 239) math:difference 9081}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9081 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 9081 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3920]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3919 a r:Inference; + r:gives { + 3921 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3921 math:notEqualTo 0}] + skolem:lemma6682 + [ a r:Fact; r:gives {((3 9 2 1) "=<") list:sort (1 2 3 9)}] + [ a r:Fact; r:gives {((3 9 2 1) ">=") list:sort (9 3 2 1)}] + skolem:lemma4295 + skolem:lemma4296 + [ a r:Fact; r:gives {(9321 1239) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3921]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3920 a r:Inference; + r:gives { + 3922 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3922 math:notEqualTo 0}] + skolem:lemma6683 + [ a r:Fact; r:gives {((3 9 2 2) "=<") list:sort (2 2 3 9)}] + [ a r:Fact; r:gives {((3 9 2 2) ">=") list:sort (9 3 2 2)}] + skolem:lemma4464 + skolem:lemma4465 + [ a r:Fact; r:gives {(9322 2239) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3922]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 2 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 2 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3921 a r:Inference; + r:gives { + 3923 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3923 math:notEqualTo 0}] + skolem:lemma6684 + [ a r:Fact; r:gives {((3 9 2 3) "=<") list:sort (2 3 3 9)}] + [ a r:Fact; r:gives {((3 9 2 3) ">=") list:sort (9 3 3 2)}] + skolem:lemma4620 + skolem:lemma4621 + [ a r:Fact; r:gives {(9332 2339) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3923]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 2 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3922 a r:Inference; + r:gives { + 3924 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3924 math:notEqualTo 0}] + skolem:lemma6685 + [ a r:Fact; r:gives {((3 9 2 4) "=<") list:sort (2 3 4 9)}] + [ a r:Fact; r:gives {((3 9 2 4) ">=") list:sort (9 4 3 2)}] + skolem:lemma4642 + skolem:lemma4643 + [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3924]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 2 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3923 a r:Inference; + r:gives { + 3925 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3925 math:notEqualTo 0}] + skolem:lemma6686 + [ a r:Fact; r:gives {((3 9 2 5) "=<") list:sort (2 3 5 9)}] + [ a r:Fact; r:gives {((3 9 2 5) ">=") list:sort (9 5 3 2)}] + skolem:lemma4662 + skolem:lemma4663 + [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3925]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 2 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3924 a r:Inference; + r:gives { + 3926 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3926 math:notEqualTo 0}] + skolem:lemma6687 + [ a r:Fact; r:gives {((3 9 2 6) "=<") list:sort (2 3 6 9)}] + [ a r:Fact; r:gives {((3 9 2 6) ">=") list:sort (9 6 3 2)}] + skolem:lemma4680 + skolem:lemma4681 + [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3926]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 2 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3925 a r:Inference; + r:gives { + 3927 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3927 math:notEqualTo 0}] + skolem:lemma6688 + [ a r:Fact; r:gives {((3 9 2 7) "=<") list:sort (2 3 7 9)}] + [ a r:Fact; r:gives {((3 9 2 7) ">=") list:sort (9 7 3 2)}] + skolem:lemma4696 + skolem:lemma4697 + [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3927]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 2 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3926 a r:Inference; + r:gives { + 3928 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3928 math:notEqualTo 0}] + skolem:lemma6689 + [ a r:Fact; r:gives {((3 9 2 8) "=<") list:sort (2 3 8 9)}] + [ a r:Fact; r:gives {((3 9 2 8) ">=") list:sort (9 8 3 2)}] + skolem:lemma4710 + skolem:lemma4711 + [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3928]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 2 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3927 a r:Inference; + r:gives { + 3929 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3929 math:notEqualTo 0}] + skolem:lemma6690 + [ a r:Fact; r:gives {((3 9 2 9) "=<") list:sort (2 3 9 9)}] + [ a r:Fact; r:gives {((3 9 2 9) ">=") list:sort (9 9 3 2)}] + skolem:lemma4722 + skolem:lemma4723 + [ a r:Fact; r:gives {(9932 2399) math:difference 7533}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7533 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7533 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3929]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 2 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9932]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3928 a r:Inference; + r:gives { + 3930 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3930 math:notEqualTo 0}] + skolem:lemma6691 + [ a r:Fact; r:gives {((3 9 3 0) "=<") list:sort (0 3 3 9)}] + [ a r:Fact; r:gives {((3 9 3 0) ">=") list:sort (9 3 3 0)}] + skolem:lemma5522 + skolem:lemma5523 + [ a r:Fact; r:gives {(9330 339) math:difference 8991}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8991 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 8991 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3930]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8991]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3929 a r:Inference; + r:gives { + 3931 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3931 math:notEqualTo 0}] + skolem:lemma6692 + [ a r:Fact; r:gives {((3 9 3 1) "=<") list:sort (1 3 3 9)}] + [ a r:Fact; r:gives {((3 9 3 1) ">=") list:sort (9 3 3 1)}] + skolem:lemma5694 + skolem:lemma5695 + [ a r:Fact; r:gives {(9331 1339) math:difference 7992}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7992 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7992 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3931]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3930 a r:Inference; + r:gives { + 3932 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3932 math:notEqualTo 0}] + skolem:lemma6693 + [ a r:Fact; r:gives {((3 9 3 2) "=<") list:sort (2 3 3 9)}] + [ a r:Fact; r:gives {((3 9 3 2) ">=") list:sort (9 3 3 2)}] + skolem:lemma4620 + skolem:lemma4621 + [ a r:Fact; r:gives {(9332 2339) math:difference 6993}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6993 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6993 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3932]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3931 a r:Inference; + r:gives { + 3933 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3933 math:notEqualTo 0}] + skolem:lemma6694 + [ a r:Fact; r:gives {((3 9 3 3) "=<") list:sort (3 3 3 9)}] + [ a r:Fact; r:gives {((3 9 3 3) ">=") list:sort (9 3 3 3)}] + skolem:lemma5947 + skolem:lemma5948 + [ a r:Fact; r:gives {(9333 3339) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3933]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 3 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3932 a r:Inference; + r:gives { + 3934 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3934 math:notEqualTo 0}] + skolem:lemma6695 + [ a r:Fact; r:gives {((3 9 3 4) "=<") list:sort (3 3 4 9)}] + [ a r:Fact; r:gives {((3 9 3 4) ">=") list:sort (9 4 3 3)}] + skolem:lemma5969 + skolem:lemma5970 + [ a r:Fact; r:gives {(9433 3349) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3934]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 3 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3933 a r:Inference; + r:gives { + 3935 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3935 math:notEqualTo 0}] + skolem:lemma6696 + [ a r:Fact; r:gives {((3 9 3 5) "=<") list:sort (3 3 5 9)}] + [ a r:Fact; r:gives {((3 9 3 5) ">=") list:sort (9 5 3 3)}] + skolem:lemma5989 + skolem:lemma5990 + [ a r:Fact; r:gives {(9533 3359) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3935]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 3 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3934 a r:Inference; + r:gives { + 3936 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3936 math:notEqualTo 0}] + skolem:lemma6697 + [ a r:Fact; r:gives {((3 9 3 6) "=<") list:sort (3 3 6 9)}] + [ a r:Fact; r:gives {((3 9 3 6) ">=") list:sort (9 6 3 3)}] + skolem:lemma6007 + skolem:lemma6008 + [ a r:Fact; r:gives {(9633 3369) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3936]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 3 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3935 a r:Inference; + r:gives { + 3937 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3937 math:notEqualTo 0}] + skolem:lemma6698 + [ a r:Fact; r:gives {((3 9 3 7) "=<") list:sort (3 3 7 9)}] + [ a r:Fact; r:gives {((3 9 3 7) ">=") list:sort (9 7 3 3)}] + skolem:lemma6023 + skolem:lemma6024 + [ a r:Fact; r:gives {(9733 3379) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3937]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 3 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3936 a r:Inference; + r:gives { + 3938 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3938 math:notEqualTo 0}] + skolem:lemma6699 + [ a r:Fact; r:gives {((3 9 3 8) "=<") list:sort (3 3 8 9)}] + [ a r:Fact; r:gives {((3 9 3 8) ">=") list:sort (9 8 3 3)}] + skolem:lemma6037 + skolem:lemma6038 + [ a r:Fact; r:gives {(9833 3389) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3938]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 3 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9833]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3937 a r:Inference; + r:gives { + 3939 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3939 math:notEqualTo 0}] + skolem:lemma6700 + [ a r:Fact; r:gives {((3 9 3 9) "=<") list:sort (3 3 9 9)}] + [ a r:Fact; r:gives {((3 9 3 9) ">=") list:sort (9 9 3 3)}] + skolem:lemma6049 + skolem:lemma6050 + [ a r:Fact; r:gives {(9933 3399) math:difference 6534}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6534 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6534 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3939]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 3 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9933]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6534]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3938 a r:Inference; + r:gives { + 3940 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3940 math:notEqualTo 0}] + skolem:lemma6701 + [ a r:Fact; r:gives {((3 9 4 0) "=<") list:sort (0 3 4 9)}] + [ a r:Fact; r:gives {((3 9 4 0) ">=") list:sort (9 4 3 0)}] + skolem:lemma5544 + skolem:lemma5545 + [ a r:Fact; r:gives {(9430 349) math:difference 9081}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9081 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 9081 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3940]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 4 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3939 a r:Inference; + r:gives { + 3941 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3941 math:notEqualTo 0}] + skolem:lemma6702 + [ a r:Fact; r:gives {((3 9 4 1) "=<") list:sort (1 3 4 9)}] + [ a r:Fact; r:gives {((3 9 4 1) ">=") list:sort (9 4 3 1)}] + skolem:lemma5716 + skolem:lemma5717 + [ a r:Fact; r:gives {(9431 1349) math:difference 8082}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8082 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 8082 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3941]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 4 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3940 a r:Inference; + r:gives { + 3942 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3942 math:notEqualTo 0}] + skolem:lemma6703 + [ a r:Fact; r:gives {((3 9 4 2) "=<") list:sort (2 3 4 9)}] + [ a r:Fact; r:gives {((3 9 4 2) ">=") list:sort (9 4 3 2)}] + skolem:lemma4642 + skolem:lemma4643 + [ a r:Fact; r:gives {(9432 2349) math:difference 7083}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7083 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7083 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3942]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 4 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3941 a r:Inference; + r:gives { + 3943 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3943 math:notEqualTo 0}] + skolem:lemma6704 + [ a r:Fact; r:gives {((3 9 4 3) "=<") list:sort (3 3 4 9)}] + [ a r:Fact; r:gives {((3 9 4 3) ">=") list:sort (9 4 3 3)}] + skolem:lemma5969 + skolem:lemma5970 + [ a r:Fact; r:gives {(9433 3349) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3943]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3942 a r:Inference; + r:gives { + 3944 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3944 math:notEqualTo 0}] + skolem:lemma6705 + [ a r:Fact; r:gives {((3 9 4 4) "=<") list:sort (3 4 4 9)}] + [ a r:Fact; r:gives {((3 9 4 4) ">=") list:sort (9 4 4 3)}] + skolem:lemma6111 + skolem:lemma6112 + [ a r:Fact; r:gives {(9443 3449) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3944]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 4 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 4 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3449]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3943 a r:Inference; + r:gives { + 3945 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3945 math:notEqualTo 0}] + skolem:lemma6706 + [ a r:Fact; r:gives {((3 9 4 5) "=<") list:sort (3 4 5 9)}] + [ a r:Fact; r:gives {((3 9 4 5) ">=") list:sort (9 5 4 3)}] + skolem:lemma6131 + skolem:lemma6132 + [ a r:Fact; r:gives {(9543 3459) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3945]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 4 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3459]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3944 a r:Inference; + r:gives { + 3946 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3946 math:notEqualTo 0}] + skolem:lemma6707 + [ a r:Fact; r:gives {((3 9 4 6) "=<") list:sort (3 4 6 9)}] + [ a r:Fact; r:gives {((3 9 4 6) ">=") list:sort (9 6 4 3)}] + skolem:lemma6149 + skolem:lemma6150 + [ a r:Fact; r:gives {(9643 3469) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3946]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 4 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3469]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3945 a r:Inference; + r:gives { + 3947 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3947 math:notEqualTo 0}] + skolem:lemma6708 + [ a r:Fact; r:gives {((3 9 4 7) "=<") list:sort (3 4 7 9)}] + [ a r:Fact; r:gives {((3 9 4 7) ">=") list:sort (9 7 4 3)}] + skolem:lemma6165 + skolem:lemma6166 + [ a r:Fact; r:gives {(9743 3479) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3947]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 4 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3479]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3946 a r:Inference; + r:gives { + 3948 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3948 math:notEqualTo 0}] + skolem:lemma6709 + [ a r:Fact; r:gives {((3 9 4 8) "=<") list:sort (3 4 8 9)}] + [ a r:Fact; r:gives {((3 9 4 8) ">=") list:sort (9 8 4 3)}] + skolem:lemma6179 + skolem:lemma6180 + [ a r:Fact; r:gives {(9843 3489) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3948]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 4 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3489]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9843]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3947 a r:Inference; + r:gives { + 3949 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3949 math:notEqualTo 0}] + skolem:lemma6710 + [ a r:Fact; r:gives {((3 9 4 9) "=<") list:sort (3 4 9 9)}] + [ a r:Fact; r:gives {((3 9 4 9) ">=") list:sort (9 9 4 3)}] + skolem:lemma6191 + skolem:lemma6192 + [ a r:Fact; r:gives {(9943 3499) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3949]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 4 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3499]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9943]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3948 a r:Inference; + r:gives { + 3950 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3950 math:notEqualTo 0}] + skolem:lemma6711 + [ a r:Fact; r:gives {((3 9 5 0) "=<") list:sort (0 3 5 9)}] + [ a r:Fact; r:gives {((3 9 5 0) ">=") list:sort (9 5 3 0)}] + skolem:lemma5564 + skolem:lemma5565 + [ a r:Fact; r:gives {(9530 359) math:difference 9171}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9171 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9171 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3950]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 5 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3949 a r:Inference; + r:gives { + 3951 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3951 math:notEqualTo 0}] + skolem:lemma6712 + [ a r:Fact; r:gives {((3 9 5 1) "=<") list:sort (1 3 5 9)}] + [ a r:Fact; r:gives {((3 9 5 1) ">=") list:sort (9 5 3 1)}] + skolem:lemma5736 + skolem:lemma5737 + [ a r:Fact; r:gives {(9531 1359) math:difference 8172}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8172 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 8172 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3951]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 5 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3950 a r:Inference; + r:gives { + 3952 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3952 math:notEqualTo 0}] + skolem:lemma6713 + [ a r:Fact; r:gives {((3 9 5 2) "=<") list:sort (2 3 5 9)}] + [ a r:Fact; r:gives {((3 9 5 2) ">=") list:sort (9 5 3 2)}] + skolem:lemma4662 + skolem:lemma4663 + [ a r:Fact; r:gives {(9532 2359) math:difference 7173}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7173 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7173 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3952]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 5 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3951 a r:Inference; + r:gives { + 3953 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3953 math:notEqualTo 0}] + skolem:lemma6714 + [ a r:Fact; r:gives {((3 9 5 3) "=<") list:sort (3 3 5 9)}] + [ a r:Fact; r:gives {((3 9 5 3) ">=") list:sort (9 5 3 3)}] + skolem:lemma5989 + skolem:lemma5990 + [ a r:Fact; r:gives {(9533 3359) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3953]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3952 a r:Inference; + r:gives { + 3954 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3954 math:notEqualTo 0}] + skolem:lemma6715 + [ a r:Fact; r:gives {((3 9 5 4) "=<") list:sort (3 4 5 9)}] + [ a r:Fact; r:gives {((3 9 5 4) ">=") list:sort (9 5 4 3)}] + skolem:lemma6131 + skolem:lemma6132 + [ a r:Fact; r:gives {(9543 3459) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3954]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 5 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3459]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3953 a r:Inference; + r:gives { + 3955 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3955 math:notEqualTo 0}] + skolem:lemma6716 + [ a r:Fact; r:gives {((3 9 5 5) "=<") list:sort (3 5 5 9)}] + [ a r:Fact; r:gives {((3 9 5 5) ">=") list:sort (9 5 5 3)}] + skolem:lemma6261 + skolem:lemma6262 + [ a r:Fact; r:gives {(9553 3559) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3955]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 5 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 5 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3559]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3954 a r:Inference; + r:gives { + 3956 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3956 math:notEqualTo 0}] + skolem:lemma6717 + [ a r:Fact; r:gives {((3 9 5 6) "=<") list:sort (3 5 6 9)}] + [ a r:Fact; r:gives {((3 9 5 6) ">=") list:sort (9 6 5 3)}] + skolem:lemma6279 + skolem:lemma6280 + [ a r:Fact; r:gives {(9653 3569) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3956]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 5 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3569]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3955 a r:Inference; + r:gives { + 3957 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3957 math:notEqualTo 0}] + skolem:lemma6718 + [ a r:Fact; r:gives {((3 9 5 7) "=<") list:sort (3 5 7 9)}] + [ a r:Fact; r:gives {((3 9 5 7) ">=") list:sort (9 7 5 3)}] + skolem:lemma6295 + skolem:lemma6296 + [ a r:Fact; r:gives {(9753 3579) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3957]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 5 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3579]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3956 a r:Inference; + r:gives { + 3958 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3958 math:notEqualTo 0}] + skolem:lemma6719 + [ a r:Fact; r:gives {((3 9 5 8) "=<") list:sort (3 5 8 9)}] + [ a r:Fact; r:gives {((3 9 5 8) ">=") list:sort (9 8 5 3)}] + skolem:lemma6309 + skolem:lemma6310 + [ a r:Fact; r:gives {(9853 3589) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3958]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 5 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3589]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9853]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3957 a r:Inference; + r:gives { + 3959 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3959 math:notEqualTo 0}] + skolem:lemma6720 + [ a r:Fact; r:gives {((3 9 5 9) "=<") list:sort (3 5 9 9)}] + [ a r:Fact; r:gives {((3 9 5 9) ">=") list:sort (9 9 5 3)}] + skolem:lemma6321 + skolem:lemma6322 + [ a r:Fact; r:gives {(9953 3599) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3959]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 5 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3599]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9953]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3958 a r:Inference; + r:gives { + 3960 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3960 math:notEqualTo 0}] + skolem:lemma6721 + [ a r:Fact; r:gives {((3 9 6 0) "=<") list:sort (0 3 6 9)}] + [ a r:Fact; r:gives {((3 9 6 0) ">=") list:sort (9 6 3 0)}] + skolem:lemma5582 + skolem:lemma5583 + [ a r:Fact; r:gives {(9630 369) math:difference 9261}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9261 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 9261 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3960]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 6 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9261]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3959 a r:Inference; + r:gives { + 3961 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3961 math:notEqualTo 0}] + skolem:lemma6722 + [ a r:Fact; r:gives {((3 9 6 1) "=<") list:sort (1 3 6 9)}] + [ a r:Fact; r:gives {((3 9 6 1) ">=") list:sort (9 6 3 1)}] + skolem:lemma5754 + skolem:lemma5755 + [ a r:Fact; r:gives {(9631 1369) math:difference 8262}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8262 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 8262 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3961]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 6 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3960 a r:Inference; + r:gives { + 3962 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3962 math:notEqualTo 0}] + skolem:lemma6723 + [ a r:Fact; r:gives {((3 9 6 2) "=<") list:sort (2 3 6 9)}] + [ a r:Fact; r:gives {((3 9 6 2) ">=") list:sort (9 6 3 2)}] + skolem:lemma4680 + skolem:lemma4681 + [ a r:Fact; r:gives {(9632 2369) math:difference 7263}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7263 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 7263 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3962]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 6 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3961 a r:Inference; + r:gives { + 3963 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3963 math:notEqualTo 0}] + skolem:lemma6724 + [ a r:Fact; r:gives {((3 9 6 3) "=<") list:sort (3 3 6 9)}] + [ a r:Fact; r:gives {((3 9 6 3) ">=") list:sort (9 6 3 3)}] + skolem:lemma6007 + skolem:lemma6008 + [ a r:Fact; r:gives {(9633 3369) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3963]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3962 a r:Inference; + r:gives { + 3964 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3964 math:notEqualTo 0}] + skolem:lemma6725 + [ a r:Fact; r:gives {((3 9 6 4) "=<") list:sort (3 4 6 9)}] + [ a r:Fact; r:gives {((3 9 6 4) ">=") list:sort (9 6 4 3)}] + skolem:lemma6149 + skolem:lemma6150 + [ a r:Fact; r:gives {(9643 3469) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3964]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 6 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3469]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3963 a r:Inference; + r:gives { + 3965 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3965 math:notEqualTo 0}] + skolem:lemma6726 + [ a r:Fact; r:gives {((3 9 6 5) "=<") list:sort (3 5 6 9)}] + [ a r:Fact; r:gives {((3 9 6 5) ">=") list:sort (9 6 5 3)}] + skolem:lemma6279 + skolem:lemma6280 + [ a r:Fact; r:gives {(9653 3569) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3965]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 6 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3569]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3964 a r:Inference; + r:gives { + 3966 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3966 math:notEqualTo 0}] + skolem:lemma6727 + [ a r:Fact; r:gives {((3 9 6 6) "=<") list:sort (3 6 6 9)}] + [ a r:Fact; r:gives {((3 9 6 6) ">=") list:sort (9 6 6 3)}] + skolem:lemma6399 + skolem:lemma6400 + [ a r:Fact; r:gives {(9663 3669) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3966]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 6 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 6 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3669]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9663]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3965 a r:Inference; + r:gives { + 3967 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3967 math:notEqualTo 0}] + skolem:lemma6728 + [ a r:Fact; r:gives {((3 9 6 7) "=<") list:sort (3 6 7 9)}] + [ a r:Fact; r:gives {((3 9 6 7) ">=") list:sort (9 7 6 3)}] + skolem:lemma6415 + skolem:lemma6416 + [ a r:Fact; r:gives {(9763 3679) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3967]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 6 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3679]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3966 a r:Inference; + r:gives { + 3968 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3968 math:notEqualTo 0}] + skolem:lemma6729 + [ a r:Fact; r:gives {((3 9 6 8) "=<") list:sort (3 6 8 9)}] + [ a r:Fact; r:gives {((3 9 6 8) ">=") list:sort (9 8 6 3)}] + skolem:lemma6429 + skolem:lemma6430 + [ a r:Fact; r:gives {(9863 3689) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3968]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 6 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3689]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9863]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3967 a r:Inference; + r:gives { + 3969 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3969 math:notEqualTo 0}] + skolem:lemma6730 + [ a r:Fact; r:gives {((3 9 6 9) "=<") list:sort (3 6 9 9)}] + [ a r:Fact; r:gives {((3 9 6 9) ">=") list:sort (9 9 6 3)}] + skolem:lemma6441 + skolem:lemma6442 + [ a r:Fact; r:gives {(9963 3699) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3969]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 6 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3699]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9963]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3968 a r:Inference; + r:gives { + 3970 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3970 math:notEqualTo 0}] + skolem:lemma6731 + [ a r:Fact; r:gives {((3 9 7 0) "=<") list:sort (0 3 7 9)}] + [ a r:Fact; r:gives {((3 9 7 0) ">=") list:sort (9 7 3 0)}] + skolem:lemma5598 + skolem:lemma5599 + [ a r:Fact; r:gives {(9730 379) math:difference 9351}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9351 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9351 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3970]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 7 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9351]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3969 a r:Inference; + r:gives { + 3971 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3971 math:notEqualTo 0}] + skolem:lemma6732 + [ a r:Fact; r:gives {((3 9 7 1) "=<") list:sort (1 3 7 9)}] + [ a r:Fact; r:gives {((3 9 7 1) ">=") list:sort (9 7 3 1)}] + skolem:lemma5770 + skolem:lemma5771 + [ a r:Fact; r:gives {(9731 1379) math:difference 8352}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8352 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8352 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3971]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 7 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9731]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3970 a r:Inference; + r:gives { + 3972 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3972 math:notEqualTo 0}] + skolem:lemma6733 + [ a r:Fact; r:gives {((3 9 7 2) "=<") list:sort (2 3 7 9)}] + [ a r:Fact; r:gives {((3 9 7 2) ">=") list:sort (9 7 3 2)}] + skolem:lemma4696 + skolem:lemma4697 + [ a r:Fact; r:gives {(9732 2379) math:difference 7353}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7353 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7353 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3972]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 7 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3971 a r:Inference; + r:gives { + 3973 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3973 math:notEqualTo 0}] + skolem:lemma6734 + [ a r:Fact; r:gives {((3 9 7 3) "=<") list:sort (3 3 7 9)}] + [ a r:Fact; r:gives {((3 9 7 3) ">=") list:sort (9 7 3 3)}] + skolem:lemma6023 + skolem:lemma6024 + [ a r:Fact; r:gives {(9733 3379) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3973]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3972 a r:Inference; + r:gives { + 3974 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3974 math:notEqualTo 0}] + skolem:lemma6735 + [ a r:Fact; r:gives {((3 9 7 4) "=<") list:sort (3 4 7 9)}] + [ a r:Fact; r:gives {((3 9 7 4) ">=") list:sort (9 7 4 3)}] + skolem:lemma6165 + skolem:lemma6166 + [ a r:Fact; r:gives {(9743 3479) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3974]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 7 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3479]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3973 a r:Inference; + r:gives { + 3975 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3975 math:notEqualTo 0}] + skolem:lemma6736 + [ a r:Fact; r:gives {((3 9 7 5) "=<") list:sort (3 5 7 9)}] + [ a r:Fact; r:gives {((3 9 7 5) ">=") list:sort (9 7 5 3)}] + skolem:lemma6295 + skolem:lemma6296 + [ a r:Fact; r:gives {(9753 3579) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3975]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 7 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3579]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3974 a r:Inference; + r:gives { + 3976 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3976 math:notEqualTo 0}] + skolem:lemma6737 + [ a r:Fact; r:gives {((3 9 7 6) "=<") list:sort (3 6 7 9)}] + [ a r:Fact; r:gives {((3 9 7 6) ">=") list:sort (9 7 6 3)}] + skolem:lemma6415 + skolem:lemma6416 + [ a r:Fact; r:gives {(9763 3679) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3976]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 7 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3679]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3975 a r:Inference; + r:gives { + 3977 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3977 math:notEqualTo 0}] + skolem:lemma6738 + [ a r:Fact; r:gives {((3 9 7 7) "=<") list:sort (3 7 7 9)}] + [ a r:Fact; r:gives {((3 9 7 7) ">=") list:sort (9 7 7 3)}] + skolem:lemma6527 + skolem:lemma6528 + [ a r:Fact; r:gives {(9773 3779) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3977]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 7 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 7 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3779]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9773]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3976 a r:Inference; + r:gives { + 3978 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3978 math:notEqualTo 0}] + skolem:lemma6739 + [ a r:Fact; r:gives {((3 9 7 8) "=<") list:sort (3 7 8 9)}] + [ a r:Fact; r:gives {((3 9 7 8) ">=") list:sort (9 8 7 3)}] + skolem:lemma6541 + skolem:lemma6542 + [ a r:Fact; r:gives {(9873 3789) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3978]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 7 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3789]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9873]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3977 a r:Inference; + r:gives { + 3979 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3979 math:notEqualTo 0}] + skolem:lemma6740 + [ a r:Fact; r:gives {((3 9 7 9) "=<") list:sort (3 7 9 9)}] + [ a r:Fact; r:gives {((3 9 7 9) ">=") list:sort (9 9 7 3)}] + skolem:lemma6553 + skolem:lemma6554 + [ a r:Fact; r:gives {(9973 3799) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3979]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 7 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3799]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9973]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3978 a r:Inference; + r:gives { + 3980 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3980 math:notEqualTo 0}] + skolem:lemma6741 + [ a r:Fact; r:gives {((3 9 8 0) "=<") list:sort (0 3 8 9)}] + [ a r:Fact; r:gives {((3 9 8 0) ">=") list:sort (9 8 3 0)}] + skolem:lemma5612 + skolem:lemma5613 + [ a r:Fact; r:gives {(9830 389) math:difference 9441}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9441 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9441 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3980]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 8 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9830]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9441]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3979 a r:Inference; + r:gives { + 3981 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3981 math:notEqualTo 0}] + skolem:lemma6742 + [ a r:Fact; r:gives {((3 9 8 1) "=<") list:sort (1 3 8 9)}] + [ a r:Fact; r:gives {((3 9 8 1) ">=") list:sort (9 8 3 1)}] + skolem:lemma5784 + skolem:lemma5785 + [ a r:Fact; r:gives {(9831 1389) math:difference 8442}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8442 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 8442 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3981]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 8 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9831]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3980 a r:Inference; + r:gives { + 3982 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3982 math:notEqualTo 0}] + skolem:lemma6743 + [ a r:Fact; r:gives {((3 9 8 2) "=<") list:sort (2 3 8 9)}] + [ a r:Fact; r:gives {((3 9 8 2) ">=") list:sort (9 8 3 2)}] + skolem:lemma4710 + skolem:lemma4711 + [ a r:Fact; r:gives {(9832 2389) math:difference 7443}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7443 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 7443 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3982]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 8 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3981 a r:Inference; + r:gives { + 3983 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3983 math:notEqualTo 0}] + skolem:lemma6744 + [ a r:Fact; r:gives {((3 9 8 3) "=<") list:sort (3 3 8 9)}] + [ a r:Fact; r:gives {((3 9 8 3) ">=") list:sort (9 8 3 3)}] + skolem:lemma6037 + skolem:lemma6038 + [ a r:Fact; r:gives {(9833 3389) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3983]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9833]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3982 a r:Inference; + r:gives { + 3984 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3984 math:notEqualTo 0}] + skolem:lemma6745 + [ a r:Fact; r:gives {((3 9 8 4) "=<") list:sort (3 4 8 9)}] + [ a r:Fact; r:gives {((3 9 8 4) ">=") list:sort (9 8 4 3)}] + skolem:lemma6179 + skolem:lemma6180 + [ a r:Fact; r:gives {(9843 3489) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3984]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 8 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3489]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9843]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3983 a r:Inference; + r:gives { + 3985 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3985 math:notEqualTo 0}] + skolem:lemma6746 + [ a r:Fact; r:gives {((3 9 8 5) "=<") list:sort (3 5 8 9)}] + [ a r:Fact; r:gives {((3 9 8 5) ">=") list:sort (9 8 5 3)}] + skolem:lemma6309 + skolem:lemma6310 + [ a r:Fact; r:gives {(9853 3589) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3985]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 8 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3589]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9853]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3984 a r:Inference; + r:gives { + 3986 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3986 math:notEqualTo 0}] + skolem:lemma6747 + [ a r:Fact; r:gives {((3 9 8 6) "=<") list:sort (3 6 8 9)}] + [ a r:Fact; r:gives {((3 9 8 6) ">=") list:sort (9 8 6 3)}] + skolem:lemma6429 + skolem:lemma6430 + [ a r:Fact; r:gives {(9863 3689) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3986]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 8 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3689]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9863]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3985 a r:Inference; + r:gives { + 3987 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3987 math:notEqualTo 0}] + skolem:lemma6748 + [ a r:Fact; r:gives {((3 9 8 7) "=<") list:sort (3 7 8 9)}] + [ a r:Fact; r:gives {((3 9 8 7) ">=") list:sort (9 8 7 3)}] + skolem:lemma6541 + skolem:lemma6542 + [ a r:Fact; r:gives {(9873 3789) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3987]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 8 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3789]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9873]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3986 a r:Inference; + r:gives { + 3988 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3988 math:notEqualTo 0}] + skolem:lemma6749 + [ a r:Fact; r:gives {((3 9 8 8) "=<") list:sort (3 8 8 9)}] + [ a r:Fact; r:gives {((3 9 8 8) ">=") list:sort (9 8 8 3)}] + skolem:lemma6647 + skolem:lemma6648 + [ a r:Fact; r:gives {(9883 3889) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3988]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 8 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 8 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 8 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3889]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9883]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3987 a r:Inference; + r:gives { + 3989 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3989 math:notEqualTo 0}] + skolem:lemma6750 + [ a r:Fact; r:gives {((3 9 8 9) "=<") list:sort (3 8 9 9)}] + [ a r:Fact; r:gives {((3 9 8 9) ">=") list:sort (9 9 8 3)}] + skolem:lemma6659 + skolem:lemma6660 + [ a r:Fact; r:gives {(9983 3899) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3989]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 8 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 8 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3899]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9983]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3988 a r:Inference; + r:gives { + 3990 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3990 math:notEqualTo 0}] + skolem:lemma6751 + [ a r:Fact; r:gives {((3 9 9 0) "=<") list:sort (0 3 9 9)}] + [ a r:Fact; r:gives {((3 9 9 0) ">=") list:sort (9 9 3 0)}] + skolem:lemma5624 + skolem:lemma5625 + [ a r:Fact; r:gives {(9930 399) math:difference 9531}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 9531 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 9531 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3990]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 9 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (0 3 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 3 0)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9930]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3989 a r:Inference; + r:gives { + 3991 :kaprekar (0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {3991 math:notEqualTo 0}] + skolem:lemma6752 + [ a r:Fact; r:gives {((3 9 9 1) "=<") list:sort (1 3 9 9)}] + [ a r:Fact; r:gives {((3 9 9 1) ">=") list:sort (9 9 3 1)}] + skolem:lemma5796 + skolem:lemma5797 + [ a r:Fact; r:gives {(9931 1399) math:difference 8532}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 8532 math:equalTo 6174. + } { + 2 log:equalTo 1. + } { + 8532 :kaprekar (1 2). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3991]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 9 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (1 3 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 3 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9931]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 2]; + r:rule skolem:lemma4001. + +skolem:lemma3990 a r:Inference; + r:gives { + 3992 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3992 math:notEqualTo 0}] + skolem:lemma6753 + [ a r:Fact; r:gives {((3 9 9 2) "=<") list:sort (2 3 9 9)}] + [ a r:Fact; r:gives {((3 9 9 2) ">=") list:sort (9 9 3 2)}] + skolem:lemma4722 + skolem:lemma4723 + [ a r:Fact; r:gives {(9932 2399) math:difference 7533}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 7533 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 7533 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 9 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 3 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 3 2)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9932]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3991 a r:Inference; + r:gives { + 3993 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3993 math:notEqualTo 0}] + skolem:lemma6754 + [ a r:Fact; r:gives {((3 9 9 3) "=<") list:sort (3 3 9 9)}] + [ a r:Fact; r:gives {((3 9 9 3) ">=") list:sort (9 9 3 3)}] + skolem:lemma6049 + skolem:lemma6050 + [ a r:Fact; r:gives {(9933 3399) math:difference 6534}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6534 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6534 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 9 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 3 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 3 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9933]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6534]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3992 a r:Inference; + r:gives { + 3994 :kaprekar (0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {3994 math:notEqualTo 0}] + skolem:lemma6755 + [ a r:Fact; r:gives {((3 9 9 4) "=<") list:sort (3 4 9 9)}] + [ a r:Fact; r:gives {((3 9 9 4) ">=") list:sort (9 9 4 3)}] + skolem:lemma6191 + skolem:lemma6192 + [ a r:Fact; r:gives {(9943 3499) math:difference 6444}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6444 math:equalTo 6174. + } { + 5 log:equalTo 1. + } { + 6444 :kaprekar (1 5). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 9 4)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 4 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 4 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3499]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9943]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 5]; + r:rule skolem:lemma4001. + +skolem:lemma3993 a r:Inference; + r:gives { + 3995 :kaprekar (0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {3995 math:notEqualTo 0}] + skolem:lemma6756 + [ a r:Fact; r:gives {((3 9 9 5) "=<") list:sort (3 5 9 9)}] + [ a r:Fact; r:gives {((3 9 9 5) ">=") list:sort (9 9 5 3)}] + skolem:lemma6321 + skolem:lemma6322 + [ a r:Fact; r:gives {(9953 3599) math:difference 6354}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6354 math:equalTo 6174. + } { + 4 log:equalTo 1. + } { + 6354 :kaprekar (1 4). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 9 5)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 5 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 5 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3599]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9953]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; + r:rule skolem:lemma4001. + +skolem:lemma3994 a r:Inference; + r:gives { + 3996 :kaprekar (0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {3996 math:notEqualTo 0}] + skolem:lemma6757 + [ a r:Fact; r:gives {((3 9 9 6) "=<") list:sort (3 6 9 9)}] + [ a r:Fact; r:gives {((3 9 9 6) ">=") list:sort (9 9 6 3)}] + skolem:lemma6441 + skolem:lemma6442 + [ a r:Fact; r:gives {(9963 3699) math:difference 6264}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6264 math:equalTo 6174. + } { + 3 log:equalTo 1. + } { + 6264 :kaprekar (1 3). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 9 6)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 6 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 6 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3699]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9963]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; + r:rule skolem:lemma4001. + +skolem:lemma3995 a r:Inference; + r:gives { + 3997 :kaprekar (0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {3997 math:notEqualTo 0}] + skolem:lemma6758 + [ a r:Fact; r:gives {((3 9 9 7) "=<") list:sort (3 7 9 9)}] + [ a r:Fact; r:gives {((3 9 9 7) ">=") list:sort (9 9 7 3)}] + skolem:lemma6553 + skolem:lemma6554 + [ a r:Fact; r:gives {(9973 3799) math:difference 6174}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6174 math:equalTo 6174. + } { + 1 log:equalTo 1. + } { + 6174 :kaprekar (1 1). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 9 7)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 7 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 7 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3799]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9973]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 1]; + r:rule skolem:lemma4001. + +skolem:lemma3996 a r:Inference; + r:gives { + 3998 :kaprekar (0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {3998 math:notEqualTo 0}] + skolem:lemma6759 + [ a r:Fact; r:gives {((3 9 9 8) "=<") list:sort (3 8 9 9)}] + [ a r:Fact; r:gives {((3 9 9 8) ">=") list:sort (9 9 8 3)}] + skolem:lemma6659 + skolem:lemma6660 + [ a r:Fact; r:gives {(9983 3899) math:difference 6084}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 6084 math:equalTo 6174. + } { + 7 log:equalTo 1. + } { + 6084 :kaprekar (1 7). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 9 8)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 8 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 8 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3899]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9983]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 7]; + r:rule skolem:lemma4001. + +skolem:lemma3997 a r:Inference; + r:gives { + 3999 :kaprekar (0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {3999 math:notEqualTo 0}] + skolem:lemma6760 + [ a r:Fact; r:gives {((3 9 9 9) "=<") list:sort (3 9 9 9)}] + [ a r:Fact; r:gives {((3 9 9 9) ">=") list:sort (9 9 9 3)}] + skolem:lemma6761 + skolem:lemma6762 + [ a r:Fact; r:gives {(9993 3999) math:difference 5994}] + [ a r:Fact; r:gives {(0 1) math:sum 1}] + [ a r:Fact; r:gives {({ + 5994 math:equalTo 6174. + } { + 6 log:equalTo 1. + } { + 5994 :kaprekar (1 6). + }) log:ifThenElseIn (() 1)}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (3 9 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (3 9 9 9)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 9 3)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 6]; + r:rule skolem:lemma4001. + +skolem:lemma3998 a r:Inference; + r:gives { + 2000 :numberToDigits (2 0 0 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2000 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2000 1000) math:remainder 0}] + [ a r:Fact; r:gives {(0 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(0 100) math:remainder 0}] + [ a r:Fact; r:gives {(0 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(0 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma3999 a r:Inference; + r:gives { + (0 0 0 2) :digitsToNumber 2 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(0 100) math:product 0}] + [ a r:Fact; r:gives {(0 10) math:product 0}] + [ a r:Fact; r:gives {(0 0 0 2) math:sum 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4000 a r:Inference; + r:gives { + (2 0 0 0) :digitsToNumber 2000 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(0 100) math:product 0}] + [ a r:Fact; r:gives {(0 10) math:product 0}] + [ a r:Fact; r:gives {(2000 0 0 0) math:sum 2000}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4001 a r:Extraction; + r:gives { + @forAll var:x_0, var:x_1, var:x_2, var:x_3, var:x_4, var:x_5, var:x_6, var:x_7, var:x_8, var:x_9, var:x_10. { + var:x_0 :kaprekar (var:x_7 var:x_9). + } <= { + var:x_0 math:notEqualTo 0 . + var:x_0 :numberToDigits var:x_1. + (var:x_1 "=<") list:sort var:x_2. + (var:x_1 ">=") list:sort var:x_3. + var:x_2 :digitsToNumber var:x_4. + var:x_3 :digitsToNumber var:x_5. + (var:x_5 var:x_4) math:difference var:x_6. + (var:x_7 1) math:sum var:x_8. + ({ + var:x_6 math:equalTo 6174. + } { + var:x_9 log:equalTo var:x_8. + } { + var:x_6 :kaprekar (var:x_8 var:x_9). + }) log:ifThenElseIn var:x_10. + }. + }; + r:because [ a r:Parsing; r:source ]. + +skolem:lemma4002 a r:Inference; + r:gives { + 2001 :numberToDigits (2 0 0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2001 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2001 1000) math:remainder 1}] + [ a r:Fact; r:gives {(1 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(1 100) math:remainder 1}] + [ a r:Fact; r:gives {(1 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(1 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2001]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4003 a r:Inference; + r:gives { + (0 0 1 2) :digitsToNumber 12 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(0 100) math:product 0}] + [ a r:Fact; r:gives {(1 10) math:product 10}] + [ a r:Fact; r:gives {(0 0 10 2) math:sum 12}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 12]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4004 a r:Inference; + r:gives { + (2 1 0 0) :digitsToNumber 2100 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(1 100) math:product 100}] + [ a r:Fact; r:gives {(0 10) math:product 0}] + [ a r:Fact; r:gives {(2000 100 0 0) math:sum 2100}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4005 a r:Inference; + r:gives { + 2002 :numberToDigits (2 0 0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2002 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2002 1000) math:remainder 2}] + [ a r:Fact; r:gives {(2 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(2 100) math:remainder 2}] + [ a r:Fact; r:gives {(2 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(2 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2002]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4006 a r:Inference; + r:gives { + (0 0 2 2) :digitsToNumber 22 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(0 100) math:product 0}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 0 20 2) math:sum 22}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 22]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4007 a r:Inference; + r:gives { + (2 2 0 0) :digitsToNumber 2200 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(0 10) math:product 0}] + [ a r:Fact; r:gives {(2000 200 0 0) math:sum 2200}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4008 a r:Inference; + r:gives { + 2003 :numberToDigits (2 0 0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2003 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2003 1000) math:remainder 3}] + [ a r:Fact; r:gives {(3 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(3 100) math:remainder 3}] + [ a r:Fact; r:gives {(3 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(3 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2003]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4009 a r:Inference; + r:gives { + (0 0 2 3) :digitsToNumber 23 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(0 100) math:product 0}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 0 20 3) math:sum 23}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. + +skolem:lemma4010 a r:Inference; + r:gives { + (3 2 0 0) :digitsToNumber 3200 . + }; + r:evidence ( + [ a r:Fact; r:gives {(3 1000) math:product 3000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(0 10) math:product 0}] + [ a r:Fact; r:gives {(3000 200 0 0) math:sum 3200}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4011 a r:Inference; + r:gives { + 2004 :numberToDigits (2 0 0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2004 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2004 1000) math:remainder 4}] + [ a r:Fact; r:gives {(4 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(4 100) math:remainder 4}] + [ a r:Fact; r:gives {(4 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(4 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2004]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4012 a r:Inference; + r:gives { + (0 0 2 4) :digitsToNumber 24 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(0 100) math:product 0}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 0 20 4) math:sum 24}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 24]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6764. + +skolem:lemma4013 a r:Inference; + r:gives { + (4 2 0 0) :digitsToNumber 4200 . + }; + r:evidence ( + [ a r:Fact; r:gives {(4 1000) math:product 4000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(0 10) math:product 0}] + [ a r:Fact; r:gives {(4000 200 0 0) math:sum 4200}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4014 a r:Inference; + r:gives { + 2005 :numberToDigits (2 0 0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2005 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2005 1000) math:remainder 5}] + [ a r:Fact; r:gives {(5 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(5 100) math:remainder 5}] + [ a r:Fact; r:gives {(5 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(5 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2005]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4015 a r:Inference; + r:gives { + (0 0 2 5) :digitsToNumber 25 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(0 100) math:product 0}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 0 20 5) math:sum 25}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 25]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6764. + +skolem:lemma4016 a r:Inference; + r:gives { + (5 2 0 0) :digitsToNumber 5200 . + }; + r:evidence ( + [ a r:Fact; r:gives {(5 1000) math:product 5000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(0 10) math:product 0}] + [ a r:Fact; r:gives {(5000 200 0 0) math:sum 5200}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4017 a r:Inference; + r:gives { + 2006 :numberToDigits (2 0 0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2006 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2006 1000) math:remainder 6}] + [ a r:Fact; r:gives {(6 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(6 100) math:remainder 6}] + [ a r:Fact; r:gives {(6 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(6 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2006]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4018 a r:Inference; + r:gives { + (0 0 2 6) :digitsToNumber 26 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(0 100) math:product 0}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 0 20 6) math:sum 26}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 26]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4019 a r:Inference; + r:gives { + (6 2 0 0) :digitsToNumber 6200 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(0 10) math:product 0}] + [ a r:Fact; r:gives {(6000 200 0 0) math:sum 6200}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4020 a r:Inference; + r:gives { + 2007 :numberToDigits (2 0 0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2007 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2007 1000) math:remainder 7}] + [ a r:Fact; r:gives {(7 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(7 100) math:remainder 7}] + [ a r:Fact; r:gives {(7 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(7 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2007]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4021 a r:Inference; + r:gives { + (0 0 2 7) :digitsToNumber 27 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(0 100) math:product 0}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 0 20 7) math:sum 27}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 27]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4022 a r:Inference; + r:gives { + (7 2 0 0) :digitsToNumber 7200 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(0 10) math:product 0}] + [ a r:Fact; r:gives {(7000 200 0 0) math:sum 7200}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4023 a r:Inference; + r:gives { + 2008 :numberToDigits (2 0 0 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2008 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2008 1000) math:remainder 8}] + [ a r:Fact; r:gives {(8 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(8 100) math:remainder 8}] + [ a r:Fact; r:gives {(8 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(8 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2008]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4024 a r:Inference; + r:gives { + (0 0 2 8) :digitsToNumber 28 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(0 100) math:product 0}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 0 20 8) math:sum 28}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 28]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4025 a r:Inference; + r:gives { + (8 2 0 0) :digitsToNumber 8200 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(0 10) math:product 0}] + [ a r:Fact; r:gives {(8000 200 0 0) math:sum 8200}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4026 a r:Inference; + r:gives { + 2009 :numberToDigits (2 0 0 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2009 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2009 1000) math:remainder 9}] + [ a r:Fact; r:gives {(9 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(9 100) math:remainder 9}] + [ a r:Fact; r:gives {(9 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(9 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2009]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4027 a r:Inference; + r:gives { + (0 0 2 9) :digitsToNumber 29 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(0 100) math:product 0}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 0 20 9) math:sum 29}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 29]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4028 a r:Inference; + r:gives { + (9 2 0 0) :digitsToNumber 9200 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(0 10) math:product 0}] + [ a r:Fact; r:gives {(9000 200 0 0) math:sum 9200}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4029 a r:Inference; + r:gives { + 2010 :numberToDigits (2 0 1 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2010 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2010 1000) math:remainder 10}] + [ a r:Fact; r:gives {(10 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(10 100) math:remainder 10}] + [ a r:Fact; r:gives {(10 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(10 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2010]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4030 a r:Inference; + r:gives { + 2011 :numberToDigits (2 0 1 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2011 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2011 1000) math:remainder 11}] + [ a r:Fact; r:gives {(11 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(11 100) math:remainder 11}] + [ a r:Fact; r:gives {(11 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(11 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2011]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 11]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 11]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4031 a r:Inference; + r:gives { + (0 1 1 2) :digitsToNumber 112 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(1 100) math:product 100}] + [ a r:Fact; r:gives {(1 10) math:product 10}] + [ a r:Fact; r:gives {(0 100 10 2) math:sum 112}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 112]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4032 a r:Inference; + r:gives { + (2 1 1 0) :digitsToNumber 2110 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(1 100) math:product 100}] + [ a r:Fact; r:gives {(1 10) math:product 10}] + [ a r:Fact; r:gives {(2000 100 10 0) math:sum 2110}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2110]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4033 a r:Inference; + r:gives { + 2012 :numberToDigits (2 0 1 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2012 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2012 1000) math:remainder 12}] + [ a r:Fact; r:gives {(12 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(12 100) math:remainder 12}] + [ a r:Fact; r:gives {(12 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(12 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2012]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 12]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4034 a r:Inference; + r:gives { + (0 1 2 2) :digitsToNumber 122 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(1 100) math:product 100}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 100 20 2) math:sum 122}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 122]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4035 a r:Inference; + r:gives { + (2 2 1 0) :digitsToNumber 2210 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(1 10) math:product 10}] + [ a r:Fact; r:gives {(2000 200 10 0) math:sum 2210}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4036 a r:Inference; + r:gives { + 2013 :numberToDigits (2 0 1 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2013 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2013 1000) math:remainder 13}] + [ a r:Fact; r:gives {(13 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(13 100) math:remainder 13}] + [ a r:Fact; r:gives {(13 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(13 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2013]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 13]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 13]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4037 a r:Inference; + r:gives { + (0 1 2 3) :digitsToNumber 123 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(1 100) math:product 100}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 100 20 3) math:sum 123}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. + +skolem:lemma4038 a r:Inference; + r:gives { + (3 2 1 0) :digitsToNumber 3210 . + }; + r:evidence ( + [ a r:Fact; r:gives {(3 1000) math:product 3000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(1 10) math:product 10}] + [ a r:Fact; r:gives {(3000 200 10 0) math:sum 3210}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4039 a r:Inference; + r:gives { + 2014 :numberToDigits (2 0 1 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2014 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2014 1000) math:remainder 14}] + [ a r:Fact; r:gives {(14 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(14 100) math:remainder 14}] + [ a r:Fact; r:gives {(14 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(14 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2014]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 14]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 14]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4040 a r:Inference; + r:gives { + (0 1 2 4) :digitsToNumber 124 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(1 100) math:product 100}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 100 20 4) math:sum 124}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6764. + +skolem:lemma4041 a r:Inference; + r:gives { + (4 2 1 0) :digitsToNumber 4210 . + }; + r:evidence ( + [ a r:Fact; r:gives {(4 1000) math:product 4000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(1 10) math:product 10}] + [ a r:Fact; r:gives {(4000 200 10 0) math:sum 4210}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4042 a r:Inference; + r:gives { + 2015 :numberToDigits (2 0 1 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2015 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2015 1000) math:remainder 15}] + [ a r:Fact; r:gives {(15 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(15 100) math:remainder 15}] + [ a r:Fact; r:gives {(15 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(15 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2015]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 15]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 15]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4043 a r:Inference; + r:gives { + (0 1 2 5) :digitsToNumber 125 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(1 100) math:product 100}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 100 20 5) math:sum 125}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6764. + +skolem:lemma4044 a r:Inference; + r:gives { + (5 2 1 0) :digitsToNumber 5210 . + }; + r:evidence ( + [ a r:Fact; r:gives {(5 1000) math:product 5000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(1 10) math:product 10}] + [ a r:Fact; r:gives {(5000 200 10 0) math:sum 5210}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4045 a r:Inference; + r:gives { + 2016 :numberToDigits (2 0 1 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2016 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2016 1000) math:remainder 16}] + [ a r:Fact; r:gives {(16 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(16 100) math:remainder 16}] + [ a r:Fact; r:gives {(16 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(16 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2016]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 16]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 16]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4046 a r:Inference; + r:gives { + (0 1 2 6) :digitsToNumber 126 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(1 100) math:product 100}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 100 20 6) math:sum 126}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4047 a r:Inference; + r:gives { + (6 2 1 0) :digitsToNumber 6210 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(1 10) math:product 10}] + [ a r:Fact; r:gives {(6000 200 10 0) math:sum 6210}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4048 a r:Inference; + r:gives { + 2017 :numberToDigits (2 0 1 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2017 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2017 1000) math:remainder 17}] + [ a r:Fact; r:gives {(17 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(17 100) math:remainder 17}] + [ a r:Fact; r:gives {(17 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(17 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2017]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 17]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 17]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4049 a r:Inference; + r:gives { + (0 1 2 7) :digitsToNumber 127 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(1 100) math:product 100}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 100 20 7) math:sum 127}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4050 a r:Inference; + r:gives { + (7 2 1 0) :digitsToNumber 7210 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(1 10) math:product 10}] + [ a r:Fact; r:gives {(7000 200 10 0) math:sum 7210}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4051 a r:Inference; + r:gives { + 2018 :numberToDigits (2 0 1 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2018 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2018 1000) math:remainder 18}] + [ a r:Fact; r:gives {(18 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(18 100) math:remainder 18}] + [ a r:Fact; r:gives {(18 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(18 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2018]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 18]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 18]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4052 a r:Inference; + r:gives { + (0 1 2 8) :digitsToNumber 128 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(1 100) math:product 100}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 100 20 8) math:sum 128}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4053 a r:Inference; + r:gives { + (8 2 1 0) :digitsToNumber 8210 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(1 10) math:product 10}] + [ a r:Fact; r:gives {(8000 200 10 0) math:sum 8210}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4054 a r:Inference; + r:gives { + 2019 :numberToDigits (2 0 1 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2019 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2019 1000) math:remainder 19}] + [ a r:Fact; r:gives {(19 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(19 100) math:remainder 19}] + [ a r:Fact; r:gives {(19 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(19 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2019]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 19]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 19]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4055 a r:Inference; + r:gives { + (0 1 2 9) :digitsToNumber 129 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(1 100) math:product 100}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 100 20 9) math:sum 129}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4056 a r:Inference; + r:gives { + (9 2 1 0) :digitsToNumber 9210 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(1 10) math:product 10}] + [ a r:Fact; r:gives {(9000 200 10 0) math:sum 9210}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4057 a r:Inference; + r:gives { + 2020 :numberToDigits (2 0 2 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2020 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2020 1000) math:remainder 20}] + [ a r:Fact; r:gives {(20 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(20 100) math:remainder 20}] + [ a r:Fact; r:gives {(20 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(20 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2020]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4058 a r:Inference; + r:gives { + 2021 :numberToDigits (2 0 2 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2021 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2021 1000) math:remainder 21}] + [ a r:Fact; r:gives {(21 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(21 100) math:remainder 21}] + [ a r:Fact; r:gives {(21 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(21 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2021]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 21]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 21]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4059 a r:Inference; + r:gives { + 2022 :numberToDigits (2 0 2 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2022 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2022 1000) math:remainder 22}] + [ a r:Fact; r:gives {(22 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(22 100) math:remainder 22}] + [ a r:Fact; r:gives {(22 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(22 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2022]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 22]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4060 a r:Inference; + r:gives { + (0 2 2 2) :digitsToNumber 222 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 200 20 2) math:sum 222}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4061 a r:Inference; + r:gives { + (2 2 2 0) :digitsToNumber 2220 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(2000 200 20 0) math:sum 2220}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4062 a r:Inference; + r:gives { + 2023 :numberToDigits (2 0 2 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2023 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2023 1000) math:remainder 23}] + [ a r:Fact; r:gives {(23 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(23 100) math:remainder 23}] + [ a r:Fact; r:gives {(23 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(23 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2023]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4063 a r:Inference; + r:gives { + (0 2 2 3) :digitsToNumber 223 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 200 20 3) math:sum 223}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. + +skolem:lemma4064 a r:Inference; + r:gives { + (3 2 2 0) :digitsToNumber 3220 . + }; + r:evidence ( + [ a r:Fact; r:gives {(3 1000) math:product 3000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(3000 200 20 0) math:sum 3220}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4065 a r:Inference; + r:gives { + 2024 :numberToDigits (2 0 2 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2024 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2024 1000) math:remainder 24}] + [ a r:Fact; r:gives {(24 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(24 100) math:remainder 24}] + [ a r:Fact; r:gives {(24 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(24 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2024]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 24]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4066 a r:Inference; + r:gives { + (0 2 2 4) :digitsToNumber 224 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 200 20 4) math:sum 224}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6764. + +skolem:lemma4067 a r:Inference; + r:gives { + (4 2 2 0) :digitsToNumber 4220 . + }; + r:evidence ( + [ a r:Fact; r:gives {(4 1000) math:product 4000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(4000 200 20 0) math:sum 4220}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4068 a r:Inference; + r:gives { + 2025 :numberToDigits (2 0 2 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2025 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2025 1000) math:remainder 25}] + [ a r:Fact; r:gives {(25 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(25 100) math:remainder 25}] + [ a r:Fact; r:gives {(25 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(25 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2025]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 25]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4069 a r:Inference; + r:gives { + (0 2 2 5) :digitsToNumber 225 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 200 20 5) math:sum 225}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6764. + +skolem:lemma4070 a r:Inference; + r:gives { + (5 2 2 0) :digitsToNumber 5220 . + }; + r:evidence ( + [ a r:Fact; r:gives {(5 1000) math:product 5000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(5000 200 20 0) math:sum 5220}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4071 a r:Inference; + r:gives { + 2026 :numberToDigits (2 0 2 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2026 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2026 1000) math:remainder 26}] + [ a r:Fact; r:gives {(26 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(26 100) math:remainder 26}] + [ a r:Fact; r:gives {(26 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(26 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2026]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 26]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4072 a r:Inference; + r:gives { + (0 2 2 6) :digitsToNumber 226 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 200 20 6) math:sum 226}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4073 a r:Inference; + r:gives { + (6 2 2 0) :digitsToNumber 6220 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(6000 200 20 0) math:sum 6220}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4074 a r:Inference; + r:gives { + 2027 :numberToDigits (2 0 2 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2027 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2027 1000) math:remainder 27}] + [ a r:Fact; r:gives {(27 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(27 100) math:remainder 27}] + [ a r:Fact; r:gives {(27 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(27 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2027]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 27]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4075 a r:Inference; + r:gives { + (0 2 2 7) :digitsToNumber 227 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 200 20 7) math:sum 227}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4076 a r:Inference; + r:gives { + (7 2 2 0) :digitsToNumber 7220 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(7000 200 20 0) math:sum 7220}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4077 a r:Inference; + r:gives { + 2028 :numberToDigits (2 0 2 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2028 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2028 1000) math:remainder 28}] + [ a r:Fact; r:gives {(28 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(28 100) math:remainder 28}] + [ a r:Fact; r:gives {(28 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(28 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2028]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 28]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4078 a r:Inference; + r:gives { + (0 2 2 8) :digitsToNumber 228 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 200 20 8) math:sum 228}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4079 a r:Inference; + r:gives { + (8 2 2 0) :digitsToNumber 8220 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(8000 200 20 0) math:sum 8220}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4080 a r:Inference; + r:gives { + 2029 :numberToDigits (2 0 2 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2029 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2029 1000) math:remainder 29}] + [ a r:Fact; r:gives {(29 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(29 100) math:remainder 29}] + [ a r:Fact; r:gives {(29 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(29 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2029]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 29]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4081 a r:Inference; + r:gives { + (0 2 2 9) :digitsToNumber 229 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(0 200 20 9) math:sum 229}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4082 a r:Inference; + r:gives { + (9 2 2 0) :digitsToNumber 9220 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 200 20 0) math:sum 9220}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4083 a r:Inference; + r:gives { + 2030 :numberToDigits (2 0 3 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2030 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2030 1000) math:remainder 30}] + [ a r:Fact; r:gives {(30 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(30 100) math:remainder 30}] + [ a r:Fact; r:gives {(30 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(30 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2030]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4084 a r:Inference; + r:gives { + 2031 :numberToDigits (2 0 3 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2031 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2031 1000) math:remainder 31}] + [ a r:Fact; r:gives {(31 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(31 100) math:remainder 31}] + [ a r:Fact; r:gives {(31 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(31 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2031]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 31]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 31]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4085 a r:Inference; + r:gives { + 2032 :numberToDigits (2 0 3 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2032 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2032 1000) math:remainder 32}] + [ a r:Fact; r:gives {(32 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(32 100) math:remainder 32}] + [ a r:Fact; r:gives {(32 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(32 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2032]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 32]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 32]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4086 a r:Inference; + r:gives { + 2033 :numberToDigits (2 0 3 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2033 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2033 1000) math:remainder 33}] + [ a r:Fact; r:gives {(33 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(33 100) math:remainder 33}] + [ a r:Fact; r:gives {(33 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(33 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2033]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 33]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 33]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4087 a r:Inference; + r:gives { + (0 2 3 3) :digitsToNumber 233 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(0 200 30 3) math:sum 233}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. + +skolem:lemma4088 a r:Inference; + r:gives { + (3 3 2 0) :digitsToNumber 3320 . + }; + r:evidence ( + [ a r:Fact; r:gives {(3 1000) math:product 3000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(3000 300 20 0) math:sum 3320}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4089 a r:Inference; + r:gives { + 2034 :numberToDigits (2 0 3 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2034 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2034 1000) math:remainder 34}] + [ a r:Fact; r:gives {(34 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(34 100) math:remainder 34}] + [ a r:Fact; r:gives {(34 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(34 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2034]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 34]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 34]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4090 a r:Inference; + r:gives { + (0 2 3 4) :digitsToNumber 234 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(0 200 30 4) math:sum 234}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6764. + +skolem:lemma4091 a r:Inference; + r:gives { + (4 3 2 0) :digitsToNumber 4320 . + }; + r:evidence ( + [ a r:Fact; r:gives {(4 1000) math:product 4000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(4000 300 20 0) math:sum 4320}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4092 a r:Inference; + r:gives { + 2035 :numberToDigits (2 0 3 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2035 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2035 1000) math:remainder 35}] + [ a r:Fact; r:gives {(35 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(35 100) math:remainder 35}] + [ a r:Fact; r:gives {(35 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(35 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2035]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 35]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 35]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4093 a r:Inference; + r:gives { + (0 2 3 5) :digitsToNumber 235 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(0 200 30 5) math:sum 235}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6764. + +skolem:lemma4094 a r:Inference; + r:gives { + (5 3 2 0) :digitsToNumber 5320 . + }; + r:evidence ( + [ a r:Fact; r:gives {(5 1000) math:product 5000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(5000 300 20 0) math:sum 5320}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4095 a r:Inference; + r:gives { + 2036 :numberToDigits (2 0 3 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2036 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2036 1000) math:remainder 36}] + [ a r:Fact; r:gives {(36 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(36 100) math:remainder 36}] + [ a r:Fact; r:gives {(36 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(36 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2036]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 36]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 36]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4096 a r:Inference; + r:gives { + (0 2 3 6) :digitsToNumber 236 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(0 200 30 6) math:sum 236}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4097 a r:Inference; + r:gives { + (6 3 2 0) :digitsToNumber 6320 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(6000 300 20 0) math:sum 6320}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4098 a r:Inference; + r:gives { + 2037 :numberToDigits (2 0 3 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2037 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2037 1000) math:remainder 37}] + [ a r:Fact; r:gives {(37 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(37 100) math:remainder 37}] + [ a r:Fact; r:gives {(37 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(37 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2037]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 37]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 37]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4099 a r:Inference; + r:gives { + (0 2 3 7) :digitsToNumber 237 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(0 200 30 7) math:sum 237}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4100 a r:Inference; + r:gives { + (7 3 2 0) :digitsToNumber 7320 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(7000 300 20 0) math:sum 7320}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4101 a r:Inference; + r:gives { + 2038 :numberToDigits (2 0 3 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2038 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2038 1000) math:remainder 38}] + [ a r:Fact; r:gives {(38 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(38 100) math:remainder 38}] + [ a r:Fact; r:gives {(38 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(38 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2038]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 38]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 38]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4102 a r:Inference; + r:gives { + (0 2 3 8) :digitsToNumber 238 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(0 200 30 8) math:sum 238}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4103 a r:Inference; + r:gives { + (8 3 2 0) :digitsToNumber 8320 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(8000 300 20 0) math:sum 8320}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4104 a r:Inference; + r:gives { + 2039 :numberToDigits (2 0 3 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2039 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2039 1000) math:remainder 39}] + [ a r:Fact; r:gives {(39 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(39 100) math:remainder 39}] + [ a r:Fact; r:gives {(39 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(39 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2039]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 39]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 39]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4105 a r:Inference; + r:gives { + (0 2 3 9) :digitsToNumber 239 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(0 200 30 9) math:sum 239}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4106 a r:Inference; + r:gives { + (9 3 2 0) :digitsToNumber 9320 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 300 20 0) math:sum 9320}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4107 a r:Inference; + r:gives { + 2040 :numberToDigits (2 0 4 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2040 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2040 1000) math:remainder 40}] + [ a r:Fact; r:gives {(40 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(40 100) math:remainder 40}] + [ a r:Fact; r:gives {(40 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(40 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2040]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4108 a r:Inference; + r:gives { + 2041 :numberToDigits (2 0 4 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2041 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2041 1000) math:remainder 41}] + [ a r:Fact; r:gives {(41 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(41 100) math:remainder 41}] + [ a r:Fact; r:gives {(41 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(41 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2041]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 41]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 41]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4109 a r:Inference; + r:gives { + 2042 :numberToDigits (2 0 4 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2042 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2042 1000) math:remainder 42}] + [ a r:Fact; r:gives {(42 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(42 100) math:remainder 42}] + [ a r:Fact; r:gives {(42 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(42 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2042]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 42]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 42]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4110 a r:Inference; + r:gives { + 2043 :numberToDigits (2 0 4 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2043 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2043 1000) math:remainder 43}] + [ a r:Fact; r:gives {(43 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(43 100) math:remainder 43}] + [ a r:Fact; r:gives {(43 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(43 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2043]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 43]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 43]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4111 a r:Inference; + r:gives { + 2044 :numberToDigits (2 0 4 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2044 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2044 1000) math:remainder 44}] + [ a r:Fact; r:gives {(44 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(44 100) math:remainder 44}] + [ a r:Fact; r:gives {(44 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(44 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2044]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 44]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 44]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4112 a r:Inference; + r:gives { + (0 2 4 4) :digitsToNumber 244 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(0 200 40 4) math:sum 244}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6764. + +skolem:lemma4113 a r:Inference; + r:gives { + (4 4 2 0) :digitsToNumber 4420 . + }; + r:evidence ( + [ a r:Fact; r:gives {(4 1000) math:product 4000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(4000 400 20 0) math:sum 4420}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4114 a r:Inference; + r:gives { + 2045 :numberToDigits (2 0 4 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2045 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2045 1000) math:remainder 45}] + [ a r:Fact; r:gives {(45 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(45 100) math:remainder 45}] + [ a r:Fact; r:gives {(45 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(45 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2045]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 45]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 45]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4115 a r:Inference; + r:gives { + (0 2 4 5) :digitsToNumber 245 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(0 200 40 5) math:sum 245}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6764. + +skolem:lemma4116 a r:Inference; + r:gives { + (5 4 2 0) :digitsToNumber 5420 . + }; + r:evidence ( + [ a r:Fact; r:gives {(5 1000) math:product 5000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(5000 400 20 0) math:sum 5420}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4117 a r:Inference; + r:gives { + 2046 :numberToDigits (2 0 4 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2046 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2046 1000) math:remainder 46}] + [ a r:Fact; r:gives {(46 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(46 100) math:remainder 46}] + [ a r:Fact; r:gives {(46 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(46 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2046]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 46]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 46]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4118 a r:Inference; + r:gives { + (0 2 4 6) :digitsToNumber 246 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(0 200 40 6) math:sum 246}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4119 a r:Inference; + r:gives { + (6 4 2 0) :digitsToNumber 6420 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(6000 400 20 0) math:sum 6420}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4120 a r:Inference; + r:gives { + 2047 :numberToDigits (2 0 4 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2047 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2047 1000) math:remainder 47}] + [ a r:Fact; r:gives {(47 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(47 100) math:remainder 47}] + [ a r:Fact; r:gives {(47 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(47 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2047]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 47]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 47]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4121 a r:Inference; + r:gives { + (0 2 4 7) :digitsToNumber 247 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(0 200 40 7) math:sum 247}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4122 a r:Inference; + r:gives { + (7 4 2 0) :digitsToNumber 7420 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(7000 400 20 0) math:sum 7420}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4123 a r:Inference; + r:gives { + 2048 :numberToDigits (2 0 4 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2048 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2048 1000) math:remainder 48}] + [ a r:Fact; r:gives {(48 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(48 100) math:remainder 48}] + [ a r:Fact; r:gives {(48 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(48 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2048]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 48]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 48]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4124 a r:Inference; + r:gives { + (0 2 4 8) :digitsToNumber 248 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(0 200 40 8) math:sum 248}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4125 a r:Inference; + r:gives { + (8 4 2 0) :digitsToNumber 8420 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(8000 400 20 0) math:sum 8420}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4126 a r:Inference; + r:gives { + 2049 :numberToDigits (2 0 4 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2049 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2049 1000) math:remainder 49}] + [ a r:Fact; r:gives {(49 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(49 100) math:remainder 49}] + [ a r:Fact; r:gives {(49 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(49 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2049]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 49]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 49]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4127 a r:Inference; + r:gives { + (0 2 4 9) :digitsToNumber 249 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(0 200 40 9) math:sum 249}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4128 a r:Inference; + r:gives { + (9 4 2 0) :digitsToNumber 9420 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 400 20 0) math:sum 9420}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4129 a r:Inference; + r:gives { + 2050 :numberToDigits (2 0 5 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2050 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2050 1000) math:remainder 50}] + [ a r:Fact; r:gives {(50 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(50 100) math:remainder 50}] + [ a r:Fact; r:gives {(50 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(50 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2050]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4130 a r:Inference; + r:gives { + 2051 :numberToDigits (2 0 5 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2051 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2051 1000) math:remainder 51}] + [ a r:Fact; r:gives {(51 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(51 100) math:remainder 51}] + [ a r:Fact; r:gives {(51 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(51 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2051]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 51]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 51]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4131 a r:Inference; + r:gives { + 2052 :numberToDigits (2 0 5 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2052 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2052 1000) math:remainder 52}] + [ a r:Fact; r:gives {(52 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(52 100) math:remainder 52}] + [ a r:Fact; r:gives {(52 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(52 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2052]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 52]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 52]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4132 a r:Inference; + r:gives { + 2053 :numberToDigits (2 0 5 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2053 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2053 1000) math:remainder 53}] + [ a r:Fact; r:gives {(53 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(53 100) math:remainder 53}] + [ a r:Fact; r:gives {(53 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(53 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2053]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 53]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 53]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4133 a r:Inference; + r:gives { + 2054 :numberToDigits (2 0 5 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2054 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2054 1000) math:remainder 54}] + [ a r:Fact; r:gives {(54 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(54 100) math:remainder 54}] + [ a r:Fact; r:gives {(54 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(54 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2054]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 54]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 54]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4134 a r:Inference; + r:gives { + 2055 :numberToDigits (2 0 5 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2055 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2055 1000) math:remainder 55}] + [ a r:Fact; r:gives {(55 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(55 100) math:remainder 55}] + [ a r:Fact; r:gives {(55 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(55 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2055]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 55]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 55]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4135 a r:Inference; + r:gives { + (0 2 5 5) :digitsToNumber 255 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(0 200 50 5) math:sum 255}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6764. + +skolem:lemma4136 a r:Inference; + r:gives { + (5 5 2 0) :digitsToNumber 5520 . + }; + r:evidence ( + [ a r:Fact; r:gives {(5 1000) math:product 5000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(5000 500 20 0) math:sum 5520}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4137 a r:Inference; + r:gives { + 2056 :numberToDigits (2 0 5 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2056 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2056 1000) math:remainder 56}] + [ a r:Fact; r:gives {(56 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(56 100) math:remainder 56}] + [ a r:Fact; r:gives {(56 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(56 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2056]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 56]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 56]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4138 a r:Inference; + r:gives { + (0 2 5 6) :digitsToNumber 256 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(0 200 50 6) math:sum 256}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4139 a r:Inference; + r:gives { + (6 5 2 0) :digitsToNumber 6520 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(6000 500 20 0) math:sum 6520}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4140 a r:Inference; + r:gives { + 2057 :numberToDigits (2 0 5 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2057 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2057 1000) math:remainder 57}] + [ a r:Fact; r:gives {(57 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(57 100) math:remainder 57}] + [ a r:Fact; r:gives {(57 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(57 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2057]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 57]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 57]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4141 a r:Inference; + r:gives { + (0 2 5 7) :digitsToNumber 257 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(0 200 50 7) math:sum 257}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4142 a r:Inference; + r:gives { + (7 5 2 0) :digitsToNumber 7520 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(7000 500 20 0) math:sum 7520}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4143 a r:Inference; + r:gives { + 2058 :numberToDigits (2 0 5 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2058 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2058 1000) math:remainder 58}] + [ a r:Fact; r:gives {(58 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(58 100) math:remainder 58}] + [ a r:Fact; r:gives {(58 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(58 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2058]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 58]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 58]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4144 a r:Inference; + r:gives { + (0 2 5 8) :digitsToNumber 258 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(0 200 50 8) math:sum 258}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4145 a r:Inference; + r:gives { + (8 5 2 0) :digitsToNumber 8520 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(8000 500 20 0) math:sum 8520}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4146 a r:Inference; + r:gives { + 2059 :numberToDigits (2 0 5 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2059 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2059 1000) math:remainder 59}] + [ a r:Fact; r:gives {(59 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(59 100) math:remainder 59}] + [ a r:Fact; r:gives {(59 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(59 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2059]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 59]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 59]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4147 a r:Inference; + r:gives { + (0 2 5 9) :digitsToNumber 259 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(0 200 50 9) math:sum 259}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4148 a r:Inference; + r:gives { + (9 5 2 0) :digitsToNumber 9520 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 500 20 0) math:sum 9520}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4149 a r:Inference; + r:gives { + 2060 :numberToDigits (2 0 6 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2060 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2060 1000) math:remainder 60}] + [ a r:Fact; r:gives {(60 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(60 100) math:remainder 60}] + [ a r:Fact; r:gives {(60 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(60 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2060]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4150 a r:Inference; + r:gives { + 2061 :numberToDigits (2 0 6 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2061 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2061 1000) math:remainder 61}] + [ a r:Fact; r:gives {(61 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(61 100) math:remainder 61}] + [ a r:Fact; r:gives {(61 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(61 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2061]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 61]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 61]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4151 a r:Inference; + r:gives { + 2062 :numberToDigits (2 0 6 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2062 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2062 1000) math:remainder 62}] + [ a r:Fact; r:gives {(62 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(62 100) math:remainder 62}] + [ a r:Fact; r:gives {(62 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(62 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2062]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 62]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 62]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4152 a r:Inference; + r:gives { + 2063 :numberToDigits (2 0 6 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2063 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2063 1000) math:remainder 63}] + [ a r:Fact; r:gives {(63 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(63 100) math:remainder 63}] + [ a r:Fact; r:gives {(63 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(63 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2063]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 63]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 63]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4153 a r:Inference; + r:gives { + 2064 :numberToDigits (2 0 6 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2064 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2064 1000) math:remainder 64}] + [ a r:Fact; r:gives {(64 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(64 100) math:remainder 64}] + [ a r:Fact; r:gives {(64 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(64 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2064]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 64]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 64]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4154 a r:Inference; + r:gives { + 2065 :numberToDigits (2 0 6 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2065 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2065 1000) math:remainder 65}] + [ a r:Fact; r:gives {(65 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(65 100) math:remainder 65}] + [ a r:Fact; r:gives {(65 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(65 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2065]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 65]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 65]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4155 a r:Inference; + r:gives { + 2066 :numberToDigits (2 0 6 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2066 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2066 1000) math:remainder 66}] + [ a r:Fact; r:gives {(66 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(66 100) math:remainder 66}] + [ a r:Fact; r:gives {(66 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(66 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2066]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 66]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 66]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4156 a r:Inference; + r:gives { + (0 2 6 6) :digitsToNumber 266 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(0 200 60 6) math:sum 266}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4157 a r:Inference; + r:gives { + (6 6 2 0) :digitsToNumber 6620 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(6000 600 20 0) math:sum 6620}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4158 a r:Inference; + r:gives { + 2067 :numberToDigits (2 0 6 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2067 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2067 1000) math:remainder 67}] + [ a r:Fact; r:gives {(67 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(67 100) math:remainder 67}] + [ a r:Fact; r:gives {(67 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(67 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2067]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 67]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 67]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4159 a r:Inference; + r:gives { + (0 2 6 7) :digitsToNumber 267 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(0 200 60 7) math:sum 267}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4160 a r:Inference; + r:gives { + (7 6 2 0) :digitsToNumber 7620 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(7000 600 20 0) math:sum 7620}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4161 a r:Inference; + r:gives { + 2068 :numberToDigits (2 0 6 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2068 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2068 1000) math:remainder 68}] + [ a r:Fact; r:gives {(68 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(68 100) math:remainder 68}] + [ a r:Fact; r:gives {(68 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(68 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2068]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 68]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 68]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4162 a r:Inference; + r:gives { + (0 2 6 8) :digitsToNumber 268 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(0 200 60 8) math:sum 268}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4163 a r:Inference; + r:gives { + (8 6 2 0) :digitsToNumber 8620 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(8000 600 20 0) math:sum 8620}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4164 a r:Inference; + r:gives { + 2069 :numberToDigits (2 0 6 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2069 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2069 1000) math:remainder 69}] + [ a r:Fact; r:gives {(69 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(69 100) math:remainder 69}] + [ a r:Fact; r:gives {(69 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(69 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2069]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 69]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 69]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4165 a r:Inference; + r:gives { + (0 2 6 9) :digitsToNumber 269 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(0 200 60 9) math:sum 269}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4166 a r:Inference; + r:gives { + (9 6 2 0) :digitsToNumber 9620 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 600 20 0) math:sum 9620}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4167 a r:Inference; + r:gives { + 2070 :numberToDigits (2 0 7 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2070 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2070 1000) math:remainder 70}] + [ a r:Fact; r:gives {(70 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(70 100) math:remainder 70}] + [ a r:Fact; r:gives {(70 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(70 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2070]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4168 a r:Inference; + r:gives { + 2071 :numberToDigits (2 0 7 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2071 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2071 1000) math:remainder 71}] + [ a r:Fact; r:gives {(71 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(71 100) math:remainder 71}] + [ a r:Fact; r:gives {(71 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(71 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2071]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 71]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 71]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4169 a r:Inference; + r:gives { + 2072 :numberToDigits (2 0 7 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2072 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2072 1000) math:remainder 72}] + [ a r:Fact; r:gives {(72 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(72 100) math:remainder 72}] + [ a r:Fact; r:gives {(72 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(72 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2072]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 72]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 72]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4170 a r:Inference; + r:gives { + 2073 :numberToDigits (2 0 7 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2073 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2073 1000) math:remainder 73}] + [ a r:Fact; r:gives {(73 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(73 100) math:remainder 73}] + [ a r:Fact; r:gives {(73 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(73 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2073]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 73]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 73]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4171 a r:Inference; + r:gives { + 2074 :numberToDigits (2 0 7 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2074 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2074 1000) math:remainder 74}] + [ a r:Fact; r:gives {(74 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(74 100) math:remainder 74}] + [ a r:Fact; r:gives {(74 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(74 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2074]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 74]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 74]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4172 a r:Inference; + r:gives { + 2075 :numberToDigits (2 0 7 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2075 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2075 1000) math:remainder 75}] + [ a r:Fact; r:gives {(75 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(75 100) math:remainder 75}] + [ a r:Fact; r:gives {(75 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(75 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2075]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 75]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 75]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4173 a r:Inference; + r:gives { + 2076 :numberToDigits (2 0 7 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2076 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2076 1000) math:remainder 76}] + [ a r:Fact; r:gives {(76 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(76 100) math:remainder 76}] + [ a r:Fact; r:gives {(76 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(76 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2076]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 76]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 76]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4174 a r:Inference; + r:gives { + 2077 :numberToDigits (2 0 7 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2077 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2077 1000) math:remainder 77}] + [ a r:Fact; r:gives {(77 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(77 100) math:remainder 77}] + [ a r:Fact; r:gives {(77 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(77 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2077]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 77]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 77]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4175 a r:Inference; + r:gives { + (0 2 7 7) :digitsToNumber 277 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(0 200 70 7) math:sum 277}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 277]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4176 a r:Inference; + r:gives { + (7 7 2 0) :digitsToNumber 7720 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(7000 700 20 0) math:sum 7720}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4177 a r:Inference; + r:gives { + 2078 :numberToDigits (2 0 7 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2078 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2078 1000) math:remainder 78}] + [ a r:Fact; r:gives {(78 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(78 100) math:remainder 78}] + [ a r:Fact; r:gives {(78 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(78 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2078]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 78]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 78]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4178 a r:Inference; + r:gives { + (0 2 7 8) :digitsToNumber 278 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(0 200 70 8) math:sum 278}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4179 a r:Inference; + r:gives { + (8 7 2 0) :digitsToNumber 8720 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(8000 700 20 0) math:sum 8720}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4180 a r:Inference; + r:gives { + 2079 :numberToDigits (2 0 7 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2079 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2079 1000) math:remainder 79}] + [ a r:Fact; r:gives {(79 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(79 100) math:remainder 79}] + [ a r:Fact; r:gives {(79 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(79 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2079]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 79]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 79]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4181 a r:Inference; + r:gives { + (0 2 7 9) :digitsToNumber 279 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(0 200 70 9) math:sum 279}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4182 a r:Inference; + r:gives { + (9 7 2 0) :digitsToNumber 9720 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 700 20 0) math:sum 9720}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4183 a r:Inference; + r:gives { + 2080 :numberToDigits (2 0 8 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2080 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2080 1000) math:remainder 80}] + [ a r:Fact; r:gives {(80 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(80 100) math:remainder 80}] + [ a r:Fact; r:gives {(80 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(80 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2080]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4184 a r:Inference; + r:gives { + 2081 :numberToDigits (2 0 8 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2081 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2081 1000) math:remainder 81}] + [ a r:Fact; r:gives {(81 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(81 100) math:remainder 81}] + [ a r:Fact; r:gives {(81 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(81 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 81]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 81]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4185 a r:Inference; + r:gives { + 2082 :numberToDigits (2 0 8 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2082 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2082 1000) math:remainder 82}] + [ a r:Fact; r:gives {(82 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(82 100) math:remainder 82}] + [ a r:Fact; r:gives {(82 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(82 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 82]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 82]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4186 a r:Inference; + r:gives { + 2083 :numberToDigits (2 0 8 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2083 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2083 1000) math:remainder 83}] + [ a r:Fact; r:gives {(83 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(83 100) math:remainder 83}] + [ a r:Fact; r:gives {(83 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(83 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 83]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 83]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4187 a r:Inference; + r:gives { + 2084 :numberToDigits (2 0 8 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2084 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2084 1000) math:remainder 84}] + [ a r:Fact; r:gives {(84 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(84 100) math:remainder 84}] + [ a r:Fact; r:gives {(84 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(84 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 84]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 84]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4188 a r:Inference; + r:gives { + 2085 :numberToDigits (2 0 8 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2085 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2085 1000) math:remainder 85}] + [ a r:Fact; r:gives {(85 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(85 100) math:remainder 85}] + [ a r:Fact; r:gives {(85 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(85 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 85]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 85]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4189 a r:Inference; + r:gives { + 2086 :numberToDigits (2 0 8 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2086 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2086 1000) math:remainder 86}] + [ a r:Fact; r:gives {(86 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(86 100) math:remainder 86}] + [ a r:Fact; r:gives {(86 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(86 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 86]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 86]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4190 a r:Inference; + r:gives { + 2087 :numberToDigits (2 0 8 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2087 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2087 1000) math:remainder 87}] + [ a r:Fact; r:gives {(87 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(87 100) math:remainder 87}] + [ a r:Fact; r:gives {(87 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(87 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 87]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 87]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4191 a r:Inference; + r:gives { + 2088 :numberToDigits (2 0 8 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2088 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2088 1000) math:remainder 88}] + [ a r:Fact; r:gives {(88 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(88 100) math:remainder 88}] + [ a r:Fact; r:gives {(88 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(88 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 88]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 88]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4192 a r:Inference; + r:gives { + (0 2 8 8) :digitsToNumber 288 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(8 10) math:product 80}] + [ a r:Fact; r:gives {(0 200 80 8) math:sum 288}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 288]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4193 a r:Inference; + r:gives { + (8 8 2 0) :digitsToNumber 8820 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(8 100) math:product 800}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(8000 800 20 0) math:sum 8820}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8820]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4194 a r:Inference; + r:gives { + 2089 :numberToDigits (2 0 8 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2089 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2089 1000) math:remainder 89}] + [ a r:Fact; r:gives {(89 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(89 100) math:remainder 89}] + [ a r:Fact; r:gives {(89 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(89 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2089]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 89]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 89]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4195 a r:Inference; + r:gives { + (0 2 8 9) :digitsToNumber 289 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(8 10) math:product 80}] + [ a r:Fact; r:gives {(0 200 80 9) math:sum 289}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4196 a r:Inference; + r:gives { + (9 8 2 0) :digitsToNumber 9820 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(8 100) math:product 800}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 800 20 0) math:sum 9820}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9820]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4197 a r:Inference; + r:gives { + 2090 :numberToDigits (2 0 9 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2090 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2090 1000) math:remainder 90}] + [ a r:Fact; r:gives {(90 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(90 100) math:remainder 90}] + [ a r:Fact; r:gives {(90 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(90 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2090]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4198 a r:Inference; + r:gives { + 2091 :numberToDigits (2 0 9 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2091 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2091 1000) math:remainder 91}] + [ a r:Fact; r:gives {(91 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(91 100) math:remainder 91}] + [ a r:Fact; r:gives {(91 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(91 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2091]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 91]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 91]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4199 a r:Inference; + r:gives { + 2092 :numberToDigits (2 0 9 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2092 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2092 1000) math:remainder 92}] + [ a r:Fact; r:gives {(92 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(92 100) math:remainder 92}] + [ a r:Fact; r:gives {(92 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(92 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2092]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 92]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 92]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4200 a r:Inference; + r:gives { + 2093 :numberToDigits (2 0 9 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2093 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2093 1000) math:remainder 93}] + [ a r:Fact; r:gives {(93 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(93 100) math:remainder 93}] + [ a r:Fact; r:gives {(93 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(93 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2093]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 93]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 93]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4201 a r:Inference; + r:gives { + 2094 :numberToDigits (2 0 9 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2094 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2094 1000) math:remainder 94}] + [ a r:Fact; r:gives {(94 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(94 100) math:remainder 94}] + [ a r:Fact; r:gives {(94 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(94 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2094]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 94]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 94]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4202 a r:Inference; + r:gives { + 2095 :numberToDigits (2 0 9 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2095 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2095 1000) math:remainder 95}] + [ a r:Fact; r:gives {(95 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(95 100) math:remainder 95}] + [ a r:Fact; r:gives {(95 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(95 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2095]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 95]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 95]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4203 a r:Inference; + r:gives { + 2096 :numberToDigits (2 0 9 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2096 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2096 1000) math:remainder 96}] + [ a r:Fact; r:gives {(96 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(96 100) math:remainder 96}] + [ a r:Fact; r:gives {(96 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(96 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2096]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 96]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 96]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4204 a r:Inference; + r:gives { + 2097 :numberToDigits (2 0 9 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2097 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2097 1000) math:remainder 97}] + [ a r:Fact; r:gives {(97 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(97 100) math:remainder 97}] + [ a r:Fact; r:gives {(97 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(97 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2097]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 97]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 97]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4205 a r:Inference; + r:gives { + 2098 :numberToDigits (2 0 9 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2098 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2098 1000) math:remainder 98}] + [ a r:Fact; r:gives {(98 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(98 100) math:remainder 98}] + [ a r:Fact; r:gives {(98 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(98 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2098]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 98]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 98]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4206 a r:Inference; + r:gives { + 2099 :numberToDigits (2 0 9 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2099 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2099 1000) math:remainder 99}] + [ a r:Fact; r:gives {(99 100) math:integerQuotient 0}] + [ a r:Fact; r:gives {(99 100) math:remainder 99}] + [ a r:Fact; r:gives {(99 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(99 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2099]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 99]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 99]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4207 a r:Inference; + r:gives { + (0 2 9 9) :digitsToNumber 299 . + }; + r:evidence ( + [ a r:Fact; r:gives {(0 1000) math:product 0}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(9 10) math:product 90}] + [ a r:Fact; r:gives {(0 200 90 9) math:sum 299}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4208 a r:Inference; + r:gives { + (9 9 2 0) :digitsToNumber 9920 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(9 100) math:product 900}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 900 20 0) math:sum 9920}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 900]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9920]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6764. + +skolem:lemma4209 a r:Inference; + r:gives { + 2100 :numberToDigits (2 1 0 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2100 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2100 1000) math:remainder 100}] + [ a r:Fact; r:gives {(100 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(100 100) math:remainder 0}] + [ a r:Fact; r:gives {(0 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(0 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4210 a r:Inference; + r:gives { + 2101 :numberToDigits (2 1 0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2101 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2101 1000) math:remainder 101}] + [ a r:Fact; r:gives {(101 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(101 100) math:remainder 1}] + [ a r:Fact; r:gives {(1 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(1 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2101]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 101]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4211 a r:Inference; + r:gives { + 2102 :numberToDigits (2 1 0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2102 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2102 1000) math:remainder 102}] + [ a r:Fact; r:gives {(102 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(102 100) math:remainder 2}] + [ a r:Fact; r:gives {(2 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(2 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2102]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 102]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4212 a r:Inference; + r:gives { + 2103 :numberToDigits (2 1 0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2103 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2103 1000) math:remainder 103}] + [ a r:Fact; r:gives {(103 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(103 100) math:remainder 3}] + [ a r:Fact; r:gives {(3 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(3 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2103]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 103]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4213 a r:Inference; + r:gives { + 2104 :numberToDigits (2 1 0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2104 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2104 1000) math:remainder 104}] + [ a r:Fact; r:gives {(104 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(104 100) math:remainder 4}] + [ a r:Fact; r:gives {(4 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(4 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2104]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 104]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4214 a r:Inference; + r:gives { + 2105 :numberToDigits (2 1 0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2105 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2105 1000) math:remainder 105}] + [ a r:Fact; r:gives {(105 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(105 100) math:remainder 5}] + [ a r:Fact; r:gives {(5 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(5 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2105]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 105]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4215 a r:Inference; + r:gives { + 2106 :numberToDigits (2 1 0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2106 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2106 1000) math:remainder 106}] + [ a r:Fact; r:gives {(106 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(106 100) math:remainder 6}] + [ a r:Fact; r:gives {(6 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(6 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2106]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 106]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4216 a r:Inference; + r:gives { + 2107 :numberToDigits (2 1 0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2107 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2107 1000) math:remainder 107}] + [ a r:Fact; r:gives {(107 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(107 100) math:remainder 7}] + [ a r:Fact; r:gives {(7 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(7 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2107]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 107]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4217 a r:Inference; + r:gives { + 2108 :numberToDigits (2 1 0 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2108 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2108 1000) math:remainder 108}] + [ a r:Fact; r:gives {(108 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(108 100) math:remainder 8}] + [ a r:Fact; r:gives {(8 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(8 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2108]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 108]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4218 a r:Inference; + r:gives { + 2109 :numberToDigits (2 1 0 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2109 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2109 1000) math:remainder 109}] + [ a r:Fact; r:gives {(109 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(109 100) math:remainder 9}] + [ a r:Fact; r:gives {(9 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(9 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2109]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 109]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4219 a r:Inference; + r:gives { + 2110 :numberToDigits (2 1 1 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2110 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2110 1000) math:remainder 110}] + [ a r:Fact; r:gives {(110 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(110 100) math:remainder 10}] + [ a r:Fact; r:gives {(10 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(10 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2110]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 110]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4220 a r:Inference; + r:gives { + 2111 :numberToDigits (2 1 1 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2111 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2111 1000) math:remainder 111}] + [ a r:Fact; r:gives {(111 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(111 100) math:remainder 11}] + [ a r:Fact; r:gives {(11 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(11 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2111]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 111]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 11]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4221 a r:Inference; + r:gives { + (1 1 1 2) :digitsToNumber 1112 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(1 100) math:product 100}] + [ a r:Fact; r:gives {(1 10) math:product 10}] + [ a r:Fact; r:gives {(1000 100 10 2) math:sum 1112}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1112]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4222 a r:Inference; + r:gives { + (2 1 1 1) :digitsToNumber 2111 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(1 100) math:product 100}] + [ a r:Fact; r:gives {(1 10) math:product 10}] + [ a r:Fact; r:gives {(2000 100 10 1) math:sum 2111}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2111]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4223 a r:Inference; + r:gives { + 2112 :numberToDigits (2 1 1 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2112 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2112 1000) math:remainder 112}] + [ a r:Fact; r:gives {(112 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(112 100) math:remainder 12}] + [ a r:Fact; r:gives {(12 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(12 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2112]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 112]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4224 a r:Inference; + r:gives { + (1 1 2 2) :digitsToNumber 1122 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(1 100) math:product 100}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(1000 100 20 2) math:sum 1122}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1122]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4225 a r:Inference; + r:gives { + (2 2 1 1) :digitsToNumber 2211 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(1 10) math:product 10}] + [ a r:Fact; r:gives {(2000 200 10 1) math:sum 2211}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4226 a r:Inference; + r:gives { + 2113 :numberToDigits (2 1 1 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2113 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2113 1000) math:remainder 113}] + [ a r:Fact; r:gives {(113 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(113 100) math:remainder 13}] + [ a r:Fact; r:gives {(13 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(13 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2113]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 113]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 13]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4227 a r:Inference; + r:gives { + (1 1 2 3) :digitsToNumber 1123 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(1 100) math:product 100}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(1000 100 20 3) math:sum 1123}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. + +skolem:lemma4228 a r:Inference; + r:gives { + (3 2 1 1) :digitsToNumber 3211 . + }; + r:evidence ( + [ a r:Fact; r:gives {(3 1000) math:product 3000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(1 10) math:product 10}] + [ a r:Fact; r:gives {(3000 200 10 1) math:sum 3211}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4229 a r:Inference; + r:gives { + 2114 :numberToDigits (2 1 1 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2114 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2114 1000) math:remainder 114}] + [ a r:Fact; r:gives {(114 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(114 100) math:remainder 14}] + [ a r:Fact; r:gives {(14 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(14 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2114]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 114]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 14]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4230 a r:Inference; + r:gives { + (1 1 2 4) :digitsToNumber 1124 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(1 100) math:product 100}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(1000 100 20 4) math:sum 1124}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6764. + +skolem:lemma4231 a r:Inference; + r:gives { + (4 2 1 1) :digitsToNumber 4211 . + }; + r:evidence ( + [ a r:Fact; r:gives {(4 1000) math:product 4000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(1 10) math:product 10}] + [ a r:Fact; r:gives {(4000 200 10 1) math:sum 4211}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4232 a r:Inference; + r:gives { + 2115 :numberToDigits (2 1 1 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2115 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2115 1000) math:remainder 115}] + [ a r:Fact; r:gives {(115 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(115 100) math:remainder 15}] + [ a r:Fact; r:gives {(15 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(15 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2115]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 115]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 15]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4233 a r:Inference; + r:gives { + (1 1 2 5) :digitsToNumber 1125 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(1 100) math:product 100}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(1000 100 20 5) math:sum 1125}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6764. + +skolem:lemma4234 a r:Inference; + r:gives { + (5 2 1 1) :digitsToNumber 5211 . + }; + r:evidence ( + [ a r:Fact; r:gives {(5 1000) math:product 5000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(1 10) math:product 10}] + [ a r:Fact; r:gives {(5000 200 10 1) math:sum 5211}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4235 a r:Inference; + r:gives { + 2116 :numberToDigits (2 1 1 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2116 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2116 1000) math:remainder 116}] + [ a r:Fact; r:gives {(116 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(116 100) math:remainder 16}] + [ a r:Fact; r:gives {(16 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(16 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2116]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 116]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 16]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4236 a r:Inference; + r:gives { + (1 1 2 6) :digitsToNumber 1126 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(1 100) math:product 100}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(1000 100 20 6) math:sum 1126}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4237 a r:Inference; + r:gives { + (6 2 1 1) :digitsToNumber 6211 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(1 10) math:product 10}] + [ a r:Fact; r:gives {(6000 200 10 1) math:sum 6211}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4238 a r:Inference; + r:gives { + 2117 :numberToDigits (2 1 1 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2117 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2117 1000) math:remainder 117}] + [ a r:Fact; r:gives {(117 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(117 100) math:remainder 17}] + [ a r:Fact; r:gives {(17 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(17 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2117]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 117]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 17]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4239 a r:Inference; + r:gives { + (1 1 2 7) :digitsToNumber 1127 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(1 100) math:product 100}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(1000 100 20 7) math:sum 1127}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4240 a r:Inference; + r:gives { + (7 2 1 1) :digitsToNumber 7211 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(1 10) math:product 10}] + [ a r:Fact; r:gives {(7000 200 10 1) math:sum 7211}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4241 a r:Inference; + r:gives { + 2118 :numberToDigits (2 1 1 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2118 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2118 1000) math:remainder 118}] + [ a r:Fact; r:gives {(118 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(118 100) math:remainder 18}] + [ a r:Fact; r:gives {(18 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(18 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2118]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 118]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 18]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4242 a r:Inference; + r:gives { + (1 1 2 8) :digitsToNumber 1128 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(1 100) math:product 100}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(1000 100 20 8) math:sum 1128}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4243 a r:Inference; + r:gives { + (8 2 1 1) :digitsToNumber 8211 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(1 10) math:product 10}] + [ a r:Fact; r:gives {(8000 200 10 1) math:sum 8211}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4244 a r:Inference; + r:gives { + 2119 :numberToDigits (2 1 1 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2119 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2119 1000) math:remainder 119}] + [ a r:Fact; r:gives {(119 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(119 100) math:remainder 19}] + [ a r:Fact; r:gives {(19 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(19 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2119]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 119]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 19]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4245 a r:Inference; + r:gives { + (1 1 2 9) :digitsToNumber 1129 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(1 100) math:product 100}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(1000 100 20 9) math:sum 1129}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4246 a r:Inference; + r:gives { + (9 2 1 1) :digitsToNumber 9211 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(1 10) math:product 10}] + [ a r:Fact; r:gives {(9000 200 10 1) math:sum 9211}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4247 a r:Inference; + r:gives { + 2120 :numberToDigits (2 1 2 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2120 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2120 1000) math:remainder 120}] + [ a r:Fact; r:gives {(120 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(120 100) math:remainder 20}] + [ a r:Fact; r:gives {(20 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(20 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2120]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 120]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4248 a r:Inference; + r:gives { + 2121 :numberToDigits (2 1 2 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2121 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2121 1000) math:remainder 121}] + [ a r:Fact; r:gives {(121 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(121 100) math:remainder 21}] + [ a r:Fact; r:gives {(21 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(21 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2121]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 121]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 21]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4249 a r:Inference; + r:gives { + 2122 :numberToDigits (2 1 2 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2122 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2122 1000) math:remainder 122}] + [ a r:Fact; r:gives {(122 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(122 100) math:remainder 22}] + [ a r:Fact; r:gives {(22 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(22 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2122]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 122]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4250 a r:Inference; + r:gives { + (1 2 2 2) :digitsToNumber 1222 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(1000 200 20 2) math:sum 1222}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4251 a r:Inference; + r:gives { + (2 2 2 1) :digitsToNumber 2221 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(2000 200 20 1) math:sum 2221}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4252 a r:Inference; + r:gives { + 2123 :numberToDigits (2 1 2 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2123 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2123 1000) math:remainder 123}] + [ a r:Fact; r:gives {(123 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(123 100) math:remainder 23}] + [ a r:Fact; r:gives {(23 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(23 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4253 a r:Inference; + r:gives { + (1 2 2 3) :digitsToNumber 1223 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(1000 200 20 3) math:sum 1223}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. + +skolem:lemma4254 a r:Inference; + r:gives { + (3 2 2 1) :digitsToNumber 3221 . + }; + r:evidence ( + [ a r:Fact; r:gives {(3 1000) math:product 3000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(3000 200 20 1) math:sum 3221}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4255 a r:Inference; + r:gives { + 2124 :numberToDigits (2 1 2 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2124 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2124 1000) math:remainder 124}] + [ a r:Fact; r:gives {(124 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(124 100) math:remainder 24}] + [ a r:Fact; r:gives {(24 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(24 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4256 a r:Inference; + r:gives { + (1 2 2 4) :digitsToNumber 1224 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(1000 200 20 4) math:sum 1224}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6764. + +skolem:lemma4257 a r:Inference; + r:gives { + (4 2 2 1) :digitsToNumber 4221 . + }; + r:evidence ( + [ a r:Fact; r:gives {(4 1000) math:product 4000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(4000 200 20 1) math:sum 4221}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4258 a r:Inference; + r:gives { + 2125 :numberToDigits (2 1 2 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2125 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2125 1000) math:remainder 125}] + [ a r:Fact; r:gives {(125 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(125 100) math:remainder 25}] + [ a r:Fact; r:gives {(25 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(25 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4259 a r:Inference; + r:gives { + (1 2 2 5) :digitsToNumber 1225 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(1000 200 20 5) math:sum 1225}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6764. + +skolem:lemma4260 a r:Inference; + r:gives { + (5 2 2 1) :digitsToNumber 5221 . + }; + r:evidence ( + [ a r:Fact; r:gives {(5 1000) math:product 5000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(5000 200 20 1) math:sum 5221}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4261 a r:Inference; + r:gives { + 2126 :numberToDigits (2 1 2 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2126 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2126 1000) math:remainder 126}] + [ a r:Fact; r:gives {(126 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(126 100) math:remainder 26}] + [ a r:Fact; r:gives {(26 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(26 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4262 a r:Inference; + r:gives { + (1 2 2 6) :digitsToNumber 1226 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(1000 200 20 6) math:sum 1226}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4263 a r:Inference; + r:gives { + (6 2 2 1) :digitsToNumber 6221 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(6000 200 20 1) math:sum 6221}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4264 a r:Inference; + r:gives { + 2127 :numberToDigits (2 1 2 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2127 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2127 1000) math:remainder 127}] + [ a r:Fact; r:gives {(127 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(127 100) math:remainder 27}] + [ a r:Fact; r:gives {(27 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(27 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4265 a r:Inference; + r:gives { + (1 2 2 7) :digitsToNumber 1227 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(1000 200 20 7) math:sum 1227}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4266 a r:Inference; + r:gives { + (7 2 2 1) :digitsToNumber 7221 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(7000 200 20 1) math:sum 7221}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4267 a r:Inference; + r:gives { + 2128 :numberToDigits (2 1 2 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2128 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2128 1000) math:remainder 128}] + [ a r:Fact; r:gives {(128 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(128 100) math:remainder 28}] + [ a r:Fact; r:gives {(28 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(28 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4268 a r:Inference; + r:gives { + (1 2 2 8) :digitsToNumber 1228 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(1000 200 20 8) math:sum 1228}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4269 a r:Inference; + r:gives { + (8 2 2 1) :digitsToNumber 8221 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(8000 200 20 1) math:sum 8221}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4270 a r:Inference; + r:gives { + 2129 :numberToDigits (2 1 2 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2129 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2129 1000) math:remainder 129}] + [ a r:Fact; r:gives {(129 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(129 100) math:remainder 29}] + [ a r:Fact; r:gives {(29 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(29 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4271 a r:Inference; + r:gives { + (1 2 2 9) :digitsToNumber 1229 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(1000 200 20 9) math:sum 1229}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4272 a r:Inference; + r:gives { + (9 2 2 1) :digitsToNumber 9221 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 200 20 1) math:sum 9221}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4273 a r:Inference; + r:gives { + 2130 :numberToDigits (2 1 3 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2130 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2130 1000) math:remainder 130}] + [ a r:Fact; r:gives {(130 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(130 100) math:remainder 30}] + [ a r:Fact; r:gives {(30 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(30 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2130]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 130]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4274 a r:Inference; + r:gives { + 2131 :numberToDigits (2 1 3 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2131 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2131 1000) math:remainder 131}] + [ a r:Fact; r:gives {(131 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(131 100) math:remainder 31}] + [ a r:Fact; r:gives {(31 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(31 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2131]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 131]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 31]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4275 a r:Inference; + r:gives { + 2132 :numberToDigits (2 1 3 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2132 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2132 1000) math:remainder 132}] + [ a r:Fact; r:gives {(132 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(132 100) math:remainder 32}] + [ a r:Fact; r:gives {(32 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(32 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2132]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 132]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 32]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4276 a r:Inference; + r:gives { + 2133 :numberToDigits (2 1 3 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2133 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2133 1000) math:remainder 133}] + [ a r:Fact; r:gives {(133 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(133 100) math:remainder 33}] + [ a r:Fact; r:gives {(33 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(33 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2133]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 133]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 33]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4277 a r:Inference; + r:gives { + (1 2 3 3) :digitsToNumber 1233 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(1000 200 30 3) math:sum 1233}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. + +skolem:lemma4278 a r:Inference; + r:gives { + (3 3 2 1) :digitsToNumber 3321 . + }; + r:evidence ( + [ a r:Fact; r:gives {(3 1000) math:product 3000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(3000 300 20 1) math:sum 3321}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4279 a r:Inference; + r:gives { + 2134 :numberToDigits (2 1 3 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2134 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2134 1000) math:remainder 134}] + [ a r:Fact; r:gives {(134 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(134 100) math:remainder 34}] + [ a r:Fact; r:gives {(34 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(34 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2134]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 134]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 34]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4280 a r:Inference; + r:gives { + (1 2 3 4) :digitsToNumber 1234 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(1000 200 30 4) math:sum 1234}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6764. + +skolem:lemma4281 a r:Inference; + r:gives { + (4 3 2 1) :digitsToNumber 4321 . + }; + r:evidence ( + [ a r:Fact; r:gives {(4 1000) math:product 4000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(4000 300 20 1) math:sum 4321}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4282 a r:Inference; + r:gives { + 2135 :numberToDigits (2 1 3 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2135 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2135 1000) math:remainder 135}] + [ a r:Fact; r:gives {(135 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(135 100) math:remainder 35}] + [ a r:Fact; r:gives {(35 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(35 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2135]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 135]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 35]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4283 a r:Inference; + r:gives { + (1 2 3 5) :digitsToNumber 1235 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(1000 200 30 5) math:sum 1235}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6764. + +skolem:lemma4284 a r:Inference; + r:gives { + (5 3 2 1) :digitsToNumber 5321 . + }; + r:evidence ( + [ a r:Fact; r:gives {(5 1000) math:product 5000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(5000 300 20 1) math:sum 5321}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4285 a r:Inference; + r:gives { + 2136 :numberToDigits (2 1 3 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2136 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2136 1000) math:remainder 136}] + [ a r:Fact; r:gives {(136 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(136 100) math:remainder 36}] + [ a r:Fact; r:gives {(36 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(36 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2136]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 136]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 36]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4286 a r:Inference; + r:gives { + (1 2 3 6) :digitsToNumber 1236 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(1000 200 30 6) math:sum 1236}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4287 a r:Inference; + r:gives { + (6 3 2 1) :digitsToNumber 6321 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(6000 300 20 1) math:sum 6321}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4288 a r:Inference; + r:gives { + 2137 :numberToDigits (2 1 3 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2137 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2137 1000) math:remainder 137}] + [ a r:Fact; r:gives {(137 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(137 100) math:remainder 37}] + [ a r:Fact; r:gives {(37 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(37 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2137]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 137]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 37]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4289 a r:Inference; + r:gives { + (1 2 3 7) :digitsToNumber 1237 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(1000 200 30 7) math:sum 1237}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4290 a r:Inference; + r:gives { + (7 3 2 1) :digitsToNumber 7321 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(7000 300 20 1) math:sum 7321}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4291 a r:Inference; + r:gives { + 2138 :numberToDigits (2 1 3 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2138 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2138 1000) math:remainder 138}] + [ a r:Fact; r:gives {(138 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(138 100) math:remainder 38}] + [ a r:Fact; r:gives {(38 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(38 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2138]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 138]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 38]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4292 a r:Inference; + r:gives { + (1 2 3 8) :digitsToNumber 1238 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(1000 200 30 8) math:sum 1238}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4293 a r:Inference; + r:gives { + (8 3 2 1) :digitsToNumber 8321 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(8000 300 20 1) math:sum 8321}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4294 a r:Inference; + r:gives { + 2139 :numberToDigits (2 1 3 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2139 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2139 1000) math:remainder 139}] + [ a r:Fact; r:gives {(139 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(139 100) math:remainder 39}] + [ a r:Fact; r:gives {(39 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(39 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2139]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 139]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 39]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4295 a r:Inference; + r:gives { + (1 2 3 9) :digitsToNumber 1239 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(1000 200 30 9) math:sum 1239}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4296 a r:Inference; + r:gives { + (9 3 2 1) :digitsToNumber 9321 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 300 20 1) math:sum 9321}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4297 a r:Inference; + r:gives { + 2140 :numberToDigits (2 1 4 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2140 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2140 1000) math:remainder 140}] + [ a r:Fact; r:gives {(140 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(140 100) math:remainder 40}] + [ a r:Fact; r:gives {(40 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(40 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2140]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 140]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4298 a r:Inference; + r:gives { + 2141 :numberToDigits (2 1 4 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2141 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2141 1000) math:remainder 141}] + [ a r:Fact; r:gives {(141 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(141 100) math:remainder 41}] + [ a r:Fact; r:gives {(41 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(41 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2141]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 141]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 41]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4299 a r:Inference; + r:gives { + 2142 :numberToDigits (2 1 4 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2142 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2142 1000) math:remainder 142}] + [ a r:Fact; r:gives {(142 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(142 100) math:remainder 42}] + [ a r:Fact; r:gives {(42 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(42 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2142]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 142]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 42]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4300 a r:Inference; + r:gives { + 2143 :numberToDigits (2 1 4 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2143 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2143 1000) math:remainder 143}] + [ a r:Fact; r:gives {(143 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(143 100) math:remainder 43}] + [ a r:Fact; r:gives {(43 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(43 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2143]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 143]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 43]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4301 a r:Inference; + r:gives { + 2144 :numberToDigits (2 1 4 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2144 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2144 1000) math:remainder 144}] + [ a r:Fact; r:gives {(144 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(144 100) math:remainder 44}] + [ a r:Fact; r:gives {(44 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(44 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2144]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 144]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 44]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4302 a r:Inference; + r:gives { + (1 2 4 4) :digitsToNumber 1244 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(1000 200 40 4) math:sum 1244}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6764. + +skolem:lemma4303 a r:Inference; + r:gives { + (4 4 2 1) :digitsToNumber 4421 . + }; + r:evidence ( + [ a r:Fact; r:gives {(4 1000) math:product 4000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(4000 400 20 1) math:sum 4421}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4304 a r:Inference; + r:gives { + 2145 :numberToDigits (2 1 4 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2145 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2145 1000) math:remainder 145}] + [ a r:Fact; r:gives {(145 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(145 100) math:remainder 45}] + [ a r:Fact; r:gives {(45 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(45 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2145]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 145]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 45]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4305 a r:Inference; + r:gives { + (1 2 4 5) :digitsToNumber 1245 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(1000 200 40 5) math:sum 1245}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6764. + +skolem:lemma4306 a r:Inference; + r:gives { + (5 4 2 1) :digitsToNumber 5421 . + }; + r:evidence ( + [ a r:Fact; r:gives {(5 1000) math:product 5000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(5000 400 20 1) math:sum 5421}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4307 a r:Inference; + r:gives { + 2146 :numberToDigits (2 1 4 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2146 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2146 1000) math:remainder 146}] + [ a r:Fact; r:gives {(146 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(146 100) math:remainder 46}] + [ a r:Fact; r:gives {(46 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(46 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2146]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 146]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 46]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4308 a r:Inference; + r:gives { + (1 2 4 6) :digitsToNumber 1246 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(1000 200 40 6) math:sum 1246}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4309 a r:Inference; + r:gives { + (6 4 2 1) :digitsToNumber 6421 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(6000 400 20 1) math:sum 6421}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4310 a r:Inference; + r:gives { + 2147 :numberToDigits (2 1 4 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2147 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2147 1000) math:remainder 147}] + [ a r:Fact; r:gives {(147 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(147 100) math:remainder 47}] + [ a r:Fact; r:gives {(47 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(47 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2147]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 147]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 47]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4311 a r:Inference; + r:gives { + (1 2 4 7) :digitsToNumber 1247 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(1000 200 40 7) math:sum 1247}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4312 a r:Inference; + r:gives { + (7 4 2 1) :digitsToNumber 7421 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(7000 400 20 1) math:sum 7421}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4313 a r:Inference; + r:gives { + 2148 :numberToDigits (2 1 4 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2148 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2148 1000) math:remainder 148}] + [ a r:Fact; r:gives {(148 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(148 100) math:remainder 48}] + [ a r:Fact; r:gives {(48 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(48 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2148]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 148]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 48]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4314 a r:Inference; + r:gives { + (1 2 4 8) :digitsToNumber 1248 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(1000 200 40 8) math:sum 1248}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4315 a r:Inference; + r:gives { + (8 4 2 1) :digitsToNumber 8421 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(8000 400 20 1) math:sum 8421}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4316 a r:Inference; + r:gives { + 2149 :numberToDigits (2 1 4 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2149 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2149 1000) math:remainder 149}] + [ a r:Fact; r:gives {(149 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(149 100) math:remainder 49}] + [ a r:Fact; r:gives {(49 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(49 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2149]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 149]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 49]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4317 a r:Inference; + r:gives { + (1 2 4 9) :digitsToNumber 1249 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(1000 200 40 9) math:sum 1249}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4318 a r:Inference; + r:gives { + (9 4 2 1) :digitsToNumber 9421 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 400 20 1) math:sum 9421}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4319 a r:Inference; + r:gives { + 2150 :numberToDigits (2 1 5 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2150 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2150 1000) math:remainder 150}] + [ a r:Fact; r:gives {(150 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(150 100) math:remainder 50}] + [ a r:Fact; r:gives {(50 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(50 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2150]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 150]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4320 a r:Inference; + r:gives { + 2151 :numberToDigits (2 1 5 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2151 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2151 1000) math:remainder 151}] + [ a r:Fact; r:gives {(151 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(151 100) math:remainder 51}] + [ a r:Fact; r:gives {(51 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(51 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2151]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 151]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 51]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4321 a r:Inference; + r:gives { + 2152 :numberToDigits (2 1 5 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2152 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2152 1000) math:remainder 152}] + [ a r:Fact; r:gives {(152 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(152 100) math:remainder 52}] + [ a r:Fact; r:gives {(52 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(52 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2152]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 152]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 52]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4322 a r:Inference; + r:gives { + 2153 :numberToDigits (2 1 5 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2153 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2153 1000) math:remainder 153}] + [ a r:Fact; r:gives {(153 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(153 100) math:remainder 53}] + [ a r:Fact; r:gives {(53 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(53 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2153]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 153]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 53]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4323 a r:Inference; + r:gives { + 2154 :numberToDigits (2 1 5 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2154 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2154 1000) math:remainder 154}] + [ a r:Fact; r:gives {(154 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(154 100) math:remainder 54}] + [ a r:Fact; r:gives {(54 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(54 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2154]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 154]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 54]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4324 a r:Inference; + r:gives { + 2155 :numberToDigits (2 1 5 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2155 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2155 1000) math:remainder 155}] + [ a r:Fact; r:gives {(155 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(155 100) math:remainder 55}] + [ a r:Fact; r:gives {(55 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(55 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2155]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 155]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 55]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4325 a r:Inference; + r:gives { + (1 2 5 5) :digitsToNumber 1255 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(1000 200 50 5) math:sum 1255}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6764. + +skolem:lemma4326 a r:Inference; + r:gives { + (5 5 2 1) :digitsToNumber 5521 . + }; + r:evidence ( + [ a r:Fact; r:gives {(5 1000) math:product 5000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(5000 500 20 1) math:sum 5521}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4327 a r:Inference; + r:gives { + 2156 :numberToDigits (2 1 5 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2156 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2156 1000) math:remainder 156}] + [ a r:Fact; r:gives {(156 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(156 100) math:remainder 56}] + [ a r:Fact; r:gives {(56 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(56 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2156]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 156]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 56]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4328 a r:Inference; + r:gives { + (1 2 5 6) :digitsToNumber 1256 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(1000 200 50 6) math:sum 1256}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4329 a r:Inference; + r:gives { + (6 5 2 1) :digitsToNumber 6521 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(6000 500 20 1) math:sum 6521}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4330 a r:Inference; + r:gives { + 2157 :numberToDigits (2 1 5 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2157 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2157 1000) math:remainder 157}] + [ a r:Fact; r:gives {(157 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(157 100) math:remainder 57}] + [ a r:Fact; r:gives {(57 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(57 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2157]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 157]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 57]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4331 a r:Inference; + r:gives { + (1 2 5 7) :digitsToNumber 1257 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(1000 200 50 7) math:sum 1257}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4332 a r:Inference; + r:gives { + (7 5 2 1) :digitsToNumber 7521 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(7000 500 20 1) math:sum 7521}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4333 a r:Inference; + r:gives { + 2158 :numberToDigits (2 1 5 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2158 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2158 1000) math:remainder 158}] + [ a r:Fact; r:gives {(158 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(158 100) math:remainder 58}] + [ a r:Fact; r:gives {(58 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(58 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2158]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 158]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 58]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4334 a r:Inference; + r:gives { + (1 2 5 8) :digitsToNumber 1258 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(1000 200 50 8) math:sum 1258}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4335 a r:Inference; + r:gives { + (8 5 2 1) :digitsToNumber 8521 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(8000 500 20 1) math:sum 8521}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4336 a r:Inference; + r:gives { + 2159 :numberToDigits (2 1 5 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2159 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2159 1000) math:remainder 159}] + [ a r:Fact; r:gives {(159 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(159 100) math:remainder 59}] + [ a r:Fact; r:gives {(59 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(59 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2159]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 159]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 59]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4337 a r:Inference; + r:gives { + (1 2 5 9) :digitsToNumber 1259 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(1000 200 50 9) math:sum 1259}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4338 a r:Inference; + r:gives { + (9 5 2 1) :digitsToNumber 9521 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 500 20 1) math:sum 9521}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4339 a r:Inference; + r:gives { + 2160 :numberToDigits (2 1 6 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2160 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2160 1000) math:remainder 160}] + [ a r:Fact; r:gives {(160 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(160 100) math:remainder 60}] + [ a r:Fact; r:gives {(60 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(60 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2160]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 160]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4340 a r:Inference; + r:gives { + 2161 :numberToDigits (2 1 6 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2161 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2161 1000) math:remainder 161}] + [ a r:Fact; r:gives {(161 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(161 100) math:remainder 61}] + [ a r:Fact; r:gives {(61 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(61 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2161]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 161]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 61]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4341 a r:Inference; + r:gives { + 2162 :numberToDigits (2 1 6 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2162 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2162 1000) math:remainder 162}] + [ a r:Fact; r:gives {(162 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(162 100) math:remainder 62}] + [ a r:Fact; r:gives {(62 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(62 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2162]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 162]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 62]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4342 a r:Inference; + r:gives { + 2163 :numberToDigits (2 1 6 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2163 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2163 1000) math:remainder 163}] + [ a r:Fact; r:gives {(163 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(163 100) math:remainder 63}] + [ a r:Fact; r:gives {(63 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(63 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2163]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 163]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 63]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4343 a r:Inference; + r:gives { + 2164 :numberToDigits (2 1 6 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2164 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2164 1000) math:remainder 164}] + [ a r:Fact; r:gives {(164 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(164 100) math:remainder 64}] + [ a r:Fact; r:gives {(64 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(64 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2164]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 164]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 64]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4344 a r:Inference; + r:gives { + 2165 :numberToDigits (2 1 6 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2165 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2165 1000) math:remainder 165}] + [ a r:Fact; r:gives {(165 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(165 100) math:remainder 65}] + [ a r:Fact; r:gives {(65 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(65 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2165]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 165]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 65]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4345 a r:Inference; + r:gives { + 2166 :numberToDigits (2 1 6 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2166 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2166 1000) math:remainder 166}] + [ a r:Fact; r:gives {(166 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(166 100) math:remainder 66}] + [ a r:Fact; r:gives {(66 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(66 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2166]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 166]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 66]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4346 a r:Inference; + r:gives { + (1 2 6 6) :digitsToNumber 1266 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(1000 200 60 6) math:sum 1266}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4347 a r:Inference; + r:gives { + (6 6 2 1) :digitsToNumber 6621 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(6000 600 20 1) math:sum 6621}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4348 a r:Inference; + r:gives { + 2167 :numberToDigits (2 1 6 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2167 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2167 1000) math:remainder 167}] + [ a r:Fact; r:gives {(167 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(167 100) math:remainder 67}] + [ a r:Fact; r:gives {(67 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(67 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2167]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 167]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 67]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4349 a r:Inference; + r:gives { + (1 2 6 7) :digitsToNumber 1267 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(1000 200 60 7) math:sum 1267}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4350 a r:Inference; + r:gives { + (7 6 2 1) :digitsToNumber 7621 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(7000 600 20 1) math:sum 7621}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4351 a r:Inference; + r:gives { + 2168 :numberToDigits (2 1 6 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2168 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2168 1000) math:remainder 168}] + [ a r:Fact; r:gives {(168 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(168 100) math:remainder 68}] + [ a r:Fact; r:gives {(68 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(68 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2168]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 168]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 68]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4352 a r:Inference; + r:gives { + (1 2 6 8) :digitsToNumber 1268 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(1000 200 60 8) math:sum 1268}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4353 a r:Inference; + r:gives { + (8 6 2 1) :digitsToNumber 8621 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(8000 600 20 1) math:sum 8621}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4354 a r:Inference; + r:gives { + 2169 :numberToDigits (2 1 6 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2169 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2169 1000) math:remainder 169}] + [ a r:Fact; r:gives {(169 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(169 100) math:remainder 69}] + [ a r:Fact; r:gives {(69 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(69 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2169]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 169]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 69]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4355 a r:Inference; + r:gives { + (1 2 6 9) :digitsToNumber 1269 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(1000 200 60 9) math:sum 1269}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4356 a r:Inference; + r:gives { + (9 6 2 1) :digitsToNumber 9621 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 600 20 1) math:sum 9621}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4357 a r:Inference; + r:gives { + 2170 :numberToDigits (2 1 7 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2170 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2170 1000) math:remainder 170}] + [ a r:Fact; r:gives {(170 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(170 100) math:remainder 70}] + [ a r:Fact; r:gives {(70 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(70 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2170]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 170]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4358 a r:Inference; + r:gives { + 2171 :numberToDigits (2 1 7 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2171 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2171 1000) math:remainder 171}] + [ a r:Fact; r:gives {(171 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(171 100) math:remainder 71}] + [ a r:Fact; r:gives {(71 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(71 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 71]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4359 a r:Inference; + r:gives { + 2172 :numberToDigits (2 1 7 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2172 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2172 1000) math:remainder 172}] + [ a r:Fact; r:gives {(172 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(172 100) math:remainder 72}] + [ a r:Fact; r:gives {(72 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(72 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 72]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4360 a r:Inference; + r:gives { + 2173 :numberToDigits (2 1 7 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2173 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2173 1000) math:remainder 173}] + [ a r:Fact; r:gives {(173 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(173 100) math:remainder 73}] + [ a r:Fact; r:gives {(73 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(73 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 73]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4361 a r:Inference; + r:gives { + 2174 :numberToDigits (2 1 7 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2174 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2174 1000) math:remainder 174}] + [ a r:Fact; r:gives {(174 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(174 100) math:remainder 74}] + [ a r:Fact; r:gives {(74 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(74 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 74]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4362 a r:Inference; + r:gives { + 2175 :numberToDigits (2 1 7 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2175 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2175 1000) math:remainder 175}] + [ a r:Fact; r:gives {(175 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(175 100) math:remainder 75}] + [ a r:Fact; r:gives {(75 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(75 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 75]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4363 a r:Inference; + r:gives { + 2176 :numberToDigits (2 1 7 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2176 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2176 1000) math:remainder 176}] + [ a r:Fact; r:gives {(176 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(176 100) math:remainder 76}] + [ a r:Fact; r:gives {(76 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(76 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 76]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4364 a r:Inference; + r:gives { + 2177 :numberToDigits (2 1 7 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2177 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2177 1000) math:remainder 177}] + [ a r:Fact; r:gives {(177 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(177 100) math:remainder 77}] + [ a r:Fact; r:gives {(77 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(77 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 77]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4365 a r:Inference; + r:gives { + (1 2 7 7) :digitsToNumber 1277 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(1000 200 70 7) math:sum 1277}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1277]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4366 a r:Inference; + r:gives { + (7 7 2 1) :digitsToNumber 7721 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(7000 700 20 1) math:sum 7721}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4367 a r:Inference; + r:gives { + 2178 :numberToDigits (2 1 7 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2178 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2178 1000) math:remainder 178}] + [ a r:Fact; r:gives {(178 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(178 100) math:remainder 78}] + [ a r:Fact; r:gives {(78 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(78 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2178]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 178]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 78]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4368 a r:Inference; + r:gives { + (1 2 7 8) :digitsToNumber 1278 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(1000 200 70 8) math:sum 1278}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4369 a r:Inference; + r:gives { + (8 7 2 1) :digitsToNumber 8721 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(8000 700 20 1) math:sum 8721}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4370 a r:Inference; + r:gives { + 2179 :numberToDigits (2 1 7 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2179 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2179 1000) math:remainder 179}] + [ a r:Fact; r:gives {(179 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(179 100) math:remainder 79}] + [ a r:Fact; r:gives {(79 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(79 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2179]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 179]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 79]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4371 a r:Inference; + r:gives { + (1 2 7 9) :digitsToNumber 1279 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(1000 200 70 9) math:sum 1279}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4372 a r:Inference; + r:gives { + (9 7 2 1) :digitsToNumber 9721 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 700 20 1) math:sum 9721}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4373 a r:Inference; + r:gives { + 2180 :numberToDigits (2 1 8 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2180 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2180 1000) math:remainder 180}] + [ a r:Fact; r:gives {(180 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(180 100) math:remainder 80}] + [ a r:Fact; r:gives {(80 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(80 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2180]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 180]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4374 a r:Inference; + r:gives { + 2181 :numberToDigits (2 1 8 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2181 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2181 1000) math:remainder 181}] + [ a r:Fact; r:gives {(181 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(181 100) math:remainder 81}] + [ a r:Fact; r:gives {(81 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(81 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2181]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 181]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 81]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4375 a r:Inference; + r:gives { + 2182 :numberToDigits (2 1 8 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2182 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2182 1000) math:remainder 182}] + [ a r:Fact; r:gives {(182 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(182 100) math:remainder 82}] + [ a r:Fact; r:gives {(82 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(82 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2182]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 182]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 82]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4376 a r:Inference; + r:gives { + 2183 :numberToDigits (2 1 8 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2183 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2183 1000) math:remainder 183}] + [ a r:Fact; r:gives {(183 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(183 100) math:remainder 83}] + [ a r:Fact; r:gives {(83 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(83 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2183]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 183]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 83]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4377 a r:Inference; + r:gives { + 2184 :numberToDigits (2 1 8 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2184 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2184 1000) math:remainder 184}] + [ a r:Fact; r:gives {(184 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(184 100) math:remainder 84}] + [ a r:Fact; r:gives {(84 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(84 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2184]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 184]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 84]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4378 a r:Inference; + r:gives { + 2185 :numberToDigits (2 1 8 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2185 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2185 1000) math:remainder 185}] + [ a r:Fact; r:gives {(185 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(185 100) math:remainder 85}] + [ a r:Fact; r:gives {(85 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(85 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2185]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 185]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 85]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4379 a r:Inference; + r:gives { + 2186 :numberToDigits (2 1 8 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2186 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2186 1000) math:remainder 186}] + [ a r:Fact; r:gives {(186 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(186 100) math:remainder 86}] + [ a r:Fact; r:gives {(86 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(86 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2186]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 186]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 86]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4380 a r:Inference; + r:gives { + 2187 :numberToDigits (2 1 8 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2187 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2187 1000) math:remainder 187}] + [ a r:Fact; r:gives {(187 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(187 100) math:remainder 87}] + [ a r:Fact; r:gives {(87 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(87 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2187]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 187]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 87]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4381 a r:Inference; + r:gives { + 2188 :numberToDigits (2 1 8 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2188 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2188 1000) math:remainder 188}] + [ a r:Fact; r:gives {(188 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(188 100) math:remainder 88}] + [ a r:Fact; r:gives {(88 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(88 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2188]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 188]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 88]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4382 a r:Inference; + r:gives { + (1 2 8 8) :digitsToNumber 1288 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(8 10) math:product 80}] + [ a r:Fact; r:gives {(1000 200 80 8) math:sum 1288}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1288]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4383 a r:Inference; + r:gives { + (8 8 2 1) :digitsToNumber 8821 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(8 100) math:product 800}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(8000 800 20 1) math:sum 8821}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8821]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4384 a r:Inference; + r:gives { + 2189 :numberToDigits (2 1 8 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2189 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2189 1000) math:remainder 189}] + [ a r:Fact; r:gives {(189 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(189 100) math:remainder 89}] + [ a r:Fact; r:gives {(89 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(89 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2189]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 189]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 89]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4385 a r:Inference; + r:gives { + (1 2 8 9) :digitsToNumber 1289 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(8 10) math:product 80}] + [ a r:Fact; r:gives {(1000 200 80 9) math:sum 1289}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4386 a r:Inference; + r:gives { + (9 8 2 1) :digitsToNumber 9821 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(8 100) math:product 800}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 800 20 1) math:sum 9821}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9821]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4387 a r:Inference; + r:gives { + 2190 :numberToDigits (2 1 9 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2190 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2190 1000) math:remainder 190}] + [ a r:Fact; r:gives {(190 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(190 100) math:remainder 90}] + [ a r:Fact; r:gives {(90 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(90 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2190]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 190]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4388 a r:Inference; + r:gives { + 2191 :numberToDigits (2 1 9 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2191 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2191 1000) math:remainder 191}] + [ a r:Fact; r:gives {(191 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(191 100) math:remainder 91}] + [ a r:Fact; r:gives {(91 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(91 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2191]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 191]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 91]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4389 a r:Inference; + r:gives { + 2192 :numberToDigits (2 1 9 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2192 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2192 1000) math:remainder 192}] + [ a r:Fact; r:gives {(192 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(192 100) math:remainder 92}] + [ a r:Fact; r:gives {(92 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(92 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2192]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 192]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 92]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4390 a r:Inference; + r:gives { + 2193 :numberToDigits (2 1 9 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2193 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2193 1000) math:remainder 193}] + [ a r:Fact; r:gives {(193 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(193 100) math:remainder 93}] + [ a r:Fact; r:gives {(93 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(93 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2193]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 193]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 93]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4391 a r:Inference; + r:gives { + 2194 :numberToDigits (2 1 9 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2194 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2194 1000) math:remainder 194}] + [ a r:Fact; r:gives {(194 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(194 100) math:remainder 94}] + [ a r:Fact; r:gives {(94 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(94 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2194]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 194]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 94]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4392 a r:Inference; + r:gives { + 2195 :numberToDigits (2 1 9 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2195 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2195 1000) math:remainder 195}] + [ a r:Fact; r:gives {(195 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(195 100) math:remainder 95}] + [ a r:Fact; r:gives {(95 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(95 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2195]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 195]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 95]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4393 a r:Inference; + r:gives { + 2196 :numberToDigits (2 1 9 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2196 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2196 1000) math:remainder 196}] + [ a r:Fact; r:gives {(196 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(196 100) math:remainder 96}] + [ a r:Fact; r:gives {(96 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(96 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2196]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 196]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 96]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4394 a r:Inference; + r:gives { + 2197 :numberToDigits (2 1 9 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2197 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2197 1000) math:remainder 197}] + [ a r:Fact; r:gives {(197 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(197 100) math:remainder 97}] + [ a r:Fact; r:gives {(97 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(97 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2197]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 197]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 97]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4395 a r:Inference; + r:gives { + 2198 :numberToDigits (2 1 9 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2198 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2198 1000) math:remainder 198}] + [ a r:Fact; r:gives {(198 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(198 100) math:remainder 98}] + [ a r:Fact; r:gives {(98 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(98 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2198]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 198]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 98]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4396 a r:Inference; + r:gives { + 2199 :numberToDigits (2 1 9 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2199 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2199 1000) math:remainder 199}] + [ a r:Fact; r:gives {(199 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(199 100) math:remainder 99}] + [ a r:Fact; r:gives {(99 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(99 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2199]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 199]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 99]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4397 a r:Inference; + r:gives { + (1 2 9 9) :digitsToNumber 1299 . + }; + r:evidence ( + [ a r:Fact; r:gives {(1 1000) math:product 1000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(9 10) math:product 90}] + [ a r:Fact; r:gives {(1000 200 90 9) math:sum 1299}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4398 a r:Inference; + r:gives { + (9 9 2 1) :digitsToNumber 9921 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(9 100) math:product 900}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 900 20 1) math:sum 9921}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 900]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9921]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6764. + +skolem:lemma4399 a r:Inference; + r:gives { + 2200 :numberToDigits (2 2 0 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2200 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2200 1000) math:remainder 200}] + [ a r:Fact; r:gives {(200 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(200 100) math:remainder 0}] + [ a r:Fact; r:gives {(0 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(0 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4400 a r:Inference; + r:gives { + 2201 :numberToDigits (2 2 0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2201 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2201 1000) math:remainder 201}] + [ a r:Fact; r:gives {(201 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(201 100) math:remainder 1}] + [ a r:Fact; r:gives {(1 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(1 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2201]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 201]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4401 a r:Inference; + r:gives { + 2202 :numberToDigits (2 2 0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2202 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2202 1000) math:remainder 202}] + [ a r:Fact; r:gives {(202 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(202 100) math:remainder 2}] + [ a r:Fact; r:gives {(2 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(2 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2202]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 202]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4402 a r:Inference; + r:gives { + 2203 :numberToDigits (2 2 0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2203 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2203 1000) math:remainder 203}] + [ a r:Fact; r:gives {(203 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(203 100) math:remainder 3}] + [ a r:Fact; r:gives {(3 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(3 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2203]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 203]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4403 a r:Inference; + r:gives { + 2204 :numberToDigits (2 2 0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2204 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2204 1000) math:remainder 204}] + [ a r:Fact; r:gives {(204 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(204 100) math:remainder 4}] + [ a r:Fact; r:gives {(4 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(4 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2204]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 204]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4404 a r:Inference; + r:gives { + 2205 :numberToDigits (2 2 0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2205 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2205 1000) math:remainder 205}] + [ a r:Fact; r:gives {(205 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(205 100) math:remainder 5}] + [ a r:Fact; r:gives {(5 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(5 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2205]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 205]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4405 a r:Inference; + r:gives { + 2206 :numberToDigits (2 2 0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2206 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2206 1000) math:remainder 206}] + [ a r:Fact; r:gives {(206 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(206 100) math:remainder 6}] + [ a r:Fact; r:gives {(6 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(6 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2206]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 206]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4406 a r:Inference; + r:gives { + 2207 :numberToDigits (2 2 0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2207 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2207 1000) math:remainder 207}] + [ a r:Fact; r:gives {(207 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(207 100) math:remainder 7}] + [ a r:Fact; r:gives {(7 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(7 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2207]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 207]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4407 a r:Inference; + r:gives { + 2208 :numberToDigits (2 2 0 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2208 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2208 1000) math:remainder 208}] + [ a r:Fact; r:gives {(208 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(208 100) math:remainder 8}] + [ a r:Fact; r:gives {(8 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(8 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2208]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 208]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4408 a r:Inference; + r:gives { + 2209 :numberToDigits (2 2 0 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2209 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2209 1000) math:remainder 209}] + [ a r:Fact; r:gives {(209 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(209 100) math:remainder 9}] + [ a r:Fact; r:gives {(9 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(9 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2209]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 209]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4409 a r:Inference; + r:gives { + 2210 :numberToDigits (2 2 1 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2210 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2210 1000) math:remainder 210}] + [ a r:Fact; r:gives {(210 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(210 100) math:remainder 10}] + [ a r:Fact; r:gives {(10 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(10 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4410 a r:Inference; + r:gives { + 2211 :numberToDigits (2 2 1 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2211 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2211 1000) math:remainder 211}] + [ a r:Fact; r:gives {(211 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(211 100) math:remainder 11}] + [ a r:Fact; r:gives {(11 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(11 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 11]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4411 a r:Inference; + r:gives { + 2212 :numberToDigits (2 2 1 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2212 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2212 1000) math:remainder 212}] + [ a r:Fact; r:gives {(212 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(212 100) math:remainder 12}] + [ a r:Fact; r:gives {(12 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(12 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2212]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 212]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4412 a r:Inference; + r:gives { + 2213 :numberToDigits (2 2 1 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2213 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2213 1000) math:remainder 213}] + [ a r:Fact; r:gives {(213 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(213 100) math:remainder 13}] + [ a r:Fact; r:gives {(13 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(13 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2213]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 213]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 13]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4413 a r:Inference; + r:gives { + 2214 :numberToDigits (2 2 1 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2214 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2214 1000) math:remainder 214}] + [ a r:Fact; r:gives {(214 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(214 100) math:remainder 14}] + [ a r:Fact; r:gives {(14 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(14 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2214]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 214]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 14]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4414 a r:Inference; + r:gives { + 2215 :numberToDigits (2 2 1 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2215 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2215 1000) math:remainder 215}] + [ a r:Fact; r:gives {(215 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(215 100) math:remainder 15}] + [ a r:Fact; r:gives {(15 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(15 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2215]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 215]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 15]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4415 a r:Inference; + r:gives { + 2216 :numberToDigits (2 2 1 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2216 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2216 1000) math:remainder 216}] + [ a r:Fact; r:gives {(216 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(216 100) math:remainder 16}] + [ a r:Fact; r:gives {(16 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(16 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2216]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 216]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 16]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4416 a r:Inference; + r:gives { + 2217 :numberToDigits (2 2 1 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2217 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2217 1000) math:remainder 217}] + [ a r:Fact; r:gives {(217 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(217 100) math:remainder 17}] + [ a r:Fact; r:gives {(17 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(17 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2217]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 217]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 17]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4417 a r:Inference; + r:gives { + 2218 :numberToDigits (2 2 1 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2218 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2218 1000) math:remainder 218}] + [ a r:Fact; r:gives {(218 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(218 100) math:remainder 18}] + [ a r:Fact; r:gives {(18 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(18 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2218]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 218]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 18]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4418 a r:Inference; + r:gives { + 2219 :numberToDigits (2 2 1 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2219 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2219 1000) math:remainder 219}] + [ a r:Fact; r:gives {(219 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(219 100) math:remainder 19}] + [ a r:Fact; r:gives {(19 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(19 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2219]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 219]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 19]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4419 a r:Inference; + r:gives { + 2220 :numberToDigits (2 2 2 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2220 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2220 1000) math:remainder 220}] + [ a r:Fact; r:gives {(220 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(220 100) math:remainder 20}] + [ a r:Fact; r:gives {(20 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(20 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4420 a r:Inference; + r:gives { + 2221 :numberToDigits (2 2 2 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2221 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2221 1000) math:remainder 221}] + [ a r:Fact; r:gives {(221 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(221 100) math:remainder 21}] + [ a r:Fact; r:gives {(21 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(21 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 21]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4421 a r:Inference; + r:gives { + 2223 :numberToDigits (2 2 2 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2223 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2223 1000) math:remainder 223}] + [ a r:Fact; r:gives {(223 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(223 100) math:remainder 23}] + [ a r:Fact; r:gives {(23 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(23 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4422 a r:Inference; + r:gives { + (2 2 2 3) :digitsToNumber 2223 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(2000 200 20 3) math:sum 2223}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. + +skolem:lemma4423 a r:Inference; + r:gives { + (3 2 2 2) :digitsToNumber 3222 . + }; + r:evidence ( + [ a r:Fact; r:gives {(3 1000) math:product 3000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(3000 200 20 2) math:sum 3222}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4424 a r:Inference; + r:gives { + 2224 :numberToDigits (2 2 2 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2224 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2224 1000) math:remainder 224}] + [ a r:Fact; r:gives {(224 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(224 100) math:remainder 24}] + [ a r:Fact; r:gives {(24 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(24 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4425 a r:Inference; + r:gives { + (2 2 2 4) :digitsToNumber 2224 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(2000 200 20 4) math:sum 2224}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6764. + +skolem:lemma4426 a r:Inference; + r:gives { + (4 2 2 2) :digitsToNumber 4222 . + }; + r:evidence ( + [ a r:Fact; r:gives {(4 1000) math:product 4000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(4000 200 20 2) math:sum 4222}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4427 a r:Inference; + r:gives { + 2225 :numberToDigits (2 2 2 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2225 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2225 1000) math:remainder 225}] + [ a r:Fact; r:gives {(225 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(225 100) math:remainder 25}] + [ a r:Fact; r:gives {(25 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(25 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4428 a r:Inference; + r:gives { + (2 2 2 5) :digitsToNumber 2225 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(2000 200 20 5) math:sum 2225}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6764. + +skolem:lemma4429 a r:Inference; + r:gives { + (5 2 2 2) :digitsToNumber 5222 . + }; + r:evidence ( + [ a r:Fact; r:gives {(5 1000) math:product 5000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(5000 200 20 2) math:sum 5222}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4430 a r:Inference; + r:gives { + 2226 :numberToDigits (2 2 2 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2226 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2226 1000) math:remainder 226}] + [ a r:Fact; r:gives {(226 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(226 100) math:remainder 26}] + [ a r:Fact; r:gives {(26 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(26 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4431 a r:Inference; + r:gives { + (2 2 2 6) :digitsToNumber 2226 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(2000 200 20 6) math:sum 2226}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4432 a r:Inference; + r:gives { + (6 2 2 2) :digitsToNumber 6222 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(6000 200 20 2) math:sum 6222}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4433 a r:Inference; + r:gives { + 2227 :numberToDigits (2 2 2 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2227 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2227 1000) math:remainder 227}] + [ a r:Fact; r:gives {(227 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(227 100) math:remainder 27}] + [ a r:Fact; r:gives {(27 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(27 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4434 a r:Inference; + r:gives { + (2 2 2 7) :digitsToNumber 2227 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(2000 200 20 7) math:sum 2227}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4435 a r:Inference; + r:gives { + (7 2 2 2) :digitsToNumber 7222 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(7000 200 20 2) math:sum 7222}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4436 a r:Inference; + r:gives { + 2228 :numberToDigits (2 2 2 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2228 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2228 1000) math:remainder 228}] + [ a r:Fact; r:gives {(228 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(228 100) math:remainder 28}] + [ a r:Fact; r:gives {(28 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(28 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4437 a r:Inference; + r:gives { + (2 2 2 8) :digitsToNumber 2228 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(2000 200 20 8) math:sum 2228}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4438 a r:Inference; + r:gives { + (8 2 2 2) :digitsToNumber 8222 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(8000 200 20 2) math:sum 8222}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4439 a r:Inference; + r:gives { + 2229 :numberToDigits (2 2 2 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2229 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2229 1000) math:remainder 229}] + [ a r:Fact; r:gives {(229 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(229 100) math:remainder 29}] + [ a r:Fact; r:gives {(29 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(29 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4440 a r:Inference; + r:gives { + (2 2 2 9) :digitsToNumber 2229 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(2000 200 20 9) math:sum 2229}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4441 a r:Inference; + r:gives { + (9 2 2 2) :digitsToNumber 9222 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 200 20 2) math:sum 9222}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4442 a r:Inference; + r:gives { + 2230 :numberToDigits (2 2 3 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2230 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2230 1000) math:remainder 230}] + [ a r:Fact; r:gives {(230 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(230 100) math:remainder 30}] + [ a r:Fact; r:gives {(30 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(30 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2230]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 230]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4443 a r:Inference; + r:gives { + 2231 :numberToDigits (2 2 3 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2231 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2231 1000) math:remainder 231}] + [ a r:Fact; r:gives {(231 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(231 100) math:remainder 31}] + [ a r:Fact; r:gives {(31 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(31 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2231]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 231]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 31]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4444 a r:Inference; + r:gives { + 2232 :numberToDigits (2 2 3 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2232 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2232 1000) math:remainder 232}] + [ a r:Fact; r:gives {(232 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(232 100) math:remainder 32}] + [ a r:Fact; r:gives {(32 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(32 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2232]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 232]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 32]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4445 a r:Inference; + r:gives { + 2233 :numberToDigits (2 2 3 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2233 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2233 1000) math:remainder 233}] + [ a r:Fact; r:gives {(233 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(233 100) math:remainder 33}] + [ a r:Fact; r:gives {(33 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(33 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 33]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4446 a r:Inference; + r:gives { + (2 2 3 3) :digitsToNumber 2233 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(2000 200 30 3) math:sum 2233}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. + +skolem:lemma4447 a r:Inference; + r:gives { + (3 3 2 2) :digitsToNumber 3322 . + }; + r:evidence ( + [ a r:Fact; r:gives {(3 1000) math:product 3000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(3000 300 20 2) math:sum 3322}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4448 a r:Inference; + r:gives { + 2234 :numberToDigits (2 2 3 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2234 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2234 1000) math:remainder 234}] + [ a r:Fact; r:gives {(234 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(234 100) math:remainder 34}] + [ a r:Fact; r:gives {(34 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(34 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 34]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4449 a r:Inference; + r:gives { + (2 2 3 4) :digitsToNumber 2234 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(2000 200 30 4) math:sum 2234}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6764. + +skolem:lemma4450 a r:Inference; + r:gives { + (4 3 2 2) :digitsToNumber 4322 . + }; + r:evidence ( + [ a r:Fact; r:gives {(4 1000) math:product 4000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(4000 300 20 2) math:sum 4322}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4451 a r:Inference; + r:gives { + 2235 :numberToDigits (2 2 3 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2235 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2235 1000) math:remainder 235}] + [ a r:Fact; r:gives {(235 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(235 100) math:remainder 35}] + [ a r:Fact; r:gives {(35 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(35 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 35]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4452 a r:Inference; + r:gives { + (2 2 3 5) :digitsToNumber 2235 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(2000 200 30 5) math:sum 2235}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6764. + +skolem:lemma4453 a r:Inference; + r:gives { + (5 3 2 2) :digitsToNumber 5322 . + }; + r:evidence ( + [ a r:Fact; r:gives {(5 1000) math:product 5000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(5000 300 20 2) math:sum 5322}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4454 a r:Inference; + r:gives { + 2236 :numberToDigits (2 2 3 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2236 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2236 1000) math:remainder 236}] + [ a r:Fact; r:gives {(236 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(236 100) math:remainder 36}] + [ a r:Fact; r:gives {(36 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(36 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 36]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4455 a r:Inference; + r:gives { + (2 2 3 6) :digitsToNumber 2236 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(2000 200 30 6) math:sum 2236}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4456 a r:Inference; + r:gives { + (6 3 2 2) :digitsToNumber 6322 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(6000 300 20 2) math:sum 6322}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4457 a r:Inference; + r:gives { + 2237 :numberToDigits (2 2 3 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2237 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2237 1000) math:remainder 237}] + [ a r:Fact; r:gives {(237 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(237 100) math:remainder 37}] + [ a r:Fact; r:gives {(37 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(37 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 37]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4458 a r:Inference; + r:gives { + (2 2 3 7) :digitsToNumber 2237 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(2000 200 30 7) math:sum 2237}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4459 a r:Inference; + r:gives { + (7 3 2 2) :digitsToNumber 7322 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(7000 300 20 2) math:sum 7322}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4460 a r:Inference; + r:gives { + 2238 :numberToDigits (2 2 3 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2238 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2238 1000) math:remainder 238}] + [ a r:Fact; r:gives {(238 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(238 100) math:remainder 38}] + [ a r:Fact; r:gives {(38 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(38 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 38]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4461 a r:Inference; + r:gives { + (2 2 3 8) :digitsToNumber 2238 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(2000 200 30 8) math:sum 2238}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4462 a r:Inference; + r:gives { + (8 3 2 2) :digitsToNumber 8322 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(8000 300 20 2) math:sum 8322}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4463 a r:Inference; + r:gives { + 2239 :numberToDigits (2 2 3 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2239 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2239 1000) math:remainder 239}] + [ a r:Fact; r:gives {(239 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(239 100) math:remainder 39}] + [ a r:Fact; r:gives {(39 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(39 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 39]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4464 a r:Inference; + r:gives { + (2 2 3 9) :digitsToNumber 2239 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(2000 200 30 9) math:sum 2239}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4465 a r:Inference; + r:gives { + (9 3 2 2) :digitsToNumber 9322 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 300 20 2) math:sum 9322}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4466 a r:Inference; + r:gives { + 2240 :numberToDigits (2 2 4 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2240 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2240 1000) math:remainder 240}] + [ a r:Fact; r:gives {(240 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(240 100) math:remainder 40}] + [ a r:Fact; r:gives {(40 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(40 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2240]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 240]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4467 a r:Inference; + r:gives { + 2241 :numberToDigits (2 2 4 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2241 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2241 1000) math:remainder 241}] + [ a r:Fact; r:gives {(241 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(241 100) math:remainder 41}] + [ a r:Fact; r:gives {(41 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(41 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2241]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 241]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 41]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4468 a r:Inference; + r:gives { + 2242 :numberToDigits (2 2 4 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2242 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2242 1000) math:remainder 242}] + [ a r:Fact; r:gives {(242 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(242 100) math:remainder 42}] + [ a r:Fact; r:gives {(42 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(42 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2242]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 242]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 42]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4469 a r:Inference; + r:gives { + 2243 :numberToDigits (2 2 4 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2243 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2243 1000) math:remainder 243}] + [ a r:Fact; r:gives {(243 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(243 100) math:remainder 43}] + [ a r:Fact; r:gives {(43 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(43 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2243]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 243]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 43]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4470 a r:Inference; + r:gives { + 2244 :numberToDigits (2 2 4 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2244 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2244 1000) math:remainder 244}] + [ a r:Fact; r:gives {(244 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(244 100) math:remainder 44}] + [ a r:Fact; r:gives {(44 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(44 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 44]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4471 a r:Inference; + r:gives { + (2 2 4 4) :digitsToNumber 2244 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(2000 200 40 4) math:sum 2244}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6764. + +skolem:lemma4472 a r:Inference; + r:gives { + (4 4 2 2) :digitsToNumber 4422 . + }; + r:evidence ( + [ a r:Fact; r:gives {(4 1000) math:product 4000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(4000 400 20 2) math:sum 4422}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4473 a r:Inference; + r:gives { + 2245 :numberToDigits (2 2 4 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2245 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2245 1000) math:remainder 245}] + [ a r:Fact; r:gives {(245 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(245 100) math:remainder 45}] + [ a r:Fact; r:gives {(45 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(45 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 45]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4474 a r:Inference; + r:gives { + (2 2 4 5) :digitsToNumber 2245 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(2000 200 40 5) math:sum 2245}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6764. + +skolem:lemma4475 a r:Inference; + r:gives { + (5 4 2 2) :digitsToNumber 5422 . + }; + r:evidence ( + [ a r:Fact; r:gives {(5 1000) math:product 5000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(5000 400 20 2) math:sum 5422}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4476 a r:Inference; + r:gives { + 2246 :numberToDigits (2 2 4 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2246 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2246 1000) math:remainder 246}] + [ a r:Fact; r:gives {(246 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(246 100) math:remainder 46}] + [ a r:Fact; r:gives {(46 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(46 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 46]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4477 a r:Inference; + r:gives { + (2 2 4 6) :digitsToNumber 2246 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(2000 200 40 6) math:sum 2246}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4478 a r:Inference; + r:gives { + (6 4 2 2) :digitsToNumber 6422 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(6000 400 20 2) math:sum 6422}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4479 a r:Inference; + r:gives { + 2247 :numberToDigits (2 2 4 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2247 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2247 1000) math:remainder 247}] + [ a r:Fact; r:gives {(247 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(247 100) math:remainder 47}] + [ a r:Fact; r:gives {(47 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(47 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 47]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4480 a r:Inference; + r:gives { + (2 2 4 7) :digitsToNumber 2247 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(2000 200 40 7) math:sum 2247}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4481 a r:Inference; + r:gives { + (7 4 2 2) :digitsToNumber 7422 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(7000 400 20 2) math:sum 7422}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4482 a r:Inference; + r:gives { + 2248 :numberToDigits (2 2 4 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2248 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2248 1000) math:remainder 248}] + [ a r:Fact; r:gives {(248 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(248 100) math:remainder 48}] + [ a r:Fact; r:gives {(48 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(48 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 48]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4483 a r:Inference; + r:gives { + (2 2 4 8) :digitsToNumber 2248 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(2000 200 40 8) math:sum 2248}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4484 a r:Inference; + r:gives { + (8 4 2 2) :digitsToNumber 8422 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(8000 400 20 2) math:sum 8422}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4485 a r:Inference; + r:gives { + 2249 :numberToDigits (2 2 4 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2249 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2249 1000) math:remainder 249}] + [ a r:Fact; r:gives {(249 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(249 100) math:remainder 49}] + [ a r:Fact; r:gives {(49 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(49 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 49]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4486 a r:Inference; + r:gives { + (2 2 4 9) :digitsToNumber 2249 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(2000 200 40 9) math:sum 2249}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4487 a r:Inference; + r:gives { + (9 4 2 2) :digitsToNumber 9422 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 400 20 2) math:sum 9422}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4488 a r:Inference; + r:gives { + 2250 :numberToDigits (2 2 5 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2250 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2250 1000) math:remainder 250}] + [ a r:Fact; r:gives {(250 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(250 100) math:remainder 50}] + [ a r:Fact; r:gives {(50 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(50 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2250]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 250]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4489 a r:Inference; + r:gives { + 2251 :numberToDigits (2 2 5 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2251 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2251 1000) math:remainder 251}] + [ a r:Fact; r:gives {(251 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(251 100) math:remainder 51}] + [ a r:Fact; r:gives {(51 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(51 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2251]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 251]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 51]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4490 a r:Inference; + r:gives { + 2252 :numberToDigits (2 2 5 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2252 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2252 1000) math:remainder 252}] + [ a r:Fact; r:gives {(252 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(252 100) math:remainder 52}] + [ a r:Fact; r:gives {(52 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(52 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2252]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 252]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 52]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4491 a r:Inference; + r:gives { + 2253 :numberToDigits (2 2 5 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2253 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2253 1000) math:remainder 253}] + [ a r:Fact; r:gives {(253 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(253 100) math:remainder 53}] + [ a r:Fact; r:gives {(53 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(53 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2253]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 253]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 53]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4492 a r:Inference; + r:gives { + 2254 :numberToDigits (2 2 5 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2254 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2254 1000) math:remainder 254}] + [ a r:Fact; r:gives {(254 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(254 100) math:remainder 54}] + [ a r:Fact; r:gives {(54 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(54 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2254]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 254]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 54]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4493 a r:Inference; + r:gives { + 2255 :numberToDigits (2 2 5 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2255 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2255 1000) math:remainder 255}] + [ a r:Fact; r:gives {(255 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(255 100) math:remainder 55}] + [ a r:Fact; r:gives {(55 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(55 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 55]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4494 a r:Inference; + r:gives { + (2 2 5 5) :digitsToNumber 2255 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(2000 200 50 5) math:sum 2255}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6764. + +skolem:lemma4495 a r:Inference; + r:gives { + (5 5 2 2) :digitsToNumber 5522 . + }; + r:evidence ( + [ a r:Fact; r:gives {(5 1000) math:product 5000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(5000 500 20 2) math:sum 5522}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4496 a r:Inference; + r:gives { + 2256 :numberToDigits (2 2 5 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2256 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2256 1000) math:remainder 256}] + [ a r:Fact; r:gives {(256 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(256 100) math:remainder 56}] + [ a r:Fact; r:gives {(56 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(56 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 56]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4497 a r:Inference; + r:gives { + (2 2 5 6) :digitsToNumber 2256 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(2000 200 50 6) math:sum 2256}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4498 a r:Inference; + r:gives { + (6 5 2 2) :digitsToNumber 6522 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(6000 500 20 2) math:sum 6522}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4499 a r:Inference; + r:gives { + 2257 :numberToDigits (2 2 5 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2257 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2257 1000) math:remainder 257}] + [ a r:Fact; r:gives {(257 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(257 100) math:remainder 57}] + [ a r:Fact; r:gives {(57 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(57 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 57]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4500 a r:Inference; + r:gives { + (2 2 5 7) :digitsToNumber 2257 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(2000 200 50 7) math:sum 2257}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4501 a r:Inference; + r:gives { + (7 5 2 2) :digitsToNumber 7522 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(7000 500 20 2) math:sum 7522}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4502 a r:Inference; + r:gives { + 2258 :numberToDigits (2 2 5 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2258 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2258 1000) math:remainder 258}] + [ a r:Fact; r:gives {(258 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(258 100) math:remainder 58}] + [ a r:Fact; r:gives {(58 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(58 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 58]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4503 a r:Inference; + r:gives { + (2 2 5 8) :digitsToNumber 2258 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(2000 200 50 8) math:sum 2258}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4504 a r:Inference; + r:gives { + (8 5 2 2) :digitsToNumber 8522 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(8000 500 20 2) math:sum 8522}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4505 a r:Inference; + r:gives { + 2259 :numberToDigits (2 2 5 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2259 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2259 1000) math:remainder 259}] + [ a r:Fact; r:gives {(259 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(259 100) math:remainder 59}] + [ a r:Fact; r:gives {(59 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(59 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 59]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4506 a r:Inference; + r:gives { + (2 2 5 9) :digitsToNumber 2259 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(2000 200 50 9) math:sum 2259}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4507 a r:Inference; + r:gives { + (9 5 2 2) :digitsToNumber 9522 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 500 20 2) math:sum 9522}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4508 a r:Inference; + r:gives { + 2260 :numberToDigits (2 2 6 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2260 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2260 1000) math:remainder 260}] + [ a r:Fact; r:gives {(260 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(260 100) math:remainder 60}] + [ a r:Fact; r:gives {(60 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(60 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2260]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 260]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4509 a r:Inference; + r:gives { + 2261 :numberToDigits (2 2 6 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2261 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2261 1000) math:remainder 261}] + [ a r:Fact; r:gives {(261 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(261 100) math:remainder 61}] + [ a r:Fact; r:gives {(61 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(61 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2261]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 261]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 61]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4510 a r:Inference; + r:gives { + 2262 :numberToDigits (2 2 6 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2262 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2262 1000) math:remainder 262}] + [ a r:Fact; r:gives {(262 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(262 100) math:remainder 62}] + [ a r:Fact; r:gives {(62 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(62 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 62]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4511 a r:Inference; + r:gives { + 2263 :numberToDigits (2 2 6 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2263 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2263 1000) math:remainder 263}] + [ a r:Fact; r:gives {(263 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(263 100) math:remainder 63}] + [ a r:Fact; r:gives {(63 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(63 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 63]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4512 a r:Inference; + r:gives { + 2264 :numberToDigits (2 2 6 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2264 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2264 1000) math:remainder 264}] + [ a r:Fact; r:gives {(264 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(264 100) math:remainder 64}] + [ a r:Fact; r:gives {(64 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(64 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 64]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4513 a r:Inference; + r:gives { + 2265 :numberToDigits (2 2 6 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2265 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2265 1000) math:remainder 265}] + [ a r:Fact; r:gives {(265 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(265 100) math:remainder 65}] + [ a r:Fact; r:gives {(65 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(65 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 65]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4514 a r:Inference; + r:gives { + 2266 :numberToDigits (2 2 6 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2266 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2266 1000) math:remainder 266}] + [ a r:Fact; r:gives {(266 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(266 100) math:remainder 66}] + [ a r:Fact; r:gives {(66 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(66 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 66]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4515 a r:Inference; + r:gives { + (2 2 6 6) :digitsToNumber 2266 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(2000 200 60 6) math:sum 2266}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4516 a r:Inference; + r:gives { + (6 6 2 2) :digitsToNumber 6622 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(6000 600 20 2) math:sum 6622}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4517 a r:Inference; + r:gives { + 2267 :numberToDigits (2 2 6 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2267 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2267 1000) math:remainder 267}] + [ a r:Fact; r:gives {(267 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(267 100) math:remainder 67}] + [ a r:Fact; r:gives {(67 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(67 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 67]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4518 a r:Inference; + r:gives { + (2 2 6 7) :digitsToNumber 2267 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(2000 200 60 7) math:sum 2267}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4519 a r:Inference; + r:gives { + (7 6 2 2) :digitsToNumber 7622 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(7000 600 20 2) math:sum 7622}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4520 a r:Inference; + r:gives { + 2268 :numberToDigits (2 2 6 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2268 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2268 1000) math:remainder 268}] + [ a r:Fact; r:gives {(268 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(268 100) math:remainder 68}] + [ a r:Fact; r:gives {(68 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(68 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 68]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4521 a r:Inference; + r:gives { + (2 2 6 8) :digitsToNumber 2268 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(2000 200 60 8) math:sum 2268}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4522 a r:Inference; + r:gives { + (8 6 2 2) :digitsToNumber 8622 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(8000 600 20 2) math:sum 8622}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4523 a r:Inference; + r:gives { + 2269 :numberToDigits (2 2 6 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2269 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2269 1000) math:remainder 269}] + [ a r:Fact; r:gives {(269 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(269 100) math:remainder 69}] + [ a r:Fact; r:gives {(69 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(69 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 69]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4524 a r:Inference; + r:gives { + (2 2 6 9) :digitsToNumber 2269 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(2000 200 60 9) math:sum 2269}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4525 a r:Inference; + r:gives { + (9 6 2 2) :digitsToNumber 9622 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 600 20 2) math:sum 9622}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4526 a r:Inference; + r:gives { + 2270 :numberToDigits (2 2 7 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2270 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2270 1000) math:remainder 270}] + [ a r:Fact; r:gives {(270 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(270 100) math:remainder 70}] + [ a r:Fact; r:gives {(70 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(70 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2270]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 270]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4527 a r:Inference; + r:gives { + 2271 :numberToDigits (2 2 7 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2271 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2271 1000) math:remainder 271}] + [ a r:Fact; r:gives {(271 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(271 100) math:remainder 71}] + [ a r:Fact; r:gives {(71 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(71 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2271]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 271]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 71]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4528 a r:Inference; + r:gives { + 2272 :numberToDigits (2 2 7 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2272 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2272 1000) math:remainder 272}] + [ a r:Fact; r:gives {(272 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(272 100) math:remainder 72}] + [ a r:Fact; r:gives {(72 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(72 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2272]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 272]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 72]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4529 a r:Inference; + r:gives { + 2273 :numberToDigits (2 2 7 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2273 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2273 1000) math:remainder 273}] + [ a r:Fact; r:gives {(273 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(273 100) math:remainder 73}] + [ a r:Fact; r:gives {(73 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(73 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2273]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 273]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 73]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4530 a r:Inference; + r:gives { + 2274 :numberToDigits (2 2 7 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2274 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2274 1000) math:remainder 274}] + [ a r:Fact; r:gives {(274 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(274 100) math:remainder 74}] + [ a r:Fact; r:gives {(74 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(74 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2274]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 274]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 74]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4531 a r:Inference; + r:gives { + 2275 :numberToDigits (2 2 7 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2275 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2275 1000) math:remainder 275}] + [ a r:Fact; r:gives {(275 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(275 100) math:remainder 75}] + [ a r:Fact; r:gives {(75 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(75 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2275]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 275]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 75]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4532 a r:Inference; + r:gives { + 2276 :numberToDigits (2 2 7 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2276 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2276 1000) math:remainder 276}] + [ a r:Fact; r:gives {(276 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(276 100) math:remainder 76}] + [ a r:Fact; r:gives {(76 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(76 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2276]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 276]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 76]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4533 a r:Inference; + r:gives { + 2277 :numberToDigits (2 2 7 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2277 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2277 1000) math:remainder 277}] + [ a r:Fact; r:gives {(277 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(277 100) math:remainder 77}] + [ a r:Fact; r:gives {(77 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(77 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2277]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 277]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 77]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4534 a r:Inference; + r:gives { + (2 2 7 7) :digitsToNumber 2277 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(2000 200 70 7) math:sum 2277}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2277]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4535 a r:Inference; + r:gives { + (7 7 2 2) :digitsToNumber 7722 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(7000 700 20 2) math:sum 7722}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4536 a r:Inference; + r:gives { + 2278 :numberToDigits (2 2 7 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2278 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2278 1000) math:remainder 278}] + [ a r:Fact; r:gives {(278 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(278 100) math:remainder 78}] + [ a r:Fact; r:gives {(78 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(78 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 78]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4537 a r:Inference; + r:gives { + (2 2 7 8) :digitsToNumber 2278 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(2000 200 70 8) math:sum 2278}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4538 a r:Inference; + r:gives { + (8 7 2 2) :digitsToNumber 8722 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(8000 700 20 2) math:sum 8722}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4539 a r:Inference; + r:gives { + 2279 :numberToDigits (2 2 7 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2279 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2279 1000) math:remainder 279}] + [ a r:Fact; r:gives {(279 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(279 100) math:remainder 79}] + [ a r:Fact; r:gives {(79 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(79 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 79]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4540 a r:Inference; + r:gives { + (2 2 7 9) :digitsToNumber 2279 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(2000 200 70 9) math:sum 2279}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4541 a r:Inference; + r:gives { + (9 7 2 2) :digitsToNumber 9722 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 700 20 2) math:sum 9722}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4542 a r:Inference; + r:gives { + 2280 :numberToDigits (2 2 8 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2280 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2280 1000) math:remainder 280}] + [ a r:Fact; r:gives {(280 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(280 100) math:remainder 80}] + [ a r:Fact; r:gives {(80 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(80 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2280]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 280]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4543 a r:Inference; + r:gives { + 2281 :numberToDigits (2 2 8 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2281 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2281 1000) math:remainder 281}] + [ a r:Fact; r:gives {(281 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(281 100) math:remainder 81}] + [ a r:Fact; r:gives {(81 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(81 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2281]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 281]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 81]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4544 a r:Inference; + r:gives { + 2282 :numberToDigits (2 2 8 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2282 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2282 1000) math:remainder 282}] + [ a r:Fact; r:gives {(282 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(282 100) math:remainder 82}] + [ a r:Fact; r:gives {(82 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(82 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2282]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 282]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 82]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4545 a r:Inference; + r:gives { + 2283 :numberToDigits (2 2 8 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2283 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2283 1000) math:remainder 283}] + [ a r:Fact; r:gives {(283 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(283 100) math:remainder 83}] + [ a r:Fact; r:gives {(83 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(83 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2283]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 283]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 83]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4546 a r:Inference; + r:gives { + 2284 :numberToDigits (2 2 8 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2284 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2284 1000) math:remainder 284}] + [ a r:Fact; r:gives {(284 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(284 100) math:remainder 84}] + [ a r:Fact; r:gives {(84 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(84 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2284]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 284]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 84]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4547 a r:Inference; + r:gives { + 2285 :numberToDigits (2 2 8 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2285 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2285 1000) math:remainder 285}] + [ a r:Fact; r:gives {(285 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(285 100) math:remainder 85}] + [ a r:Fact; r:gives {(85 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(85 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2285]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 285]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 85]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4548 a r:Inference; + r:gives { + 2286 :numberToDigits (2 2 8 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2286 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2286 1000) math:remainder 286}] + [ a r:Fact; r:gives {(286 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(286 100) math:remainder 86}] + [ a r:Fact; r:gives {(86 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(86 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2286]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 286]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 86]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4549 a r:Inference; + r:gives { + 2287 :numberToDigits (2 2 8 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2287 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2287 1000) math:remainder 287}] + [ a r:Fact; r:gives {(287 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(287 100) math:remainder 87}] + [ a r:Fact; r:gives {(87 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(87 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2287]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 287]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 87]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4550 a r:Inference; + r:gives { + 2288 :numberToDigits (2 2 8 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2288 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2288 1000) math:remainder 288}] + [ a r:Fact; r:gives {(288 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(288 100) math:remainder 88}] + [ a r:Fact; r:gives {(88 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(88 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2288]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 288]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 88]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4551 a r:Inference; + r:gives { + (2 2 8 8) :digitsToNumber 2288 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(8 10) math:product 80}] + [ a r:Fact; r:gives {(2000 200 80 8) math:sum 2288}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2288]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4552 a r:Inference; + r:gives { + (8 8 2 2) :digitsToNumber 8822 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(8 100) math:product 800}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(8000 800 20 2) math:sum 8822}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8822]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4553 a r:Inference; + r:gives { + 2289 :numberToDigits (2 2 8 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2289 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2289 1000) math:remainder 289}] + [ a r:Fact; r:gives {(289 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(289 100) math:remainder 89}] + [ a r:Fact; r:gives {(89 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(89 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 89]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4554 a r:Inference; + r:gives { + (2 2 8 9) :digitsToNumber 2289 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(8 10) math:product 80}] + [ a r:Fact; r:gives {(2000 200 80 9) math:sum 2289}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4555 a r:Inference; + r:gives { + (9 8 2 2) :digitsToNumber 9822 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(8 100) math:product 800}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 800 20 2) math:sum 9822}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9822]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4556 a r:Inference; + r:gives { + 2290 :numberToDigits (2 2 9 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2290 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2290 1000) math:remainder 290}] + [ a r:Fact; r:gives {(290 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(290 100) math:remainder 90}] + [ a r:Fact; r:gives {(90 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(90 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2290]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 290]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4557 a r:Inference; + r:gives { + 2291 :numberToDigits (2 2 9 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2291 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2291 1000) math:remainder 291}] + [ a r:Fact; r:gives {(291 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(291 100) math:remainder 91}] + [ a r:Fact; r:gives {(91 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(91 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2291]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 291]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 91]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4558 a r:Inference; + r:gives { + 2292 :numberToDigits (2 2 9 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2292 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2292 1000) math:remainder 292}] + [ a r:Fact; r:gives {(292 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(292 100) math:remainder 92}] + [ a r:Fact; r:gives {(92 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(92 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2292]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 292]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 92]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4559 a r:Inference; + r:gives { + 2293 :numberToDigits (2 2 9 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2293 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2293 1000) math:remainder 293}] + [ a r:Fact; r:gives {(293 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(293 100) math:remainder 93}] + [ a r:Fact; r:gives {(93 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(93 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2293]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 293]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 93]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4560 a r:Inference; + r:gives { + 2294 :numberToDigits (2 2 9 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2294 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2294 1000) math:remainder 294}] + [ a r:Fact; r:gives {(294 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(294 100) math:remainder 94}] + [ a r:Fact; r:gives {(94 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(94 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2294]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 294]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 94]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4561 a r:Inference; + r:gives { + 2295 :numberToDigits (2 2 9 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2295 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2295 1000) math:remainder 295}] + [ a r:Fact; r:gives {(295 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(295 100) math:remainder 95}] + [ a r:Fact; r:gives {(95 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(95 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2295]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 295]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 95]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4562 a r:Inference; + r:gives { + 2296 :numberToDigits (2 2 9 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2296 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2296 1000) math:remainder 296}] + [ a r:Fact; r:gives {(296 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(296 100) math:remainder 96}] + [ a r:Fact; r:gives {(96 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(96 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2296]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 296]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 96]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4563 a r:Inference; + r:gives { + 2297 :numberToDigits (2 2 9 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2297 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2297 1000) math:remainder 297}] + [ a r:Fact; r:gives {(297 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(297 100) math:remainder 97}] + [ a r:Fact; r:gives {(97 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(97 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2297]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 297]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 97]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4564 a r:Inference; + r:gives { + 2298 :numberToDigits (2 2 9 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2298 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2298 1000) math:remainder 298}] + [ a r:Fact; r:gives {(298 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(298 100) math:remainder 98}] + [ a r:Fact; r:gives {(98 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(98 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2298]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 298]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 98]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4565 a r:Inference; + r:gives { + 2299 :numberToDigits (2 2 9 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2299 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2299 1000) math:remainder 299}] + [ a r:Fact; r:gives {(299 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(299 100) math:remainder 99}] + [ a r:Fact; r:gives {(99 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(99 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 99]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4566 a r:Inference; + r:gives { + (2 2 9 9) :digitsToNumber 2299 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(9 10) math:product 90}] + [ a r:Fact; r:gives {(2000 200 90 9) math:sum 2299}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4567 a r:Inference; + r:gives { + (9 9 2 2) :digitsToNumber 9922 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(9 100) math:product 900}] + [ a r:Fact; r:gives {(2 10) math:product 20}] + [ a r:Fact; r:gives {(9000 900 20 2) math:sum 9922}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 900]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9922]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4568 a r:Inference; + r:gives { + 2300 :numberToDigits (2 3 0 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2300 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2300 1000) math:remainder 300}] + [ a r:Fact; r:gives {(300 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(300 100) math:remainder 0}] + [ a r:Fact; r:gives {(0 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(0 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4569 a r:Inference; + r:gives { + 2301 :numberToDigits (2 3 0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2301 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2301 1000) math:remainder 301}] + [ a r:Fact; r:gives {(301 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(301 100) math:remainder 1}] + [ a r:Fact; r:gives {(1 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(1 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2301]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 301]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4570 a r:Inference; + r:gives { + 2302 :numberToDigits (2 3 0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2302 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2302 1000) math:remainder 302}] + [ a r:Fact; r:gives {(302 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(302 100) math:remainder 2}] + [ a r:Fact; r:gives {(2 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(2 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2302]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 302]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4571 a r:Inference; + r:gives { + 2303 :numberToDigits (2 3 0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2303 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2303 1000) math:remainder 303}] + [ a r:Fact; r:gives {(303 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(303 100) math:remainder 3}] + [ a r:Fact; r:gives {(3 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(3 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2303]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 303]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4572 a r:Inference; + r:gives { + 2304 :numberToDigits (2 3 0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2304 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2304 1000) math:remainder 304}] + [ a r:Fact; r:gives {(304 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(304 100) math:remainder 4}] + [ a r:Fact; r:gives {(4 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(4 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2304]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 304]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4573 a r:Inference; + r:gives { + 2305 :numberToDigits (2 3 0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2305 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2305 1000) math:remainder 305}] + [ a r:Fact; r:gives {(305 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(305 100) math:remainder 5}] + [ a r:Fact; r:gives {(5 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(5 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2305]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 305]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4574 a r:Inference; + r:gives { + 2306 :numberToDigits (2 3 0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2306 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2306 1000) math:remainder 306}] + [ a r:Fact; r:gives {(306 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(306 100) math:remainder 6}] + [ a r:Fact; r:gives {(6 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(6 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2306]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 306]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4575 a r:Inference; + r:gives { + 2307 :numberToDigits (2 3 0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2307 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2307 1000) math:remainder 307}] + [ a r:Fact; r:gives {(307 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(307 100) math:remainder 7}] + [ a r:Fact; r:gives {(7 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(7 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2307]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 307]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4576 a r:Inference; + r:gives { + 2308 :numberToDigits (2 3 0 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2308 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2308 1000) math:remainder 308}] + [ a r:Fact; r:gives {(308 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(308 100) math:remainder 8}] + [ a r:Fact; r:gives {(8 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(8 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2308]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 308]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4577 a r:Inference; + r:gives { + 2309 :numberToDigits (2 3 0 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2309 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2309 1000) math:remainder 309}] + [ a r:Fact; r:gives {(309 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(309 100) math:remainder 9}] + [ a r:Fact; r:gives {(9 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(9 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2309]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 309]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4578 a r:Inference; + r:gives { + 2310 :numberToDigits (2 3 1 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2310 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2310 1000) math:remainder 310}] + [ a r:Fact; r:gives {(310 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(310 100) math:remainder 10}] + [ a r:Fact; r:gives {(10 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(10 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4579 a r:Inference; + r:gives { + 2311 :numberToDigits (2 3 1 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2311 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2311 1000) math:remainder 311}] + [ a r:Fact; r:gives {(311 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(311 100) math:remainder 11}] + [ a r:Fact; r:gives {(11 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(11 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 11]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4580 a r:Inference; + r:gives { + 2312 :numberToDigits (2 3 1 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2312 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2312 1000) math:remainder 312}] + [ a r:Fact; r:gives {(312 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(312 100) math:remainder 12}] + [ a r:Fact; r:gives {(12 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(12 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2312]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 312]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4581 a r:Inference; + r:gives { + 2313 :numberToDigits (2 3 1 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2313 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2313 1000) math:remainder 313}] + [ a r:Fact; r:gives {(313 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(313 100) math:remainder 13}] + [ a r:Fact; r:gives {(13 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(13 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2313]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 313]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 13]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4582 a r:Inference; + r:gives { + 2314 :numberToDigits (2 3 1 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2314 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2314 1000) math:remainder 314}] + [ a r:Fact; r:gives {(314 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(314 100) math:remainder 14}] + [ a r:Fact; r:gives {(14 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(14 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2314]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 314]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 14]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4583 a r:Inference; + r:gives { + 2315 :numberToDigits (2 3 1 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2315 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2315 1000) math:remainder 315}] + [ a r:Fact; r:gives {(315 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(315 100) math:remainder 15}] + [ a r:Fact; r:gives {(15 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(15 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2315]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 315]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 15]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4584 a r:Inference; + r:gives { + 2316 :numberToDigits (2 3 1 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2316 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2316 1000) math:remainder 316}] + [ a r:Fact; r:gives {(316 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(316 100) math:remainder 16}] + [ a r:Fact; r:gives {(16 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(16 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2316]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 316]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 16]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4585 a r:Inference; + r:gives { + 2317 :numberToDigits (2 3 1 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2317 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2317 1000) math:remainder 317}] + [ a r:Fact; r:gives {(317 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(317 100) math:remainder 17}] + [ a r:Fact; r:gives {(17 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(17 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2317]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 317]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 17]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4586 a r:Inference; + r:gives { + 2318 :numberToDigits (2 3 1 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2318 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2318 1000) math:remainder 318}] + [ a r:Fact; r:gives {(318 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(318 100) math:remainder 18}] + [ a r:Fact; r:gives {(18 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(18 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2318]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 318]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 18]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4587 a r:Inference; + r:gives { + 2319 :numberToDigits (2 3 1 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2319 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2319 1000) math:remainder 319}] + [ a r:Fact; r:gives {(319 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(319 100) math:remainder 19}] + [ a r:Fact; r:gives {(19 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(19 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2319]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 319]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 19]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4588 a r:Inference; + r:gives { + 2320 :numberToDigits (2 3 2 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2320 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2320 1000) math:remainder 320}] + [ a r:Fact; r:gives {(320 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(320 100) math:remainder 20}] + [ a r:Fact; r:gives {(20 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(20 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4589 a r:Inference; + r:gives { + 2321 :numberToDigits (2 3 2 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2321 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2321 1000) math:remainder 321}] + [ a r:Fact; r:gives {(321 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(321 100) math:remainder 21}] + [ a r:Fact; r:gives {(21 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(21 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 21]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4590 a r:Inference; + r:gives { + 2322 :numberToDigits (2 3 2 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2322 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2322 1000) math:remainder 322}] + [ a r:Fact; r:gives {(322 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(322 100) math:remainder 22}] + [ a r:Fact; r:gives {(22 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(22 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4591 a r:Inference; + r:gives { + 2323 :numberToDigits (2 3 2 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2323 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2323 1000) math:remainder 323}] + [ a r:Fact; r:gives {(323 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(323 100) math:remainder 23}] + [ a r:Fact; r:gives {(23 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(23 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2323]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 323]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4592 a r:Inference; + r:gives { + 2324 :numberToDigits (2 3 2 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2324 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2324 1000) math:remainder 324}] + [ a r:Fact; r:gives {(324 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(324 100) math:remainder 24}] + [ a r:Fact; r:gives {(24 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(24 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2324]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 324]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4593 a r:Inference; + r:gives { + 2325 :numberToDigits (2 3 2 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2325 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2325 1000) math:remainder 325}] + [ a r:Fact; r:gives {(325 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(325 100) math:remainder 25}] + [ a r:Fact; r:gives {(25 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(25 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2325]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 325]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4594 a r:Inference; + r:gives { + 2326 :numberToDigits (2 3 2 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2326 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2326 1000) math:remainder 326}] + [ a r:Fact; r:gives {(326 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(326 100) math:remainder 26}] + [ a r:Fact; r:gives {(26 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(26 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2326]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 326]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4595 a r:Inference; + r:gives { + 2327 :numberToDigits (2 3 2 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2327 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2327 1000) math:remainder 327}] + [ a r:Fact; r:gives {(327 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(327 100) math:remainder 27}] + [ a r:Fact; r:gives {(27 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(27 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2327]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 327]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4596 a r:Inference; + r:gives { + 2328 :numberToDigits (2 3 2 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2328 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2328 1000) math:remainder 328}] + [ a r:Fact; r:gives {(328 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(328 100) math:remainder 28}] + [ a r:Fact; r:gives {(28 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(28 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2328]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 328]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4597 a r:Inference; + r:gives { + 2329 :numberToDigits (2 3 2 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2329 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2329 1000) math:remainder 329}] + [ a r:Fact; r:gives {(329 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(329 100) math:remainder 29}] + [ a r:Fact; r:gives {(29 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(29 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2329]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 329]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4598 a r:Inference; + r:gives { + 2330 :numberToDigits (2 3 3 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2330 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2330 1000) math:remainder 330}] + [ a r:Fact; r:gives {(330 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(330 100) math:remainder 30}] + [ a r:Fact; r:gives {(30 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(30 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4599 a r:Inference; + r:gives { + 2331 :numberToDigits (2 3 3 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2331 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2331 1000) math:remainder 331}] + [ a r:Fact; r:gives {(331 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(331 100) math:remainder 31}] + [ a r:Fact; r:gives {(31 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(31 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 31]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4600 a r:Inference; + r:gives { + 2332 :numberToDigits (2 3 3 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2332 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2332 1000) math:remainder 332}] + [ a r:Fact; r:gives {(332 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(332 100) math:remainder 32}] + [ a r:Fact; r:gives {(32 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(32 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 32]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4601 a r:Inference; + r:gives { + 2333 :numberToDigits (2 3 3 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2333 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2333 1000) math:remainder 333}] + [ a r:Fact; r:gives {(333 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(333 100) math:remainder 33}] + [ a r:Fact; r:gives {(33 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(33 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 33]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4602 a r:Inference; + r:gives { + (2 3 3 3) :digitsToNumber 2333 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(2000 300 30 3) math:sum 2333}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. + +skolem:lemma4603 a r:Inference; + r:gives { + (3 3 3 2) :digitsToNumber 3332 . + }; + r:evidence ( + [ a r:Fact; r:gives {(3 1000) math:product 3000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(3000 300 30 2) math:sum 3332}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4604 a r:Inference; + r:gives { + 2334 :numberToDigits (2 3 3 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2334 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2334 1000) math:remainder 334}] + [ a r:Fact; r:gives {(334 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(334 100) math:remainder 34}] + [ a r:Fact; r:gives {(34 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(34 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 34]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4605 a r:Inference; + r:gives { + (2 3 3 4) :digitsToNumber 2334 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(2000 300 30 4) math:sum 2334}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6764. + +skolem:lemma4606 a r:Inference; + r:gives { + (4 3 3 2) :digitsToNumber 4332 . + }; + r:evidence ( + [ a r:Fact; r:gives {(4 1000) math:product 4000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(4000 300 30 2) math:sum 4332}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4607 a r:Inference; + r:gives { + 2335 :numberToDigits (2 3 3 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2335 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2335 1000) math:remainder 335}] + [ a r:Fact; r:gives {(335 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(335 100) math:remainder 35}] + [ a r:Fact; r:gives {(35 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(35 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 35]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4608 a r:Inference; + r:gives { + (2 3 3 5) :digitsToNumber 2335 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(2000 300 30 5) math:sum 2335}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6764. + +skolem:lemma4609 a r:Inference; + r:gives { + (5 3 3 2) :digitsToNumber 5332 . + }; + r:evidence ( + [ a r:Fact; r:gives {(5 1000) math:product 5000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(5000 300 30 2) math:sum 5332}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4610 a r:Inference; + r:gives { + 2336 :numberToDigits (2 3 3 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2336 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2336 1000) math:remainder 336}] + [ a r:Fact; r:gives {(336 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(336 100) math:remainder 36}] + [ a r:Fact; r:gives {(36 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(36 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 36]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4611 a r:Inference; + r:gives { + (2 3 3 6) :digitsToNumber 2336 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(2000 300 30 6) math:sum 2336}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4612 a r:Inference; + r:gives { + (6 3 3 2) :digitsToNumber 6332 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(6000 300 30 2) math:sum 6332}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4613 a r:Inference; + r:gives { + 2337 :numberToDigits (2 3 3 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2337 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2337 1000) math:remainder 337}] + [ a r:Fact; r:gives {(337 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(337 100) math:remainder 37}] + [ a r:Fact; r:gives {(37 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(37 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 37]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4614 a r:Inference; + r:gives { + (2 3 3 7) :digitsToNumber 2337 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(2000 300 30 7) math:sum 2337}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4615 a r:Inference; + r:gives { + (7 3 3 2) :digitsToNumber 7332 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(7000 300 30 2) math:sum 7332}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4616 a r:Inference; + r:gives { + 2338 :numberToDigits (2 3 3 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2338 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2338 1000) math:remainder 338}] + [ a r:Fact; r:gives {(338 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(338 100) math:remainder 38}] + [ a r:Fact; r:gives {(38 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(38 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 38]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4617 a r:Inference; + r:gives { + (2 3 3 8) :digitsToNumber 2338 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(2000 300 30 8) math:sum 2338}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4618 a r:Inference; + r:gives { + (8 3 3 2) :digitsToNumber 8332 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(8000 300 30 2) math:sum 8332}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4619 a r:Inference; + r:gives { + 2339 :numberToDigits (2 3 3 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2339 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2339 1000) math:remainder 339}] + [ a r:Fact; r:gives {(339 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(339 100) math:remainder 39}] + [ a r:Fact; r:gives {(39 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(39 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 39]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4620 a r:Inference; + r:gives { + (2 3 3 9) :digitsToNumber 2339 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(2000 300 30 9) math:sum 2339}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4621 a r:Inference; + r:gives { + (9 3 3 2) :digitsToNumber 9332 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(9000 300 30 2) math:sum 9332}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4622 a r:Inference; + r:gives { + 2340 :numberToDigits (2 3 4 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2340 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2340 1000) math:remainder 340}] + [ a r:Fact; r:gives {(340 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(340 100) math:remainder 40}] + [ a r:Fact; r:gives {(40 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(40 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2340]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 340]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4623 a r:Inference; + r:gives { + 2341 :numberToDigits (2 3 4 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2341 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2341 1000) math:remainder 341}] + [ a r:Fact; r:gives {(341 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(341 100) math:remainder 41}] + [ a r:Fact; r:gives {(41 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(41 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2341]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 341]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 41]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4624 a r:Inference; + r:gives { + 2342 :numberToDigits (2 3 4 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2342 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2342 1000) math:remainder 342}] + [ a r:Fact; r:gives {(342 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(342 100) math:remainder 42}] + [ a r:Fact; r:gives {(42 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(42 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2342]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 342]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 42]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4625 a r:Inference; + r:gives { + 2343 :numberToDigits (2 3 4 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2343 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2343 1000) math:remainder 343}] + [ a r:Fact; r:gives {(343 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(343 100) math:remainder 43}] + [ a r:Fact; r:gives {(43 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(43 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2343]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 343]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 43]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4626 a r:Inference; + r:gives { + 2344 :numberToDigits (2 3 4 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2344 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2344 1000) math:remainder 344}] + [ a r:Fact; r:gives {(344 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(344 100) math:remainder 44}] + [ a r:Fact; r:gives {(44 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(44 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 44]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4627 a r:Inference; + r:gives { + (2 3 4 4) :digitsToNumber 2344 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(2000 300 40 4) math:sum 2344}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6764. + +skolem:lemma4628 a r:Inference; + r:gives { + (4 4 3 2) :digitsToNumber 4432 . + }; + r:evidence ( + [ a r:Fact; r:gives {(4 1000) math:product 4000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(4000 400 30 2) math:sum 4432}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4629 a r:Inference; + r:gives { + 2345 :numberToDigits (2 3 4 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2345 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2345 1000) math:remainder 345}] + [ a r:Fact; r:gives {(345 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(345 100) math:remainder 45}] + [ a r:Fact; r:gives {(45 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(45 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 45]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4630 a r:Inference; + r:gives { + (2 3 4 5) :digitsToNumber 2345 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(2000 300 40 5) math:sum 2345}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6764. + +skolem:lemma4631 a r:Inference; + r:gives { + (5 4 3 2) :digitsToNumber 5432 . + }; + r:evidence ( + [ a r:Fact; r:gives {(5 1000) math:product 5000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(5000 400 30 2) math:sum 5432}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4632 a r:Inference; + r:gives { + 2346 :numberToDigits (2 3 4 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2346 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2346 1000) math:remainder 346}] + [ a r:Fact; r:gives {(346 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(346 100) math:remainder 46}] + [ a r:Fact; r:gives {(46 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(46 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 46]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4633 a r:Inference; + r:gives { + (2 3 4 6) :digitsToNumber 2346 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(2000 300 40 6) math:sum 2346}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4634 a r:Inference; + r:gives { + (6 4 3 2) :digitsToNumber 6432 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(6000 400 30 2) math:sum 6432}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4635 a r:Inference; + r:gives { + 2347 :numberToDigits (2 3 4 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2347 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2347 1000) math:remainder 347}] + [ a r:Fact; r:gives {(347 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(347 100) math:remainder 47}] + [ a r:Fact; r:gives {(47 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(47 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 47]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4636 a r:Inference; + r:gives { + (2 3 4 7) :digitsToNumber 2347 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(2000 300 40 7) math:sum 2347}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4637 a r:Inference; + r:gives { + (7 4 3 2) :digitsToNumber 7432 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(7000 400 30 2) math:sum 7432}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4638 a r:Inference; + r:gives { + 2348 :numberToDigits (2 3 4 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2348 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2348 1000) math:remainder 348}] + [ a r:Fact; r:gives {(348 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(348 100) math:remainder 48}] + [ a r:Fact; r:gives {(48 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(48 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 48]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4639 a r:Inference; + r:gives { + (2 3 4 8) :digitsToNumber 2348 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(2000 300 40 8) math:sum 2348}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4640 a r:Inference; + r:gives { + (8 4 3 2) :digitsToNumber 8432 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(8000 400 30 2) math:sum 8432}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4641 a r:Inference; + r:gives { + 2349 :numberToDigits (2 3 4 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2349 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2349 1000) math:remainder 349}] + [ a r:Fact; r:gives {(349 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(349 100) math:remainder 49}] + [ a r:Fact; r:gives {(49 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(49 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 49]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4642 a r:Inference; + r:gives { + (2 3 4 9) :digitsToNumber 2349 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(2000 300 40 9) math:sum 2349}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4643 a r:Inference; + r:gives { + (9 4 3 2) :digitsToNumber 9432 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(9000 400 30 2) math:sum 9432}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4644 a r:Inference; + r:gives { + 2350 :numberToDigits (2 3 5 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2350 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2350 1000) math:remainder 350}] + [ a r:Fact; r:gives {(350 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(350 100) math:remainder 50}] + [ a r:Fact; r:gives {(50 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(50 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2350]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 350]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4645 a r:Inference; + r:gives { + 2351 :numberToDigits (2 3 5 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2351 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2351 1000) math:remainder 351}] + [ a r:Fact; r:gives {(351 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(351 100) math:remainder 51}] + [ a r:Fact; r:gives {(51 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(51 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2351]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 351]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 51]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4646 a r:Inference; + r:gives { + 2352 :numberToDigits (2 3 5 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2352 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2352 1000) math:remainder 352}] + [ a r:Fact; r:gives {(352 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(352 100) math:remainder 52}] + [ a r:Fact; r:gives {(52 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(52 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 52]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4647 a r:Inference; + r:gives { + 2353 :numberToDigits (2 3 5 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2353 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2353 1000) math:remainder 353}] + [ a r:Fact; r:gives {(353 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(353 100) math:remainder 53}] + [ a r:Fact; r:gives {(53 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(53 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 53]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4648 a r:Inference; + r:gives { + 2354 :numberToDigits (2 3 5 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2354 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2354 1000) math:remainder 354}] + [ a r:Fact; r:gives {(354 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(354 100) math:remainder 54}] + [ a r:Fact; r:gives {(54 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(54 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 54]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4649 a r:Inference; + r:gives { + 2355 :numberToDigits (2 3 5 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2355 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2355 1000) math:remainder 355}] + [ a r:Fact; r:gives {(355 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(355 100) math:remainder 55}] + [ a r:Fact; r:gives {(55 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(55 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 55]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4650 a r:Inference; + r:gives { + (2 3 5 5) :digitsToNumber 2355 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(2000 300 50 5) math:sum 2355}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6764. + +skolem:lemma4651 a r:Inference; + r:gives { + (5 5 3 2) :digitsToNumber 5532 . + }; + r:evidence ( + [ a r:Fact; r:gives {(5 1000) math:product 5000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(5000 500 30 2) math:sum 5532}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4652 a r:Inference; + r:gives { + 2356 :numberToDigits (2 3 5 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2356 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2356 1000) math:remainder 356}] + [ a r:Fact; r:gives {(356 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(356 100) math:remainder 56}] + [ a r:Fact; r:gives {(56 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(56 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 56]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4653 a r:Inference; + r:gives { + (2 3 5 6) :digitsToNumber 2356 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(2000 300 50 6) math:sum 2356}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4654 a r:Inference; + r:gives { + (6 5 3 2) :digitsToNumber 6532 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(6000 500 30 2) math:sum 6532}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4655 a r:Inference; + r:gives { + 2357 :numberToDigits (2 3 5 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2357 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2357 1000) math:remainder 357}] + [ a r:Fact; r:gives {(357 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(357 100) math:remainder 57}] + [ a r:Fact; r:gives {(57 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(57 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 57]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4656 a r:Inference; + r:gives { + (2 3 5 7) :digitsToNumber 2357 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(2000 300 50 7) math:sum 2357}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4657 a r:Inference; + r:gives { + (7 5 3 2) :digitsToNumber 7532 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(7000 500 30 2) math:sum 7532}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4658 a r:Inference; + r:gives { + 2358 :numberToDigits (2 3 5 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2358 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2358 1000) math:remainder 358}] + [ a r:Fact; r:gives {(358 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(358 100) math:remainder 58}] + [ a r:Fact; r:gives {(58 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(58 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 58]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4659 a r:Inference; + r:gives { + (2 3 5 8) :digitsToNumber 2358 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(2000 300 50 8) math:sum 2358}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4660 a r:Inference; + r:gives { + (8 5 3 2) :digitsToNumber 8532 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(8000 500 30 2) math:sum 8532}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4661 a r:Inference; + r:gives { + 2359 :numberToDigits (2 3 5 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2359 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2359 1000) math:remainder 359}] + [ a r:Fact; r:gives {(359 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(359 100) math:remainder 59}] + [ a r:Fact; r:gives {(59 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(59 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 59]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4662 a r:Inference; + r:gives { + (2 3 5 9) :digitsToNumber 2359 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(2000 300 50 9) math:sum 2359}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4663 a r:Inference; + r:gives { + (9 5 3 2) :digitsToNumber 9532 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(9000 500 30 2) math:sum 9532}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4664 a r:Inference; + r:gives { + 2360 :numberToDigits (2 3 6 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2360 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2360 1000) math:remainder 360}] + [ a r:Fact; r:gives {(360 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(360 100) math:remainder 60}] + [ a r:Fact; r:gives {(60 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(60 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2360]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 360]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4665 a r:Inference; + r:gives { + 2361 :numberToDigits (2 3 6 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2361 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2361 1000) math:remainder 361}] + [ a r:Fact; r:gives {(361 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(361 100) math:remainder 61}] + [ a r:Fact; r:gives {(61 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(61 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2361]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 361]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 61]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4666 a r:Inference; + r:gives { + 2362 :numberToDigits (2 3 6 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2362 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2362 1000) math:remainder 362}] + [ a r:Fact; r:gives {(362 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(362 100) math:remainder 62}] + [ a r:Fact; r:gives {(62 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(62 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2362]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 362]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 62]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4667 a r:Inference; + r:gives { + 2363 :numberToDigits (2 3 6 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2363 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2363 1000) math:remainder 363}] + [ a r:Fact; r:gives {(363 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(363 100) math:remainder 63}] + [ a r:Fact; r:gives {(63 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(63 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2363]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 363]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 63]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4668 a r:Inference; + r:gives { + 2364 :numberToDigits (2 3 6 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2364 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2364 1000) math:remainder 364}] + [ a r:Fact; r:gives {(364 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(364 100) math:remainder 64}] + [ a r:Fact; r:gives {(64 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(64 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2364]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 364]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 64]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4669 a r:Inference; + r:gives { + 2365 :numberToDigits (2 3 6 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2365 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2365 1000) math:remainder 365}] + [ a r:Fact; r:gives {(365 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(365 100) math:remainder 65}] + [ a r:Fact; r:gives {(65 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(65 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2365]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 365]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 65]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4670 a r:Inference; + r:gives { + 2366 :numberToDigits (2 3 6 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2366 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2366 1000) math:remainder 366}] + [ a r:Fact; r:gives {(366 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(366 100) math:remainder 66}] + [ a r:Fact; r:gives {(66 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(66 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 66]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4671 a r:Inference; + r:gives { + (2 3 6 6) :digitsToNumber 2366 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(2000 300 60 6) math:sum 2366}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4672 a r:Inference; + r:gives { + (6 6 3 2) :digitsToNumber 6632 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(6000 600 30 2) math:sum 6632}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4673 a r:Inference; + r:gives { + 2367 :numberToDigits (2 3 6 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2367 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2367 1000) math:remainder 367}] + [ a r:Fact; r:gives {(367 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(367 100) math:remainder 67}] + [ a r:Fact; r:gives {(67 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(67 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 67]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4674 a r:Inference; + r:gives { + (2 3 6 7) :digitsToNumber 2367 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(2000 300 60 7) math:sum 2367}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4675 a r:Inference; + r:gives { + (7 6 3 2) :digitsToNumber 7632 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(7000 600 30 2) math:sum 7632}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4676 a r:Inference; + r:gives { + 2368 :numberToDigits (2 3 6 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2368 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2368 1000) math:remainder 368}] + [ a r:Fact; r:gives {(368 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(368 100) math:remainder 68}] + [ a r:Fact; r:gives {(68 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(68 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 68]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4677 a r:Inference; + r:gives { + (2 3 6 8) :digitsToNumber 2368 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(2000 300 60 8) math:sum 2368}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4678 a r:Inference; + r:gives { + (8 6 3 2) :digitsToNumber 8632 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(8000 600 30 2) math:sum 8632}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4679 a r:Inference; + r:gives { + 2369 :numberToDigits (2 3 6 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2369 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2369 1000) math:remainder 369}] + [ a r:Fact; r:gives {(369 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(369 100) math:remainder 69}] + [ a r:Fact; r:gives {(69 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(69 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 69]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4680 a r:Inference; + r:gives { + (2 3 6 9) :digitsToNumber 2369 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(2000 300 60 9) math:sum 2369}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4681 a r:Inference; + r:gives { + (9 6 3 2) :digitsToNumber 9632 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(9000 600 30 2) math:sum 9632}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4682 a r:Inference; + r:gives { + 2370 :numberToDigits (2 3 7 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2370 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2370 1000) math:remainder 370}] + [ a r:Fact; r:gives {(370 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(370 100) math:remainder 70}] + [ a r:Fact; r:gives {(70 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(70 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2370]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 370]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4683 a r:Inference; + r:gives { + 2371 :numberToDigits (2 3 7 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2371 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2371 1000) math:remainder 371}] + [ a r:Fact; r:gives {(371 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(371 100) math:remainder 71}] + [ a r:Fact; r:gives {(71 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(71 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2371]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 371]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 71]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4684 a r:Inference; + r:gives { + 2372 :numberToDigits (2 3 7 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2372 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2372 1000) math:remainder 372}] + [ a r:Fact; r:gives {(372 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(372 100) math:remainder 72}] + [ a r:Fact; r:gives {(72 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(72 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2372]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 372]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 72]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4685 a r:Inference; + r:gives { + 2373 :numberToDigits (2 3 7 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2373 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2373 1000) math:remainder 373}] + [ a r:Fact; r:gives {(373 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(373 100) math:remainder 73}] + [ a r:Fact; r:gives {(73 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(73 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2373]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 373]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 73]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4686 a r:Inference; + r:gives { + 2374 :numberToDigits (2 3 7 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2374 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2374 1000) math:remainder 374}] + [ a r:Fact; r:gives {(374 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(374 100) math:remainder 74}] + [ a r:Fact; r:gives {(74 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(74 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2374]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 374]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 74]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4687 a r:Inference; + r:gives { + 2375 :numberToDigits (2 3 7 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2375 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2375 1000) math:remainder 375}] + [ a r:Fact; r:gives {(375 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(375 100) math:remainder 75}] + [ a r:Fact; r:gives {(75 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(75 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2375]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 375]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 75]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4688 a r:Inference; + r:gives { + 2376 :numberToDigits (2 3 7 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2376 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2376 1000) math:remainder 376}] + [ a r:Fact; r:gives {(376 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(376 100) math:remainder 76}] + [ a r:Fact; r:gives {(76 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(76 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2376]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 376]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 76]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4689 a r:Inference; + r:gives { + 2377 :numberToDigits (2 3 7 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2377 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2377 1000) math:remainder 377}] + [ a r:Fact; r:gives {(377 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(377 100) math:remainder 77}] + [ a r:Fact; r:gives {(77 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(77 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 77]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4690 a r:Inference; + r:gives { + (2 3 7 7) :digitsToNumber 2377 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(2000 300 70 7) math:sum 2377}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4691 a r:Inference; + r:gives { + (7 7 3 2) :digitsToNumber 7732 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(7000 700 30 2) math:sum 7732}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4692 a r:Inference; + r:gives { + 2378 :numberToDigits (2 3 7 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2378 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2378 1000) math:remainder 378}] + [ a r:Fact; r:gives {(378 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(378 100) math:remainder 78}] + [ a r:Fact; r:gives {(78 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(78 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 78]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4693 a r:Inference; + r:gives { + (2 3 7 8) :digitsToNumber 2378 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(2000 300 70 8) math:sum 2378}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4694 a r:Inference; + r:gives { + (8 7 3 2) :digitsToNumber 8732 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(8000 700 30 2) math:sum 8732}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4695 a r:Inference; + r:gives { + 2379 :numberToDigits (2 3 7 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2379 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2379 1000) math:remainder 379}] + [ a r:Fact; r:gives {(379 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(379 100) math:remainder 79}] + [ a r:Fact; r:gives {(79 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(79 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 79]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4696 a r:Inference; + r:gives { + (2 3 7 9) :digitsToNumber 2379 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(2000 300 70 9) math:sum 2379}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4697 a r:Inference; + r:gives { + (9 7 3 2) :digitsToNumber 9732 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(9000 700 30 2) math:sum 9732}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4698 a r:Inference; + r:gives { + 2380 :numberToDigits (2 3 8 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2380 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2380 1000) math:remainder 380}] + [ a r:Fact; r:gives {(380 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(380 100) math:remainder 80}] + [ a r:Fact; r:gives {(80 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(80 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2380]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 380]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4699 a r:Inference; + r:gives { + 2381 :numberToDigits (2 3 8 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2381 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2381 1000) math:remainder 381}] + [ a r:Fact; r:gives {(381 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(381 100) math:remainder 81}] + [ a r:Fact; r:gives {(81 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(81 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2381]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 381]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 81]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4700 a r:Inference; + r:gives { + 2382 :numberToDigits (2 3 8 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2382 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2382 1000) math:remainder 382}] + [ a r:Fact; r:gives {(382 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(382 100) math:remainder 82}] + [ a r:Fact; r:gives {(82 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(82 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2382]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 382]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 82]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4701 a r:Inference; + r:gives { + 2383 :numberToDigits (2 3 8 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2383 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2383 1000) math:remainder 383}] + [ a r:Fact; r:gives {(383 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(383 100) math:remainder 83}] + [ a r:Fact; r:gives {(83 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(83 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2383]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 383]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 83]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4702 a r:Inference; + r:gives { + 2384 :numberToDigits (2 3 8 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2384 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2384 1000) math:remainder 384}] + [ a r:Fact; r:gives {(384 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(384 100) math:remainder 84}] + [ a r:Fact; r:gives {(84 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(84 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2384]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 384]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 84]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4703 a r:Inference; + r:gives { + 2385 :numberToDigits (2 3 8 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2385 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2385 1000) math:remainder 385}] + [ a r:Fact; r:gives {(385 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(385 100) math:remainder 85}] + [ a r:Fact; r:gives {(85 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(85 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2385]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 385]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 85]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4704 a r:Inference; + r:gives { + 2386 :numberToDigits (2 3 8 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2386 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2386 1000) math:remainder 386}] + [ a r:Fact; r:gives {(386 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(386 100) math:remainder 86}] + [ a r:Fact; r:gives {(86 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(86 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2386]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 386]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 86]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4705 a r:Inference; + r:gives { + 2387 :numberToDigits (2 3 8 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2387 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2387 1000) math:remainder 387}] + [ a r:Fact; r:gives {(387 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(387 100) math:remainder 87}] + [ a r:Fact; r:gives {(87 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(87 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2387]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 387]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 87]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4706 a r:Inference; + r:gives { + 2388 :numberToDigits (2 3 8 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2388 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2388 1000) math:remainder 388}] + [ a r:Fact; r:gives {(388 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(388 100) math:remainder 88}] + [ a r:Fact; r:gives {(88 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(88 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 88]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4707 a r:Inference; + r:gives { + (2 3 8 8) :digitsToNumber 2388 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(8 10) math:product 80}] + [ a r:Fact; r:gives {(2000 300 80 8) math:sum 2388}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4708 a r:Inference; + r:gives { + (8 8 3 2) :digitsToNumber 8832 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(8 100) math:product 800}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(8000 800 30 2) math:sum 8832}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4709 a r:Inference; + r:gives { + 2389 :numberToDigits (2 3 8 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2389 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2389 1000) math:remainder 389}] + [ a r:Fact; r:gives {(389 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(389 100) math:remainder 89}] + [ a r:Fact; r:gives {(89 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(89 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 89]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4710 a r:Inference; + r:gives { + (2 3 8 9) :digitsToNumber 2389 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(8 10) math:product 80}] + [ a r:Fact; r:gives {(2000 300 80 9) math:sum 2389}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4711 a r:Inference; + r:gives { + (9 8 3 2) :digitsToNumber 9832 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(8 100) math:product 800}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(9000 800 30 2) math:sum 9832}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4712 a r:Inference; + r:gives { + 2390 :numberToDigits (2 3 9 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2390 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2390 1000) math:remainder 390}] + [ a r:Fact; r:gives {(390 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(390 100) math:remainder 90}] + [ a r:Fact; r:gives {(90 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(90 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2390]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 390]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4713 a r:Inference; + r:gives { + 2391 :numberToDigits (2 3 9 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2391 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2391 1000) math:remainder 391}] + [ a r:Fact; r:gives {(391 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(391 100) math:remainder 91}] + [ a r:Fact; r:gives {(91 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(91 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2391]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 391]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 91]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4714 a r:Inference; + r:gives { + 2392 :numberToDigits (2 3 9 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2392 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2392 1000) math:remainder 392}] + [ a r:Fact; r:gives {(392 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(392 100) math:remainder 92}] + [ a r:Fact; r:gives {(92 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(92 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2392]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 392]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 92]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4715 a r:Inference; + r:gives { + 2393 :numberToDigits (2 3 9 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2393 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2393 1000) math:remainder 393}] + [ a r:Fact; r:gives {(393 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(393 100) math:remainder 93}] + [ a r:Fact; r:gives {(93 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(93 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2393]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 393]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 93]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4716 a r:Inference; + r:gives { + 2394 :numberToDigits (2 3 9 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2394 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2394 1000) math:remainder 394}] + [ a r:Fact; r:gives {(394 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(394 100) math:remainder 94}] + [ a r:Fact; r:gives {(94 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(94 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2394]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 394]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 94]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4717 a r:Inference; + r:gives { + 2395 :numberToDigits (2 3 9 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2395 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2395 1000) math:remainder 395}] + [ a r:Fact; r:gives {(395 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(395 100) math:remainder 95}] + [ a r:Fact; r:gives {(95 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(95 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2395]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 395]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 95]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4718 a r:Inference; + r:gives { + 2396 :numberToDigits (2 3 9 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2396 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2396 1000) math:remainder 396}] + [ a r:Fact; r:gives {(396 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(396 100) math:remainder 96}] + [ a r:Fact; r:gives {(96 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(96 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2396]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 396]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 96]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4719 a r:Inference; + r:gives { + 2397 :numberToDigits (2 3 9 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2397 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2397 1000) math:remainder 397}] + [ a r:Fact; r:gives {(397 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(397 100) math:remainder 97}] + [ a r:Fact; r:gives {(97 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(97 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2397]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 397]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 97]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4720 a r:Inference; + r:gives { + 2398 :numberToDigits (2 3 9 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2398 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2398 1000) math:remainder 398}] + [ a r:Fact; r:gives {(398 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(398 100) math:remainder 98}] + [ a r:Fact; r:gives {(98 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(98 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2398]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 398]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 98]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4721 a r:Inference; + r:gives { + 2399 :numberToDigits (2 3 9 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2399 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2399 1000) math:remainder 399}] + [ a r:Fact; r:gives {(399 100) math:integerQuotient 3}] + [ a r:Fact; r:gives {(399 100) math:remainder 99}] + [ a r:Fact; r:gives {(99 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(99 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 99]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4722 a r:Inference; + r:gives { + (2 3 9 9) :digitsToNumber 2399 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 100) math:product 300}] + [ a r:Fact; r:gives {(9 10) math:product 90}] + [ a r:Fact; r:gives {(2000 300 90 9) math:sum 2399}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4723 a r:Inference; + r:gives { + (9 9 3 2) :digitsToNumber 9932 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(9 100) math:product 900}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(9000 900 30 2) math:sum 9932}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 900]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9932]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4724 a r:Inference; + r:gives { + 2400 :numberToDigits (2 4 0 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2400 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2400 1000) math:remainder 400}] + [ a r:Fact; r:gives {(400 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(400 100) math:remainder 0}] + [ a r:Fact; r:gives {(0 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(0 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4725 a r:Inference; + r:gives { + 2401 :numberToDigits (2 4 0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2401 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2401 1000) math:remainder 401}] + [ a r:Fact; r:gives {(401 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(401 100) math:remainder 1}] + [ a r:Fact; r:gives {(1 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(1 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2401]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 401]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4726 a r:Inference; + r:gives { + 2402 :numberToDigits (2 4 0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2402 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2402 1000) math:remainder 402}] + [ a r:Fact; r:gives {(402 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(402 100) math:remainder 2}] + [ a r:Fact; r:gives {(2 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(2 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2402]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 402]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4727 a r:Inference; + r:gives { + 2403 :numberToDigits (2 4 0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2403 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2403 1000) math:remainder 403}] + [ a r:Fact; r:gives {(403 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(403 100) math:remainder 3}] + [ a r:Fact; r:gives {(3 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(3 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2403]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 403]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4728 a r:Inference; + r:gives { + 2404 :numberToDigits (2 4 0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2404 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2404 1000) math:remainder 404}] + [ a r:Fact; r:gives {(404 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(404 100) math:remainder 4}] + [ a r:Fact; r:gives {(4 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(4 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2404]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 404]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4729 a r:Inference; + r:gives { + 2405 :numberToDigits (2 4 0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2405 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2405 1000) math:remainder 405}] + [ a r:Fact; r:gives {(405 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(405 100) math:remainder 5}] + [ a r:Fact; r:gives {(5 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(5 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2405]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 405]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4730 a r:Inference; + r:gives { + 2406 :numberToDigits (2 4 0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2406 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2406 1000) math:remainder 406}] + [ a r:Fact; r:gives {(406 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(406 100) math:remainder 6}] + [ a r:Fact; r:gives {(6 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(6 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2406]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 406]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4731 a r:Inference; + r:gives { + 2407 :numberToDigits (2 4 0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2407 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2407 1000) math:remainder 407}] + [ a r:Fact; r:gives {(407 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(407 100) math:remainder 7}] + [ a r:Fact; r:gives {(7 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(7 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2407]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 407]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4732 a r:Inference; + r:gives { + 2408 :numberToDigits (2 4 0 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2408 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2408 1000) math:remainder 408}] + [ a r:Fact; r:gives {(408 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(408 100) math:remainder 8}] + [ a r:Fact; r:gives {(8 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(8 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2408]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 408]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4733 a r:Inference; + r:gives { + 2409 :numberToDigits (2 4 0 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2409 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2409 1000) math:remainder 409}] + [ a r:Fact; r:gives {(409 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(409 100) math:remainder 9}] + [ a r:Fact; r:gives {(9 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(9 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2409]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 409]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4734 a r:Inference; + r:gives { + 2410 :numberToDigits (2 4 1 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2410 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2410 1000) math:remainder 410}] + [ a r:Fact; r:gives {(410 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(410 100) math:remainder 10}] + [ a r:Fact; r:gives {(10 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(10 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2410]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 410]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4735 a r:Inference; + r:gives { + 2411 :numberToDigits (2 4 1 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2411 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2411 1000) math:remainder 411}] + [ a r:Fact; r:gives {(411 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(411 100) math:remainder 11}] + [ a r:Fact; r:gives {(11 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(11 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2411]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 411]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 11]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4736 a r:Inference; + r:gives { + 2412 :numberToDigits (2 4 1 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2412 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2412 1000) math:remainder 412}] + [ a r:Fact; r:gives {(412 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(412 100) math:remainder 12}] + [ a r:Fact; r:gives {(12 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(12 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2412]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 412]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4737 a r:Inference; + r:gives { + 2413 :numberToDigits (2 4 1 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2413 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2413 1000) math:remainder 413}] + [ a r:Fact; r:gives {(413 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(413 100) math:remainder 13}] + [ a r:Fact; r:gives {(13 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(13 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2413]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 413]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 13]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4738 a r:Inference; + r:gives { + 2414 :numberToDigits (2 4 1 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2414 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2414 1000) math:remainder 414}] + [ a r:Fact; r:gives {(414 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(414 100) math:remainder 14}] + [ a r:Fact; r:gives {(14 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(14 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2414]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 414]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 14]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4739 a r:Inference; + r:gives { + 2415 :numberToDigits (2 4 1 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2415 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2415 1000) math:remainder 415}] + [ a r:Fact; r:gives {(415 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(415 100) math:remainder 15}] + [ a r:Fact; r:gives {(15 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(15 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2415]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 415]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 15]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4740 a r:Inference; + r:gives { + 2416 :numberToDigits (2 4 1 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2416 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2416 1000) math:remainder 416}] + [ a r:Fact; r:gives {(416 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(416 100) math:remainder 16}] + [ a r:Fact; r:gives {(16 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(16 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2416]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 416]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 16]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4741 a r:Inference; + r:gives { + 2417 :numberToDigits (2 4 1 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2417 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2417 1000) math:remainder 417}] + [ a r:Fact; r:gives {(417 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(417 100) math:remainder 17}] + [ a r:Fact; r:gives {(17 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(17 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2417]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 417]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 17]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4742 a r:Inference; + r:gives { + 2418 :numberToDigits (2 4 1 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2418 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2418 1000) math:remainder 418}] + [ a r:Fact; r:gives {(418 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(418 100) math:remainder 18}] + [ a r:Fact; r:gives {(18 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(18 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2418]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 418]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 18]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4743 a r:Inference; + r:gives { + 2419 :numberToDigits (2 4 1 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2419 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2419 1000) math:remainder 419}] + [ a r:Fact; r:gives {(419 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(419 100) math:remainder 19}] + [ a r:Fact; r:gives {(19 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(19 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2419]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 419]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 19]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4744 a r:Inference; + r:gives { + 2420 :numberToDigits (2 4 2 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2420 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2420 1000) math:remainder 420}] + [ a r:Fact; r:gives {(420 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(420 100) math:remainder 20}] + [ a r:Fact; r:gives {(20 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(20 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4745 a r:Inference; + r:gives { + 2421 :numberToDigits (2 4 2 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2421 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2421 1000) math:remainder 421}] + [ a r:Fact; r:gives {(421 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(421 100) math:remainder 21}] + [ a r:Fact; r:gives {(21 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(21 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 21]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4746 a r:Inference; + r:gives { + 2422 :numberToDigits (2 4 2 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2422 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2422 1000) math:remainder 422}] + [ a r:Fact; r:gives {(422 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(422 100) math:remainder 22}] + [ a r:Fact; r:gives {(22 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(22 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4747 a r:Inference; + r:gives { + 2423 :numberToDigits (2 4 2 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2423 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2423 1000) math:remainder 423}] + [ a r:Fact; r:gives {(423 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(423 100) math:remainder 23}] + [ a r:Fact; r:gives {(23 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(23 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2423]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 423]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4748 a r:Inference; + r:gives { + 2424 :numberToDigits (2 4 2 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2424 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2424 1000) math:remainder 424}] + [ a r:Fact; r:gives {(424 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(424 100) math:remainder 24}] + [ a r:Fact; r:gives {(24 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(24 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2424]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 424]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4749 a r:Inference; + r:gives { + 2425 :numberToDigits (2 4 2 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2425 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2425 1000) math:remainder 425}] + [ a r:Fact; r:gives {(425 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(425 100) math:remainder 25}] + [ a r:Fact; r:gives {(25 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(25 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2425]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 425]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4750 a r:Inference; + r:gives { + 2426 :numberToDigits (2 4 2 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2426 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2426 1000) math:remainder 426}] + [ a r:Fact; r:gives {(426 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(426 100) math:remainder 26}] + [ a r:Fact; r:gives {(26 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(26 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2426]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 426]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4751 a r:Inference; + r:gives { + 2427 :numberToDigits (2 4 2 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2427 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2427 1000) math:remainder 427}] + [ a r:Fact; r:gives {(427 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(427 100) math:remainder 27}] + [ a r:Fact; r:gives {(27 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(27 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2427]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 427]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4752 a r:Inference; + r:gives { + 2428 :numberToDigits (2 4 2 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2428 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2428 1000) math:remainder 428}] + [ a r:Fact; r:gives {(428 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(428 100) math:remainder 28}] + [ a r:Fact; r:gives {(28 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(28 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2428]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 428]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4753 a r:Inference; + r:gives { + 2429 :numberToDigits (2 4 2 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2429 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2429 1000) math:remainder 429}] + [ a r:Fact; r:gives {(429 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(429 100) math:remainder 29}] + [ a r:Fact; r:gives {(29 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(29 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2429]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 429]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4754 a r:Inference; + r:gives { + 2430 :numberToDigits (2 4 3 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2430 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2430 1000) math:remainder 430}] + [ a r:Fact; r:gives {(430 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(430 100) math:remainder 30}] + [ a r:Fact; r:gives {(30 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(30 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4755 a r:Inference; + r:gives { + 2431 :numberToDigits (2 4 3 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2431 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2431 1000) math:remainder 431}] + [ a r:Fact; r:gives {(431 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(431 100) math:remainder 31}] + [ a r:Fact; r:gives {(31 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(31 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 31]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4756 a r:Inference; + r:gives { + 2432 :numberToDigits (2 4 3 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2432 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2432 1000) math:remainder 432}] + [ a r:Fact; r:gives {(432 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(432 100) math:remainder 32}] + [ a r:Fact; r:gives {(32 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(32 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 32]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4757 a r:Inference; + r:gives { + 2433 :numberToDigits (2 4 3 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2433 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2433 1000) math:remainder 433}] + [ a r:Fact; r:gives {(433 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(433 100) math:remainder 33}] + [ a r:Fact; r:gives {(33 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(33 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 33]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4758 a r:Inference; + r:gives { + 2434 :numberToDigits (2 4 3 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2434 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2434 1000) math:remainder 434}] + [ a r:Fact; r:gives {(434 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(434 100) math:remainder 34}] + [ a r:Fact; r:gives {(34 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(34 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2434]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 434]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 34]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4759 a r:Inference; + r:gives { + 2435 :numberToDigits (2 4 3 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2435 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2435 1000) math:remainder 435}] + [ a r:Fact; r:gives {(435 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(435 100) math:remainder 35}] + [ a r:Fact; r:gives {(35 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(35 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2435]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 435]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 35]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4760 a r:Inference; + r:gives { + 2436 :numberToDigits (2 4 3 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2436 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2436 1000) math:remainder 436}] + [ a r:Fact; r:gives {(436 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(436 100) math:remainder 36}] + [ a r:Fact; r:gives {(36 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(36 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2436]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 436]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 36]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4761 a r:Inference; + r:gives { + 2437 :numberToDigits (2 4 3 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2437 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2437 1000) math:remainder 437}] + [ a r:Fact; r:gives {(437 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(437 100) math:remainder 37}] + [ a r:Fact; r:gives {(37 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(37 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2437]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 437]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 37]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4762 a r:Inference; + r:gives { + 2438 :numberToDigits (2 4 3 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2438 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2438 1000) math:remainder 438}] + [ a r:Fact; r:gives {(438 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(438 100) math:remainder 38}] + [ a r:Fact; r:gives {(38 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(38 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2438]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 438]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 38]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4763 a r:Inference; + r:gives { + 2439 :numberToDigits (2 4 3 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2439 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2439 1000) math:remainder 439}] + [ a r:Fact; r:gives {(439 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(439 100) math:remainder 39}] + [ a r:Fact; r:gives {(39 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(39 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2439]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 439]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 39]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4764 a r:Inference; + r:gives { + 2440 :numberToDigits (2 4 4 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2440 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2440 1000) math:remainder 440}] + [ a r:Fact; r:gives {(440 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(440 100) math:remainder 40}] + [ a r:Fact; r:gives {(40 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(40 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2440]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 440]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4765 a r:Inference; + r:gives { + 2441 :numberToDigits (2 4 4 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2441 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2441 1000) math:remainder 441}] + [ a r:Fact; r:gives {(441 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(441 100) math:remainder 41}] + [ a r:Fact; r:gives {(41 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(41 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2441]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 441]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 41]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4766 a r:Inference; + r:gives { + 2442 :numberToDigits (2 4 4 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2442 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2442 1000) math:remainder 442}] + [ a r:Fact; r:gives {(442 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(442 100) math:remainder 42}] + [ a r:Fact; r:gives {(42 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(42 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 42]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4767 a r:Inference; + r:gives { + 2443 :numberToDigits (2 4 4 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2443 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2443 1000) math:remainder 443}] + [ a r:Fact; r:gives {(443 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(443 100) math:remainder 43}] + [ a r:Fact; r:gives {(43 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(43 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 43]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4768 a r:Inference; + r:gives { + 2444 :numberToDigits (2 4 4 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2444 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2444 1000) math:remainder 444}] + [ a r:Fact; r:gives {(444 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(444 100) math:remainder 44}] + [ a r:Fact; r:gives {(44 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(44 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 44]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4769 a r:Inference; + r:gives { + (2 4 4 4) :digitsToNumber 2444 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(2000 400 40 4) math:sum 2444}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6764. + +skolem:lemma4770 a r:Inference; + r:gives { + (4 4 4 2) :digitsToNumber 4442 . + }; + r:evidence ( + [ a r:Fact; r:gives {(4 1000) math:product 4000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(4000 400 40 2) math:sum 4442}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4771 a r:Inference; + r:gives { + 2445 :numberToDigits (2 4 4 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2445 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2445 1000) math:remainder 445}] + [ a r:Fact; r:gives {(445 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(445 100) math:remainder 45}] + [ a r:Fact; r:gives {(45 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(45 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2445]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 445]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 45]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4772 a r:Inference; + r:gives { + (2 4 4 5) :digitsToNumber 2445 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(2000 400 40 5) math:sum 2445}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2445]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6764. + +skolem:lemma4773 a r:Inference; + r:gives { + (5 4 4 2) :digitsToNumber 5442 . + }; + r:evidence ( + [ a r:Fact; r:gives {(5 1000) math:product 5000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(5000 400 40 2) math:sum 5442}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4774 a r:Inference; + r:gives { + 2446 :numberToDigits (2 4 4 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2446 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2446 1000) math:remainder 446}] + [ a r:Fact; r:gives {(446 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(446 100) math:remainder 46}] + [ a r:Fact; r:gives {(46 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(46 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2446]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 446]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 46]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4775 a r:Inference; + r:gives { + (2 4 4 6) :digitsToNumber 2446 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(2000 400 40 6) math:sum 2446}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2446]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4776 a r:Inference; + r:gives { + (6 4 4 2) :digitsToNumber 6442 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(6000 400 40 2) math:sum 6442}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4777 a r:Inference; + r:gives { + 2447 :numberToDigits (2 4 4 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2447 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2447 1000) math:remainder 447}] + [ a r:Fact; r:gives {(447 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(447 100) math:remainder 47}] + [ a r:Fact; r:gives {(47 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(47 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2447]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 447]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 47]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4778 a r:Inference; + r:gives { + (2 4 4 7) :digitsToNumber 2447 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(2000 400 40 7) math:sum 2447}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2447]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4779 a r:Inference; + r:gives { + (7 4 4 2) :digitsToNumber 7442 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(7000 400 40 2) math:sum 7442}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4780 a r:Inference; + r:gives { + 2448 :numberToDigits (2 4 4 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2448 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2448 1000) math:remainder 448}] + [ a r:Fact; r:gives {(448 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(448 100) math:remainder 48}] + [ a r:Fact; r:gives {(48 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(48 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2448]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 448]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 48]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4781 a r:Inference; + r:gives { + (2 4 4 8) :digitsToNumber 2448 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(2000 400 40 8) math:sum 2448}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2448]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4782 a r:Inference; + r:gives { + (8 4 4 2) :digitsToNumber 8442 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(8000 400 40 2) math:sum 8442}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4783 a r:Inference; + r:gives { + 2449 :numberToDigits (2 4 4 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2449 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2449 1000) math:remainder 449}] + [ a r:Fact; r:gives {(449 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(449 100) math:remainder 49}] + [ a r:Fact; r:gives {(49 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(49 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2449]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 449]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 49]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4784 a r:Inference; + r:gives { + (2 4 4 9) :digitsToNumber 2449 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(2000 400 40 9) math:sum 2449}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2449]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4785 a r:Inference; + r:gives { + (9 4 4 2) :digitsToNumber 9442 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(9000 400 40 2) math:sum 9442}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4786 a r:Inference; + r:gives { + 2450 :numberToDigits (2 4 5 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2450 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2450 1000) math:remainder 450}] + [ a r:Fact; r:gives {(450 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(450 100) math:remainder 50}] + [ a r:Fact; r:gives {(50 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(50 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2450]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 450]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4787 a r:Inference; + r:gives { + 2451 :numberToDigits (2 4 5 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2451 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2451 1000) math:remainder 451}] + [ a r:Fact; r:gives {(451 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(451 100) math:remainder 51}] + [ a r:Fact; r:gives {(51 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(51 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2451]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 451]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 51]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4788 a r:Inference; + r:gives { + 2452 :numberToDigits (2 4 5 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2452 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2452 1000) math:remainder 452}] + [ a r:Fact; r:gives {(452 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(452 100) math:remainder 52}] + [ a r:Fact; r:gives {(52 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(52 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2452]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 452]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 52]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4789 a r:Inference; + r:gives { + 2453 :numberToDigits (2 4 5 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2453 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2453 1000) math:remainder 453}] + [ a r:Fact; r:gives {(453 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(453 100) math:remainder 53}] + [ a r:Fact; r:gives {(53 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(53 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2453]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 453]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 53]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4790 a r:Inference; + r:gives { + 2454 :numberToDigits (2 4 5 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2454 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2454 1000) math:remainder 454}] + [ a r:Fact; r:gives {(454 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(454 100) math:remainder 54}] + [ a r:Fact; r:gives {(54 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(54 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2454]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 454]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 54]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4791 a r:Inference; + r:gives { + 2455 :numberToDigits (2 4 5 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2455 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2455 1000) math:remainder 455}] + [ a r:Fact; r:gives {(455 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(455 100) math:remainder 55}] + [ a r:Fact; r:gives {(55 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(55 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2455]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 455]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 55]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4792 a r:Inference; + r:gives { + (2 4 5 5) :digitsToNumber 2455 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(2000 400 50 5) math:sum 2455}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2455]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6764. + +skolem:lemma4793 a r:Inference; + r:gives { + (5 5 4 2) :digitsToNumber 5542 . + }; + r:evidence ( + [ a r:Fact; r:gives {(5 1000) math:product 5000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(5000 500 40 2) math:sum 5542}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4794 a r:Inference; + r:gives { + 2456 :numberToDigits (2 4 5 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2456 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2456 1000) math:remainder 456}] + [ a r:Fact; r:gives {(456 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(456 100) math:remainder 56}] + [ a r:Fact; r:gives {(56 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(56 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 56]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4795 a r:Inference; + r:gives { + (2 4 5 6) :digitsToNumber 2456 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(2000 400 50 6) math:sum 2456}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4796 a r:Inference; + r:gives { + (6 5 4 2) :digitsToNumber 6542 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(6000 500 40 2) math:sum 6542}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4797 a r:Inference; + r:gives { + 2457 :numberToDigits (2 4 5 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2457 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2457 1000) math:remainder 457}] + [ a r:Fact; r:gives {(457 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(457 100) math:remainder 57}] + [ a r:Fact; r:gives {(57 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(57 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2457]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 457]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 57]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4798 a r:Inference; + r:gives { + (2 4 5 7) :digitsToNumber 2457 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(2000 400 50 7) math:sum 2457}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2457]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4799 a r:Inference; + r:gives { + (7 5 4 2) :digitsToNumber 7542 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(7000 500 40 2) math:sum 7542}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4800 a r:Inference; + r:gives { + 2458 :numberToDigits (2 4 5 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2458 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2458 1000) math:remainder 458}] + [ a r:Fact; r:gives {(458 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(458 100) math:remainder 58}] + [ a r:Fact; r:gives {(58 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(58 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2458]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 458]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 58]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4801 a r:Inference; + r:gives { + (2 4 5 8) :digitsToNumber 2458 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(2000 400 50 8) math:sum 2458}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2458]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4802 a r:Inference; + r:gives { + (8 5 4 2) :digitsToNumber 8542 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(8000 500 40 2) math:sum 8542}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4803 a r:Inference; + r:gives { + 2459 :numberToDigits (2 4 5 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2459 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2459 1000) math:remainder 459}] + [ a r:Fact; r:gives {(459 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(459 100) math:remainder 59}] + [ a r:Fact; r:gives {(59 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(59 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2459]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 459]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 59]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4804 a r:Inference; + r:gives { + (2 4 5 9) :digitsToNumber 2459 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(2000 400 50 9) math:sum 2459}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2459]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4805 a r:Inference; + r:gives { + (9 5 4 2) :digitsToNumber 9542 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(9000 500 40 2) math:sum 9542}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4806 a r:Inference; + r:gives { + 2460 :numberToDigits (2 4 6 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2460 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2460 1000) math:remainder 460}] + [ a r:Fact; r:gives {(460 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(460 100) math:remainder 60}] + [ a r:Fact; r:gives {(60 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(60 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2460]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 460]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4807 a r:Inference; + r:gives { + 2461 :numberToDigits (2 4 6 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2461 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2461 1000) math:remainder 461}] + [ a r:Fact; r:gives {(461 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(461 100) math:remainder 61}] + [ a r:Fact; r:gives {(61 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(61 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2461]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 461]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 61]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4808 a r:Inference; + r:gives { + 2462 :numberToDigits (2 4 6 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2462 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2462 1000) math:remainder 462}] + [ a r:Fact; r:gives {(462 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(462 100) math:remainder 62}] + [ a r:Fact; r:gives {(62 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(62 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2462]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 462]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 62]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4809 a r:Inference; + r:gives { + 2463 :numberToDigits (2 4 6 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2463 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2463 1000) math:remainder 463}] + [ a r:Fact; r:gives {(463 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(463 100) math:remainder 63}] + [ a r:Fact; r:gives {(63 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(63 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2463]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 463]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 63]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4810 a r:Inference; + r:gives { + 2464 :numberToDigits (2 4 6 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2464 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2464 1000) math:remainder 464}] + [ a r:Fact; r:gives {(464 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(464 100) math:remainder 64}] + [ a r:Fact; r:gives {(64 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(64 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2464]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 464]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 64]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4811 a r:Inference; + r:gives { + 2465 :numberToDigits (2 4 6 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2465 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2465 1000) math:remainder 465}] + [ a r:Fact; r:gives {(465 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(465 100) math:remainder 65}] + [ a r:Fact; r:gives {(65 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(65 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2465]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 465]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 65]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4812 a r:Inference; + r:gives { + 2466 :numberToDigits (2 4 6 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2466 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2466 1000) math:remainder 466}] + [ a r:Fact; r:gives {(466 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(466 100) math:remainder 66}] + [ a r:Fact; r:gives {(66 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(66 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2466]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 466]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 66]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4813 a r:Inference; + r:gives { + (2 4 6 6) :digitsToNumber 2466 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(2000 400 60 6) math:sum 2466}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2466]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4814 a r:Inference; + r:gives { + (6 6 4 2) :digitsToNumber 6642 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(6000 600 40 2) math:sum 6642}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4815 a r:Inference; + r:gives { + 2467 :numberToDigits (2 4 6 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2467 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2467 1000) math:remainder 467}] + [ a r:Fact; r:gives {(467 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(467 100) math:remainder 67}] + [ a r:Fact; r:gives {(67 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(67 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2467]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 467]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 67]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4816 a r:Inference; + r:gives { + (2 4 6 7) :digitsToNumber 2467 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(2000 400 60 7) math:sum 2467}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2467]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4817 a r:Inference; + r:gives { + (7 6 4 2) :digitsToNumber 7642 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(7000 600 40 2) math:sum 7642}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4818 a r:Inference; + r:gives { + 2468 :numberToDigits (2 4 6 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2468 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2468 1000) math:remainder 468}] + [ a r:Fact; r:gives {(468 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(468 100) math:remainder 68}] + [ a r:Fact; r:gives {(68 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(68 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2468]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 468]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 68]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4819 a r:Inference; + r:gives { + (2 4 6 8) :digitsToNumber 2468 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(2000 400 60 8) math:sum 2468}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2468]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4820 a r:Inference; + r:gives { + (8 6 4 2) :digitsToNumber 8642 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(8000 600 40 2) math:sum 8642}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4821 a r:Inference; + r:gives { + 2469 :numberToDigits (2 4 6 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2469 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2469 1000) math:remainder 469}] + [ a r:Fact; r:gives {(469 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(469 100) math:remainder 69}] + [ a r:Fact; r:gives {(69 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(69 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2469]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 469]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 69]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4822 a r:Inference; + r:gives { + (2 4 6 9) :digitsToNumber 2469 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(2000 400 60 9) math:sum 2469}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2469]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4823 a r:Inference; + r:gives { + (9 6 4 2) :digitsToNumber 9642 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(9000 600 40 2) math:sum 9642}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4824 a r:Inference; + r:gives { + 2470 :numberToDigits (2 4 7 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2470 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2470 1000) math:remainder 470}] + [ a r:Fact; r:gives {(470 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(470 100) math:remainder 70}] + [ a r:Fact; r:gives {(70 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(70 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2470]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 470]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4825 a r:Inference; + r:gives { + 2471 :numberToDigits (2 4 7 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2471 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2471 1000) math:remainder 471}] + [ a r:Fact; r:gives {(471 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(471 100) math:remainder 71}] + [ a r:Fact; r:gives {(71 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(71 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2471]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 471]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 71]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4826 a r:Inference; + r:gives { + 2472 :numberToDigits (2 4 7 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2472 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2472 1000) math:remainder 472}] + [ a r:Fact; r:gives {(472 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(472 100) math:remainder 72}] + [ a r:Fact; r:gives {(72 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(72 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2472]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 472]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 72]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4827 a r:Inference; + r:gives { + 2473 :numberToDigits (2 4 7 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2473 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2473 1000) math:remainder 473}] + [ a r:Fact; r:gives {(473 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(473 100) math:remainder 73}] + [ a r:Fact; r:gives {(73 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(73 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2473]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 473]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 73]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4828 a r:Inference; + r:gives { + 2474 :numberToDigits (2 4 7 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2474 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2474 1000) math:remainder 474}] + [ a r:Fact; r:gives {(474 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(474 100) math:remainder 74}] + [ a r:Fact; r:gives {(74 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(74 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2474]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 474]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 74]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4829 a r:Inference; + r:gives { + 2475 :numberToDigits (2 4 7 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2475 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2475 1000) math:remainder 475}] + [ a r:Fact; r:gives {(475 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(475 100) math:remainder 75}] + [ a r:Fact; r:gives {(75 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(75 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2475]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 475]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 75]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4830 a r:Inference; + r:gives { + 2476 :numberToDigits (2 4 7 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2476 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2476 1000) math:remainder 476}] + [ a r:Fact; r:gives {(476 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(476 100) math:remainder 76}] + [ a r:Fact; r:gives {(76 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(76 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2476]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 476]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 76]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4831 a r:Inference; + r:gives { + 2477 :numberToDigits (2 4 7 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2477 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2477 1000) math:remainder 477}] + [ a r:Fact; r:gives {(477 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(477 100) math:remainder 77}] + [ a r:Fact; r:gives {(77 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(77 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2477]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 477]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 77]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4832 a r:Inference; + r:gives { + (2 4 7 7) :digitsToNumber 2477 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(2000 400 70 7) math:sum 2477}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2477]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4833 a r:Inference; + r:gives { + (7 7 4 2) :digitsToNumber 7742 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(7000 700 40 2) math:sum 7742}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4834 a r:Inference; + r:gives { + 2478 :numberToDigits (2 4 7 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2478 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2478 1000) math:remainder 478}] + [ a r:Fact; r:gives {(478 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(478 100) math:remainder 78}] + [ a r:Fact; r:gives {(78 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(78 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2478]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 478]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 78]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4835 a r:Inference; + r:gives { + (2 4 7 8) :digitsToNumber 2478 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(2000 400 70 8) math:sum 2478}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2478]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4836 a r:Inference; + r:gives { + (8 7 4 2) :digitsToNumber 8742 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(8000 700 40 2) math:sum 8742}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4837 a r:Inference; + r:gives { + 2479 :numberToDigits (2 4 7 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2479 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2479 1000) math:remainder 479}] + [ a r:Fact; r:gives {(479 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(479 100) math:remainder 79}] + [ a r:Fact; r:gives {(79 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(79 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2479]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 479]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 79]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4838 a r:Inference; + r:gives { + (2 4 7 9) :digitsToNumber 2479 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(2000 400 70 9) math:sum 2479}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2479]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4839 a r:Inference; + r:gives { + (9 7 4 2) :digitsToNumber 9742 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(9000 700 40 2) math:sum 9742}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4840 a r:Inference; + r:gives { + 2480 :numberToDigits (2 4 8 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2480 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2480 1000) math:remainder 480}] + [ a r:Fact; r:gives {(480 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(480 100) math:remainder 80}] + [ a r:Fact; r:gives {(80 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(80 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2480]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 480]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4841 a r:Inference; + r:gives { + 2481 :numberToDigits (2 4 8 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2481 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2481 1000) math:remainder 481}] + [ a r:Fact; r:gives {(481 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(481 100) math:remainder 81}] + [ a r:Fact; r:gives {(81 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(81 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2481]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 481]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 81]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4842 a r:Inference; + r:gives { + 2482 :numberToDigits (2 4 8 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2482 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2482 1000) math:remainder 482}] + [ a r:Fact; r:gives {(482 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(482 100) math:remainder 82}] + [ a r:Fact; r:gives {(82 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(82 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2482]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 482]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 82]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4843 a r:Inference; + r:gives { + 2483 :numberToDigits (2 4 8 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2483 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2483 1000) math:remainder 483}] + [ a r:Fact; r:gives {(483 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(483 100) math:remainder 83}] + [ a r:Fact; r:gives {(83 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(83 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2483]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 483]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 83]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4844 a r:Inference; + r:gives { + 2484 :numberToDigits (2 4 8 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2484 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2484 1000) math:remainder 484}] + [ a r:Fact; r:gives {(484 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(484 100) math:remainder 84}] + [ a r:Fact; r:gives {(84 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(84 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2484]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 484]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 84]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4845 a r:Inference; + r:gives { + 2485 :numberToDigits (2 4 8 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2485 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2485 1000) math:remainder 485}] + [ a r:Fact; r:gives {(485 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(485 100) math:remainder 85}] + [ a r:Fact; r:gives {(85 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(85 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2485]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 485]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 85]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4846 a r:Inference; + r:gives { + 2486 :numberToDigits (2 4 8 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2486 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2486 1000) math:remainder 486}] + [ a r:Fact; r:gives {(486 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(486 100) math:remainder 86}] + [ a r:Fact; r:gives {(86 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(86 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2486]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 486]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 86]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4847 a r:Inference; + r:gives { + 2487 :numberToDigits (2 4 8 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2487 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2487 1000) math:remainder 487}] + [ a r:Fact; r:gives {(487 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(487 100) math:remainder 87}] + [ a r:Fact; r:gives {(87 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(87 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2487]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 487]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 87]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4848 a r:Inference; + r:gives { + 2488 :numberToDigits (2 4 8 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2488 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2488 1000) math:remainder 488}] + [ a r:Fact; r:gives {(488 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(488 100) math:remainder 88}] + [ a r:Fact; r:gives {(88 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(88 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2488]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 488]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 88]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4849 a r:Inference; + r:gives { + (2 4 8 8) :digitsToNumber 2488 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(8 10) math:product 80}] + [ a r:Fact; r:gives {(2000 400 80 8) math:sum 2488}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2488]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4850 a r:Inference; + r:gives { + (8 8 4 2) :digitsToNumber 8842 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(8 100) math:product 800}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(8000 800 40 2) math:sum 8842}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8842]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4851 a r:Inference; + r:gives { + 2489 :numberToDigits (2 4 8 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2489 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2489 1000) math:remainder 489}] + [ a r:Fact; r:gives {(489 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(489 100) math:remainder 89}] + [ a r:Fact; r:gives {(89 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(89 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2489]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 489]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 89]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4852 a r:Inference; + r:gives { + (2 4 8 9) :digitsToNumber 2489 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(8 10) math:product 80}] + [ a r:Fact; r:gives {(2000 400 80 9) math:sum 2489}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2489]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4853 a r:Inference; + r:gives { + (9 8 4 2) :digitsToNumber 9842 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(8 100) math:product 800}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(9000 800 40 2) math:sum 9842}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9842]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4854 a r:Inference; + r:gives { + 2490 :numberToDigits (2 4 9 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2490 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2490 1000) math:remainder 490}] + [ a r:Fact; r:gives {(490 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(490 100) math:remainder 90}] + [ a r:Fact; r:gives {(90 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(90 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2490]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 490]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4855 a r:Inference; + r:gives { + 2491 :numberToDigits (2 4 9 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2491 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2491 1000) math:remainder 491}] + [ a r:Fact; r:gives {(491 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(491 100) math:remainder 91}] + [ a r:Fact; r:gives {(91 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(91 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2491]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 491]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 91]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4856 a r:Inference; + r:gives { + 2492 :numberToDigits (2 4 9 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2492 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2492 1000) math:remainder 492}] + [ a r:Fact; r:gives {(492 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(492 100) math:remainder 92}] + [ a r:Fact; r:gives {(92 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(92 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2492]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 492]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 92]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4857 a r:Inference; + r:gives { + 2493 :numberToDigits (2 4 9 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2493 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2493 1000) math:remainder 493}] + [ a r:Fact; r:gives {(493 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(493 100) math:remainder 93}] + [ a r:Fact; r:gives {(93 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(93 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2493]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 493]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 93]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4858 a r:Inference; + r:gives { + 2494 :numberToDigits (2 4 9 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2494 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2494 1000) math:remainder 494}] + [ a r:Fact; r:gives {(494 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(494 100) math:remainder 94}] + [ a r:Fact; r:gives {(94 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(94 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2494]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 494]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 94]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4859 a r:Inference; + r:gives { + 2495 :numberToDigits (2 4 9 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2495 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2495 1000) math:remainder 495}] + [ a r:Fact; r:gives {(495 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(495 100) math:remainder 95}] + [ a r:Fact; r:gives {(95 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(95 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2495]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 495]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 95]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4860 a r:Inference; + r:gives { + 2496 :numberToDigits (2 4 9 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2496 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2496 1000) math:remainder 496}] + [ a r:Fact; r:gives {(496 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(496 100) math:remainder 96}] + [ a r:Fact; r:gives {(96 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(96 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2496]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 496]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 96]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4861 a r:Inference; + r:gives { + 2497 :numberToDigits (2 4 9 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2497 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2497 1000) math:remainder 497}] + [ a r:Fact; r:gives {(497 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(497 100) math:remainder 97}] + [ a r:Fact; r:gives {(97 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(97 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2497]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 497]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 97]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4862 a r:Inference; + r:gives { + 2498 :numberToDigits (2 4 9 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2498 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2498 1000) math:remainder 498}] + [ a r:Fact; r:gives {(498 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(498 100) math:remainder 98}] + [ a r:Fact; r:gives {(98 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(98 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2498]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 498]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 98]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4863 a r:Inference; + r:gives { + 2499 :numberToDigits (2 4 9 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2499 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2499 1000) math:remainder 499}] + [ a r:Fact; r:gives {(499 100) math:integerQuotient 4}] + [ a r:Fact; r:gives {(499 100) math:remainder 99}] + [ a r:Fact; r:gives {(99 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(99 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2499]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 499]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 99]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4864 a r:Inference; + r:gives { + (2 4 9 9) :digitsToNumber 2499 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(4 100) math:product 400}] + [ a r:Fact; r:gives {(9 10) math:product 90}] + [ a r:Fact; r:gives {(2000 400 90 9) math:sum 2499}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2499]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4865 a r:Inference; + r:gives { + (9 9 4 2) :digitsToNumber 9942 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(9 100) math:product 900}] + [ a r:Fact; r:gives {(4 10) math:product 40}] + [ a r:Fact; r:gives {(9000 900 40 2) math:sum 9942}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 900]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9942]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4866 a r:Inference; + r:gives { + 2500 :numberToDigits (2 5 0 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2500 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2500 1000) math:remainder 500}] + [ a r:Fact; r:gives {(500 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(500 100) math:remainder 0}] + [ a r:Fact; r:gives {(0 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(0 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4867 a r:Inference; + r:gives { + 2501 :numberToDigits (2 5 0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2501 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2501 1000) math:remainder 501}] + [ a r:Fact; r:gives {(501 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(501 100) math:remainder 1}] + [ a r:Fact; r:gives {(1 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(1 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2501]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 501]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4868 a r:Inference; + r:gives { + 2502 :numberToDigits (2 5 0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2502 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2502 1000) math:remainder 502}] + [ a r:Fact; r:gives {(502 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(502 100) math:remainder 2}] + [ a r:Fact; r:gives {(2 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(2 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2502]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 502]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4869 a r:Inference; + r:gives { + 2503 :numberToDigits (2 5 0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2503 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2503 1000) math:remainder 503}] + [ a r:Fact; r:gives {(503 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(503 100) math:remainder 3}] + [ a r:Fact; r:gives {(3 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(3 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2503]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 503]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4870 a r:Inference; + r:gives { + 2504 :numberToDigits (2 5 0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2504 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2504 1000) math:remainder 504}] + [ a r:Fact; r:gives {(504 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(504 100) math:remainder 4}] + [ a r:Fact; r:gives {(4 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(4 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2504]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 504]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4871 a r:Inference; + r:gives { + 2505 :numberToDigits (2 5 0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2505 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2505 1000) math:remainder 505}] + [ a r:Fact; r:gives {(505 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(505 100) math:remainder 5}] + [ a r:Fact; r:gives {(5 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(5 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2505]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 505]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4872 a r:Inference; + r:gives { + 2506 :numberToDigits (2 5 0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2506 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2506 1000) math:remainder 506}] + [ a r:Fact; r:gives {(506 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(506 100) math:remainder 6}] + [ a r:Fact; r:gives {(6 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(6 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2506]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 506]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4873 a r:Inference; + r:gives { + 2507 :numberToDigits (2 5 0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2507 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2507 1000) math:remainder 507}] + [ a r:Fact; r:gives {(507 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(507 100) math:remainder 7}] + [ a r:Fact; r:gives {(7 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(7 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2507]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 507]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4874 a r:Inference; + r:gives { + 2508 :numberToDigits (2 5 0 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2508 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2508 1000) math:remainder 508}] + [ a r:Fact; r:gives {(508 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(508 100) math:remainder 8}] + [ a r:Fact; r:gives {(8 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(8 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2508]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 508]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4875 a r:Inference; + r:gives { + 2509 :numberToDigits (2 5 0 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2509 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2509 1000) math:remainder 509}] + [ a r:Fact; r:gives {(509 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(509 100) math:remainder 9}] + [ a r:Fact; r:gives {(9 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(9 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2509]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 509]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4876 a r:Inference; + r:gives { + 2510 :numberToDigits (2 5 1 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2510 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2510 1000) math:remainder 510}] + [ a r:Fact; r:gives {(510 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(510 100) math:remainder 10}] + [ a r:Fact; r:gives {(10 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(10 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2510]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 510]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4877 a r:Inference; + r:gives { + 2511 :numberToDigits (2 5 1 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2511 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2511 1000) math:remainder 511}] + [ a r:Fact; r:gives {(511 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(511 100) math:remainder 11}] + [ a r:Fact; r:gives {(11 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(11 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2511]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 511]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 11]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4878 a r:Inference; + r:gives { + 2512 :numberToDigits (2 5 1 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2512 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2512 1000) math:remainder 512}] + [ a r:Fact; r:gives {(512 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(512 100) math:remainder 12}] + [ a r:Fact; r:gives {(12 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(12 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2512]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 512]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4879 a r:Inference; + r:gives { + 2513 :numberToDigits (2 5 1 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2513 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2513 1000) math:remainder 513}] + [ a r:Fact; r:gives {(513 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(513 100) math:remainder 13}] + [ a r:Fact; r:gives {(13 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(13 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2513]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 513]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 13]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4880 a r:Inference; + r:gives { + 2514 :numberToDigits (2 5 1 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2514 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2514 1000) math:remainder 514}] + [ a r:Fact; r:gives {(514 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(514 100) math:remainder 14}] + [ a r:Fact; r:gives {(14 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(14 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2514]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 514]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 14]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4881 a r:Inference; + r:gives { + 2515 :numberToDigits (2 5 1 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2515 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2515 1000) math:remainder 515}] + [ a r:Fact; r:gives {(515 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(515 100) math:remainder 15}] + [ a r:Fact; r:gives {(15 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(15 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2515]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 515]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 15]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4882 a r:Inference; + r:gives { + 2516 :numberToDigits (2 5 1 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2516 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2516 1000) math:remainder 516}] + [ a r:Fact; r:gives {(516 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(516 100) math:remainder 16}] + [ a r:Fact; r:gives {(16 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(16 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2516]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 516]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 16]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4883 a r:Inference; + r:gives { + 2517 :numberToDigits (2 5 1 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2517 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2517 1000) math:remainder 517}] + [ a r:Fact; r:gives {(517 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(517 100) math:remainder 17}] + [ a r:Fact; r:gives {(17 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(17 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2517]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 517]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 17]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4884 a r:Inference; + r:gives { + 2518 :numberToDigits (2 5 1 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2518 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2518 1000) math:remainder 518}] + [ a r:Fact; r:gives {(518 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(518 100) math:remainder 18}] + [ a r:Fact; r:gives {(18 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(18 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2518]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 518]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 18]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4885 a r:Inference; + r:gives { + 2519 :numberToDigits (2 5 1 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2519 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2519 1000) math:remainder 519}] + [ a r:Fact; r:gives {(519 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(519 100) math:remainder 19}] + [ a r:Fact; r:gives {(19 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(19 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2519]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 519]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 19]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4886 a r:Inference; + r:gives { + 2520 :numberToDigits (2 5 2 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2520 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2520 1000) math:remainder 520}] + [ a r:Fact; r:gives {(520 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(520 100) math:remainder 20}] + [ a r:Fact; r:gives {(20 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(20 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4887 a r:Inference; + r:gives { + 2521 :numberToDigits (2 5 2 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2521 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2521 1000) math:remainder 521}] + [ a r:Fact; r:gives {(521 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(521 100) math:remainder 21}] + [ a r:Fact; r:gives {(21 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(21 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 21]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4888 a r:Inference; + r:gives { + 2522 :numberToDigits (2 5 2 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2522 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2522 1000) math:remainder 522}] + [ a r:Fact; r:gives {(522 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(522 100) math:remainder 22}] + [ a r:Fact; r:gives {(22 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(22 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4889 a r:Inference; + r:gives { + 2523 :numberToDigits (2 5 2 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2523 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2523 1000) math:remainder 523}] + [ a r:Fact; r:gives {(523 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(523 100) math:remainder 23}] + [ a r:Fact; r:gives {(23 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(23 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2523]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 523]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4890 a r:Inference; + r:gives { + 2524 :numberToDigits (2 5 2 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2524 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2524 1000) math:remainder 524}] + [ a r:Fact; r:gives {(524 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(524 100) math:remainder 24}] + [ a r:Fact; r:gives {(24 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(24 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2524]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 524]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4891 a r:Inference; + r:gives { + 2525 :numberToDigits (2 5 2 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2525 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2525 1000) math:remainder 525}] + [ a r:Fact; r:gives {(525 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(525 100) math:remainder 25}] + [ a r:Fact; r:gives {(25 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(25 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2525]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 525]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4892 a r:Inference; + r:gives { + 2526 :numberToDigits (2 5 2 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2526 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2526 1000) math:remainder 526}] + [ a r:Fact; r:gives {(526 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(526 100) math:remainder 26}] + [ a r:Fact; r:gives {(26 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(26 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2526]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 526]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4893 a r:Inference; + r:gives { + 2527 :numberToDigits (2 5 2 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2527 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2527 1000) math:remainder 527}] + [ a r:Fact; r:gives {(527 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(527 100) math:remainder 27}] + [ a r:Fact; r:gives {(27 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(27 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2527]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 527]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4894 a r:Inference; + r:gives { + 2528 :numberToDigits (2 5 2 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2528 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2528 1000) math:remainder 528}] + [ a r:Fact; r:gives {(528 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(528 100) math:remainder 28}] + [ a r:Fact; r:gives {(28 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(28 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2528]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 528]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4895 a r:Inference; + r:gives { + 2529 :numberToDigits (2 5 2 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2529 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2529 1000) math:remainder 529}] + [ a r:Fact; r:gives {(529 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(529 100) math:remainder 29}] + [ a r:Fact; r:gives {(29 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(29 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2529]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 529]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4896 a r:Inference; + r:gives { + 2530 :numberToDigits (2 5 3 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2530 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2530 1000) math:remainder 530}] + [ a r:Fact; r:gives {(530 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(530 100) math:remainder 30}] + [ a r:Fact; r:gives {(30 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(30 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4897 a r:Inference; + r:gives { + 2531 :numberToDigits (2 5 3 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2531 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2531 1000) math:remainder 531}] + [ a r:Fact; r:gives {(531 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(531 100) math:remainder 31}] + [ a r:Fact; r:gives {(31 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(31 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 31]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4898 a r:Inference; + r:gives { + 2532 :numberToDigits (2 5 3 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2532 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2532 1000) math:remainder 532}] + [ a r:Fact; r:gives {(532 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(532 100) math:remainder 32}] + [ a r:Fact; r:gives {(32 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(32 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 32]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4899 a r:Inference; + r:gives { + 2533 :numberToDigits (2 5 3 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2533 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2533 1000) math:remainder 533}] + [ a r:Fact; r:gives {(533 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(533 100) math:remainder 33}] + [ a r:Fact; r:gives {(33 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(33 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 33]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4900 a r:Inference; + r:gives { + 2534 :numberToDigits (2 5 3 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2534 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2534 1000) math:remainder 534}] + [ a r:Fact; r:gives {(534 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(534 100) math:remainder 34}] + [ a r:Fact; r:gives {(34 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(34 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2534]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 534]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 34]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4901 a r:Inference; + r:gives { + 2535 :numberToDigits (2 5 3 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2535 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2535 1000) math:remainder 535}] + [ a r:Fact; r:gives {(535 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(535 100) math:remainder 35}] + [ a r:Fact; r:gives {(35 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(35 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2535]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 535]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 35]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4902 a r:Inference; + r:gives { + 2536 :numberToDigits (2 5 3 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2536 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2536 1000) math:remainder 536}] + [ a r:Fact; r:gives {(536 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(536 100) math:remainder 36}] + [ a r:Fact; r:gives {(36 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(36 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2536]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 536]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 36]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4903 a r:Inference; + r:gives { + 2537 :numberToDigits (2 5 3 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2537 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2537 1000) math:remainder 537}] + [ a r:Fact; r:gives {(537 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(537 100) math:remainder 37}] + [ a r:Fact; r:gives {(37 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(37 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2537]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 537]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 37]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4904 a r:Inference; + r:gives { + 2538 :numberToDigits (2 5 3 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2538 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2538 1000) math:remainder 538}] + [ a r:Fact; r:gives {(538 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(538 100) math:remainder 38}] + [ a r:Fact; r:gives {(38 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(38 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2538]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 538]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 38]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4905 a r:Inference; + r:gives { + 2539 :numberToDigits (2 5 3 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2539 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2539 1000) math:remainder 539}] + [ a r:Fact; r:gives {(539 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(539 100) math:remainder 39}] + [ a r:Fact; r:gives {(39 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(39 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2539]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 539]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 39]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4906 a r:Inference; + r:gives { + 2540 :numberToDigits (2 5 4 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2540 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2540 1000) math:remainder 540}] + [ a r:Fact; r:gives {(540 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(540 100) math:remainder 40}] + [ a r:Fact; r:gives {(40 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(40 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2540]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 540]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4907 a r:Inference; + r:gives { + 2541 :numberToDigits (2 5 4 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2541 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2541 1000) math:remainder 541}] + [ a r:Fact; r:gives {(541 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(541 100) math:remainder 41}] + [ a r:Fact; r:gives {(41 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(41 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2541]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 541]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 41]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4908 a r:Inference; + r:gives { + 2542 :numberToDigits (2 5 4 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2542 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2542 1000) math:remainder 542}] + [ a r:Fact; r:gives {(542 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(542 100) math:remainder 42}] + [ a r:Fact; r:gives {(42 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(42 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 42]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4909 a r:Inference; + r:gives { + 2543 :numberToDigits (2 5 4 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2543 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2543 1000) math:remainder 543}] + [ a r:Fact; r:gives {(543 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(543 100) math:remainder 43}] + [ a r:Fact; r:gives {(43 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(43 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 43]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4910 a r:Inference; + r:gives { + 2544 :numberToDigits (2 5 4 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2544 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2544 1000) math:remainder 544}] + [ a r:Fact; r:gives {(544 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(544 100) math:remainder 44}] + [ a r:Fact; r:gives {(44 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(44 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2544]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 544]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 44]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4911 a r:Inference; + r:gives { + 2545 :numberToDigits (2 5 4 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2545 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2545 1000) math:remainder 545}] + [ a r:Fact; r:gives {(545 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(545 100) math:remainder 45}] + [ a r:Fact; r:gives {(45 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(45 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2545]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 545]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 45]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4912 a r:Inference; + r:gives { + 2546 :numberToDigits (2 5 4 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2546 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2546 1000) math:remainder 546}] + [ a r:Fact; r:gives {(546 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(546 100) math:remainder 46}] + [ a r:Fact; r:gives {(46 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(46 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2546]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 546]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 46]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4913 a r:Inference; + r:gives { + 2547 :numberToDigits (2 5 4 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2547 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2547 1000) math:remainder 547}] + [ a r:Fact; r:gives {(547 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(547 100) math:remainder 47}] + [ a r:Fact; r:gives {(47 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(47 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2547]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 547]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 47]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4914 a r:Inference; + r:gives { + 2548 :numberToDigits (2 5 4 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2548 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2548 1000) math:remainder 548}] + [ a r:Fact; r:gives {(548 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(548 100) math:remainder 48}] + [ a r:Fact; r:gives {(48 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(48 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2548]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 548]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 48]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4915 a r:Inference; + r:gives { + 2549 :numberToDigits (2 5 4 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2549 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2549 1000) math:remainder 549}] + [ a r:Fact; r:gives {(549 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(549 100) math:remainder 49}] + [ a r:Fact; r:gives {(49 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(49 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2549]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 549]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 49]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4916 a r:Inference; + r:gives { + 2550 :numberToDigits (2 5 5 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2550 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2550 1000) math:remainder 550}] + [ a r:Fact; r:gives {(550 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(550 100) math:remainder 50}] + [ a r:Fact; r:gives {(50 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(50 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2550]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 550]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4917 a r:Inference; + r:gives { + 2551 :numberToDigits (2 5 5 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2551 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2551 1000) math:remainder 551}] + [ a r:Fact; r:gives {(551 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(551 100) math:remainder 51}] + [ a r:Fact; r:gives {(51 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(51 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2551]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 551]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 51]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4918 a r:Inference; + r:gives { + 2552 :numberToDigits (2 5 5 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2552 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2552 1000) math:remainder 552}] + [ a r:Fact; r:gives {(552 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(552 100) math:remainder 52}] + [ a r:Fact; r:gives {(52 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(52 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 52]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4919 a r:Inference; + r:gives { + 2553 :numberToDigits (2 5 5 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2553 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2553 1000) math:remainder 553}] + [ a r:Fact; r:gives {(553 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(553 100) math:remainder 53}] + [ a r:Fact; r:gives {(53 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(53 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 53]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4920 a r:Inference; + r:gives { + 2554 :numberToDigits (2 5 5 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2554 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2554 1000) math:remainder 554}] + [ a r:Fact; r:gives {(554 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(554 100) math:remainder 54}] + [ a r:Fact; r:gives {(54 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(54 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2554]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 554]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 54]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4921 a r:Inference; + r:gives { + 2555 :numberToDigits (2 5 5 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2555 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2555 1000) math:remainder 555}] + [ a r:Fact; r:gives {(555 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(555 100) math:remainder 55}] + [ a r:Fact; r:gives {(55 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(55 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2555]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 555]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 55]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4922 a r:Inference; + r:gives { + (2 5 5 5) :digitsToNumber 2555 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(2000 500 50 5) math:sum 2555}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2555]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6764. + +skolem:lemma4923 a r:Inference; + r:gives { + (5 5 5 2) :digitsToNumber 5552 . + }; + r:evidence ( + [ a r:Fact; r:gives {(5 1000) math:product 5000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(5000 500 50 2) math:sum 5552}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4924 a r:Inference; + r:gives { + 2556 :numberToDigits (2 5 5 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2556 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2556 1000) math:remainder 556}] + [ a r:Fact; r:gives {(556 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(556 100) math:remainder 56}] + [ a r:Fact; r:gives {(56 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(56 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2556]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 556]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 56]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4925 a r:Inference; + r:gives { + (2 5 5 6) :digitsToNumber 2556 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(2000 500 50 6) math:sum 2556}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2556]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4926 a r:Inference; + r:gives { + (6 5 5 2) :digitsToNumber 6552 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(6000 500 50 2) math:sum 6552}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4927 a r:Inference; + r:gives { + 2557 :numberToDigits (2 5 5 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2557 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2557 1000) math:remainder 557}] + [ a r:Fact; r:gives {(557 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(557 100) math:remainder 57}] + [ a r:Fact; r:gives {(57 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(57 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2557]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 557]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 57]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4928 a r:Inference; + r:gives { + (2 5 5 7) :digitsToNumber 2557 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(2000 500 50 7) math:sum 2557}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2557]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4929 a r:Inference; + r:gives { + (7 5 5 2) :digitsToNumber 7552 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(7000 500 50 2) math:sum 7552}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4930 a r:Inference; + r:gives { + 2558 :numberToDigits (2 5 5 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2558 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2558 1000) math:remainder 558}] + [ a r:Fact; r:gives {(558 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(558 100) math:remainder 58}] + [ a r:Fact; r:gives {(58 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(58 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2558]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 558]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 58]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4931 a r:Inference; + r:gives { + (2 5 5 8) :digitsToNumber 2558 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(2000 500 50 8) math:sum 2558}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2558]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4932 a r:Inference; + r:gives { + (8 5 5 2) :digitsToNumber 8552 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(8000 500 50 2) math:sum 8552}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4933 a r:Inference; + r:gives { + 2559 :numberToDigits (2 5 5 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2559 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2559 1000) math:remainder 559}] + [ a r:Fact; r:gives {(559 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(559 100) math:remainder 59}] + [ a r:Fact; r:gives {(59 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(59 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2559]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 559]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 59]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4934 a r:Inference; + r:gives { + (2 5 5 9) :digitsToNumber 2559 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(2000 500 50 9) math:sum 2559}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2559]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4935 a r:Inference; + r:gives { + (9 5 5 2) :digitsToNumber 9552 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(9000 500 50 2) math:sum 9552}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4936 a r:Inference; + r:gives { + 2560 :numberToDigits (2 5 6 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2560 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2560 1000) math:remainder 560}] + [ a r:Fact; r:gives {(560 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(560 100) math:remainder 60}] + [ a r:Fact; r:gives {(60 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(60 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2560]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 560]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4937 a r:Inference; + r:gives { + 2561 :numberToDigits (2 5 6 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2561 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2561 1000) math:remainder 561}] + [ a r:Fact; r:gives {(561 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(561 100) math:remainder 61}] + [ a r:Fact; r:gives {(61 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(61 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2561]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 561]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 61]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4938 a r:Inference; + r:gives { + 2562 :numberToDigits (2 5 6 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2562 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2562 1000) math:remainder 562}] + [ a r:Fact; r:gives {(562 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(562 100) math:remainder 62}] + [ a r:Fact; r:gives {(62 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(62 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2562]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 562]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 62]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4939 a r:Inference; + r:gives { + 2563 :numberToDigits (2 5 6 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2563 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2563 1000) math:remainder 563}] + [ a r:Fact; r:gives {(563 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(563 100) math:remainder 63}] + [ a r:Fact; r:gives {(63 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(63 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2563]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 563]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 63]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4940 a r:Inference; + r:gives { + 2564 :numberToDigits (2 5 6 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2564 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2564 1000) math:remainder 564}] + [ a r:Fact; r:gives {(564 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(564 100) math:remainder 64}] + [ a r:Fact; r:gives {(64 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(64 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2564]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 564]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 64]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4941 a r:Inference; + r:gives { + 2565 :numberToDigits (2 5 6 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2565 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2565 1000) math:remainder 565}] + [ a r:Fact; r:gives {(565 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(565 100) math:remainder 65}] + [ a r:Fact; r:gives {(65 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(65 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2565]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 565]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 65]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4942 a r:Inference; + r:gives { + 2566 :numberToDigits (2 5 6 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2566 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2566 1000) math:remainder 566}] + [ a r:Fact; r:gives {(566 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(566 100) math:remainder 66}] + [ a r:Fact; r:gives {(66 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(66 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2566]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 566]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 66]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4943 a r:Inference; + r:gives { + (2 5 6 6) :digitsToNumber 2566 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(2000 500 60 6) math:sum 2566}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2566]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma4944 a r:Inference; + r:gives { + (6 6 5 2) :digitsToNumber 6652 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(6000 600 50 2) math:sum 6652}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4945 a r:Inference; + r:gives { + 2567 :numberToDigits (2 5 6 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2567 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2567 1000) math:remainder 567}] + [ a r:Fact; r:gives {(567 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(567 100) math:remainder 67}] + [ a r:Fact; r:gives {(67 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(67 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2567]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 567]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 67]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4946 a r:Inference; + r:gives { + (2 5 6 7) :digitsToNumber 2567 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(2000 500 60 7) math:sum 2567}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2567]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4947 a r:Inference; + r:gives { + (7 6 5 2) :digitsToNumber 7652 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(7000 600 50 2) math:sum 7652}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4948 a r:Inference; + r:gives { + 2568 :numberToDigits (2 5 6 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2568 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2568 1000) math:remainder 568}] + [ a r:Fact; r:gives {(568 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(568 100) math:remainder 68}] + [ a r:Fact; r:gives {(68 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(68 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2568]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 568]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 68]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4949 a r:Inference; + r:gives { + (2 5 6 8) :digitsToNumber 2568 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(2000 500 60 8) math:sum 2568}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2568]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4950 a r:Inference; + r:gives { + (8 6 5 2) :digitsToNumber 8652 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(8000 600 50 2) math:sum 8652}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4951 a r:Inference; + r:gives { + 2569 :numberToDigits (2 5 6 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2569 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2569 1000) math:remainder 569}] + [ a r:Fact; r:gives {(569 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(569 100) math:remainder 69}] + [ a r:Fact; r:gives {(69 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(69 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2569]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 569]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 69]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4952 a r:Inference; + r:gives { + (2 5 6 9) :digitsToNumber 2569 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(2000 500 60 9) math:sum 2569}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2569]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4953 a r:Inference; + r:gives { + (9 6 5 2) :digitsToNumber 9652 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(9000 600 50 2) math:sum 9652}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4954 a r:Inference; + r:gives { + 2570 :numberToDigits (2 5 7 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2570 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2570 1000) math:remainder 570}] + [ a r:Fact; r:gives {(570 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(570 100) math:remainder 70}] + [ a r:Fact; r:gives {(70 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(70 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2570]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 570]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4955 a r:Inference; + r:gives { + 2571 :numberToDigits (2 5 7 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2571 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2571 1000) math:remainder 571}] + [ a r:Fact; r:gives {(571 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(571 100) math:remainder 71}] + [ a r:Fact; r:gives {(71 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(71 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2571]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 571]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 71]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4956 a r:Inference; + r:gives { + 2572 :numberToDigits (2 5 7 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2572 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2572 1000) math:remainder 572}] + [ a r:Fact; r:gives {(572 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(572 100) math:remainder 72}] + [ a r:Fact; r:gives {(72 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(72 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2572]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 572]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 72]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4957 a r:Inference; + r:gives { + 2573 :numberToDigits (2 5 7 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2573 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2573 1000) math:remainder 573}] + [ a r:Fact; r:gives {(573 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(573 100) math:remainder 73}] + [ a r:Fact; r:gives {(73 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(73 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2573]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 573]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 73]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4958 a r:Inference; + r:gives { + 2574 :numberToDigits (2 5 7 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2574 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2574 1000) math:remainder 574}] + [ a r:Fact; r:gives {(574 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(574 100) math:remainder 74}] + [ a r:Fact; r:gives {(74 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(74 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2574]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 574]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 74]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4959 a r:Inference; + r:gives { + 2575 :numberToDigits (2 5 7 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2575 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2575 1000) math:remainder 575}] + [ a r:Fact; r:gives {(575 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(575 100) math:remainder 75}] + [ a r:Fact; r:gives {(75 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(75 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2575]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 575]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 75]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4960 a r:Inference; + r:gives { + 2576 :numberToDigits (2 5 7 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2576 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2576 1000) math:remainder 576}] + [ a r:Fact; r:gives {(576 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(576 100) math:remainder 76}] + [ a r:Fact; r:gives {(76 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(76 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2576]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 576]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 76]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4961 a r:Inference; + r:gives { + 2577 :numberToDigits (2 5 7 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2577 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2577 1000) math:remainder 577}] + [ a r:Fact; r:gives {(577 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(577 100) math:remainder 77}] + [ a r:Fact; r:gives {(77 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(77 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2577]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 577]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 77]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4962 a r:Inference; + r:gives { + (2 5 7 7) :digitsToNumber 2577 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(2000 500 70 7) math:sum 2577}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2577]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma4963 a r:Inference; + r:gives { + (7 7 5 2) :digitsToNumber 7752 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(7000 700 50 2) math:sum 7752}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4964 a r:Inference; + r:gives { + 2578 :numberToDigits (2 5 7 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2578 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2578 1000) math:remainder 578}] + [ a r:Fact; r:gives {(578 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(578 100) math:remainder 78}] + [ a r:Fact; r:gives {(78 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(78 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2578]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 578]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 78]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4965 a r:Inference; + r:gives { + (2 5 7 8) :digitsToNumber 2578 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(2000 500 70 8) math:sum 2578}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2578]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4966 a r:Inference; + r:gives { + (8 7 5 2) :digitsToNumber 8752 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(8000 700 50 2) math:sum 8752}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4967 a r:Inference; + r:gives { + 2579 :numberToDigits (2 5 7 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2579 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2579 1000) math:remainder 579}] + [ a r:Fact; r:gives {(579 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(579 100) math:remainder 79}] + [ a r:Fact; r:gives {(79 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(79 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2579]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 579]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 79]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4968 a r:Inference; + r:gives { + (2 5 7 9) :digitsToNumber 2579 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(2000 500 70 9) math:sum 2579}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2579]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4969 a r:Inference; + r:gives { + (9 7 5 2) :digitsToNumber 9752 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(9000 700 50 2) math:sum 9752}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4970 a r:Inference; + r:gives { + 2580 :numberToDigits (2 5 8 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2580 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2580 1000) math:remainder 580}] + [ a r:Fact; r:gives {(580 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(580 100) math:remainder 80}] + [ a r:Fact; r:gives {(80 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(80 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2580]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 580]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4971 a r:Inference; + r:gives { + 2581 :numberToDigits (2 5 8 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2581 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2581 1000) math:remainder 581}] + [ a r:Fact; r:gives {(581 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(581 100) math:remainder 81}] + [ a r:Fact; r:gives {(81 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(81 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2581]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 581]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 81]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4972 a r:Inference; + r:gives { + 2582 :numberToDigits (2 5 8 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2582 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2582 1000) math:remainder 582}] + [ a r:Fact; r:gives {(582 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(582 100) math:remainder 82}] + [ a r:Fact; r:gives {(82 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(82 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2582]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 582]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 82]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4973 a r:Inference; + r:gives { + 2583 :numberToDigits (2 5 8 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2583 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2583 1000) math:remainder 583}] + [ a r:Fact; r:gives {(583 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(583 100) math:remainder 83}] + [ a r:Fact; r:gives {(83 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(83 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2583]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 583]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 83]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4974 a r:Inference; + r:gives { + 2584 :numberToDigits (2 5 8 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2584 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2584 1000) math:remainder 584}] + [ a r:Fact; r:gives {(584 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(584 100) math:remainder 84}] + [ a r:Fact; r:gives {(84 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(84 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2584]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 584]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 84]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4975 a r:Inference; + r:gives { + 2585 :numberToDigits (2 5 8 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2585 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2585 1000) math:remainder 585}] + [ a r:Fact; r:gives {(585 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(585 100) math:remainder 85}] + [ a r:Fact; r:gives {(85 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(85 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2585]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 585]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 85]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4976 a r:Inference; + r:gives { + 2586 :numberToDigits (2 5 8 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2586 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2586 1000) math:remainder 586}] + [ a r:Fact; r:gives {(586 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(586 100) math:remainder 86}] + [ a r:Fact; r:gives {(86 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(86 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2586]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 586]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 86]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4977 a r:Inference; + r:gives { + 2587 :numberToDigits (2 5 8 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2587 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2587 1000) math:remainder 587}] + [ a r:Fact; r:gives {(587 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(587 100) math:remainder 87}] + [ a r:Fact; r:gives {(87 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(87 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2587]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 587]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 87]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4978 a r:Inference; + r:gives { + 2588 :numberToDigits (2 5 8 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2588 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2588 1000) math:remainder 588}] + [ a r:Fact; r:gives {(588 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(588 100) math:remainder 88}] + [ a r:Fact; r:gives {(88 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(88 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2588]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 588]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 88]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4979 a r:Inference; + r:gives { + (2 5 8 8) :digitsToNumber 2588 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(8 10) math:product 80}] + [ a r:Fact; r:gives {(2000 500 80 8) math:sum 2588}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2588]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma4980 a r:Inference; + r:gives { + (8 8 5 2) :digitsToNumber 8852 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(8 100) math:product 800}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(8000 800 50 2) math:sum 8852}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8852]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4981 a r:Inference; + r:gives { + 2589 :numberToDigits (2 5 8 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2589 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2589 1000) math:remainder 589}] + [ a r:Fact; r:gives {(589 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(589 100) math:remainder 89}] + [ a r:Fact; r:gives {(89 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(89 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2589]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 589]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 89]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4982 a r:Inference; + r:gives { + (2 5 8 9) :digitsToNumber 2589 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(8 10) math:product 80}] + [ a r:Fact; r:gives {(2000 500 80 9) math:sum 2589}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2589]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4983 a r:Inference; + r:gives { + (9 8 5 2) :digitsToNumber 9852 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(8 100) math:product 800}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(9000 800 50 2) math:sum 9852}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9852]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4984 a r:Inference; + r:gives { + 2590 :numberToDigits (2 5 9 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2590 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2590 1000) math:remainder 590}] + [ a r:Fact; r:gives {(590 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(590 100) math:remainder 90}] + [ a r:Fact; r:gives {(90 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(90 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2590]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 590]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4985 a r:Inference; + r:gives { + 2591 :numberToDigits (2 5 9 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2591 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2591 1000) math:remainder 591}] + [ a r:Fact; r:gives {(591 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(591 100) math:remainder 91}] + [ a r:Fact; r:gives {(91 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(91 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2591]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 591]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 91]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4986 a r:Inference; + r:gives { + 2592 :numberToDigits (2 5 9 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2592 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2592 1000) math:remainder 592}] + [ a r:Fact; r:gives {(592 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(592 100) math:remainder 92}] + [ a r:Fact; r:gives {(92 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(92 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2592]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 592]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 92]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4987 a r:Inference; + r:gives { + 2593 :numberToDigits (2 5 9 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2593 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2593 1000) math:remainder 593}] + [ a r:Fact; r:gives {(593 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(593 100) math:remainder 93}] + [ a r:Fact; r:gives {(93 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(93 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2593]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 593]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 93]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma4988 a r:Inference; + r:gives { + 2594 :numberToDigits (2 5 9 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2594 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2594 1000) math:remainder 594}] + [ a r:Fact; r:gives {(594 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(594 100) math:remainder 94}] + [ a r:Fact; r:gives {(94 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(94 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2594]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 594]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 94]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma4989 a r:Inference; + r:gives { + 2595 :numberToDigits (2 5 9 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2595 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2595 1000) math:remainder 595}] + [ a r:Fact; r:gives {(595 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(595 100) math:remainder 95}] + [ a r:Fact; r:gives {(95 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(95 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2595]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 595]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 95]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma4990 a r:Inference; + r:gives { + 2596 :numberToDigits (2 5 9 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2596 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2596 1000) math:remainder 596}] + [ a r:Fact; r:gives {(596 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(596 100) math:remainder 96}] + [ a r:Fact; r:gives {(96 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(96 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2596]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 596]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 96]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma4991 a r:Inference; + r:gives { + 2597 :numberToDigits (2 5 9 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2597 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2597 1000) math:remainder 597}] + [ a r:Fact; r:gives {(597 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(597 100) math:remainder 97}] + [ a r:Fact; r:gives {(97 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(97 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2597]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 597]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 97]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma4992 a r:Inference; + r:gives { + 2598 :numberToDigits (2 5 9 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2598 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2598 1000) math:remainder 598}] + [ a r:Fact; r:gives {(598 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(598 100) math:remainder 98}] + [ a r:Fact; r:gives {(98 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(98 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2598]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 598]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 98]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma4993 a r:Inference; + r:gives { + 2599 :numberToDigits (2 5 9 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2599 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2599 1000) math:remainder 599}] + [ a r:Fact; r:gives {(599 100) math:integerQuotient 5}] + [ a r:Fact; r:gives {(599 100) math:remainder 99}] + [ a r:Fact; r:gives {(99 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(99 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2599]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 599]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 99]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma4994 a r:Inference; + r:gives { + (2 5 9 9) :digitsToNumber 2599 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(5 100) math:product 500}] + [ a r:Fact; r:gives {(9 10) math:product 90}] + [ a r:Fact; r:gives {(2000 500 90 9) math:sum 2599}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2599]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma4995 a r:Inference; + r:gives { + (9 9 5 2) :digitsToNumber 9952 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(9 100) math:product 900}] + [ a r:Fact; r:gives {(5 10) math:product 50}] + [ a r:Fact; r:gives {(9000 900 50 2) math:sum 9952}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 900]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9952]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma4996 a r:Inference; + r:gives { + 2600 :numberToDigits (2 6 0 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2600 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2600 1000) math:remainder 600}] + [ a r:Fact; r:gives {(600 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(600 100) math:remainder 0}] + [ a r:Fact; r:gives {(0 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(0 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma4997 a r:Inference; + r:gives { + 2601 :numberToDigits (2 6 0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2601 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2601 1000) math:remainder 601}] + [ a r:Fact; r:gives {(601 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(601 100) math:remainder 1}] + [ a r:Fact; r:gives {(1 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(1 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2601]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 601]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma4998 a r:Inference; + r:gives { + 2602 :numberToDigits (2 6 0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2602 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2602 1000) math:remainder 602}] + [ a r:Fact; r:gives {(602 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(602 100) math:remainder 2}] + [ a r:Fact; r:gives {(2 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(2 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2602]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 602]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma4999 a r:Inference; + r:gives { + 2603 :numberToDigits (2 6 0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2603 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2603 1000) math:remainder 603}] + [ a r:Fact; r:gives {(603 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(603 100) math:remainder 3}] + [ a r:Fact; r:gives {(3 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(3 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2603]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 603]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5000 a r:Inference; + r:gives { + 2604 :numberToDigits (2 6 0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2604 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2604 1000) math:remainder 604}] + [ a r:Fact; r:gives {(604 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(604 100) math:remainder 4}] + [ a r:Fact; r:gives {(4 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(4 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2604]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 604]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5001 a r:Inference; + r:gives { + 2605 :numberToDigits (2 6 0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2605 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2605 1000) math:remainder 605}] + [ a r:Fact; r:gives {(605 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(605 100) math:remainder 5}] + [ a r:Fact; r:gives {(5 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(5 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2605]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 605]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5002 a r:Inference; + r:gives { + 2606 :numberToDigits (2 6 0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2606 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2606 1000) math:remainder 606}] + [ a r:Fact; r:gives {(606 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(606 100) math:remainder 6}] + [ a r:Fact; r:gives {(6 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(6 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2606]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 606]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5003 a r:Inference; + r:gives { + 2607 :numberToDigits (2 6 0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2607 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2607 1000) math:remainder 607}] + [ a r:Fact; r:gives {(607 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(607 100) math:remainder 7}] + [ a r:Fact; r:gives {(7 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(7 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2607]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 607]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5004 a r:Inference; + r:gives { + 2608 :numberToDigits (2 6 0 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2608 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2608 1000) math:remainder 608}] + [ a r:Fact; r:gives {(608 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(608 100) math:remainder 8}] + [ a r:Fact; r:gives {(8 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(8 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2608]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 608]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5005 a r:Inference; + r:gives { + 2609 :numberToDigits (2 6 0 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2609 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2609 1000) math:remainder 609}] + [ a r:Fact; r:gives {(609 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(609 100) math:remainder 9}] + [ a r:Fact; r:gives {(9 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(9 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2609]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 609]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5006 a r:Inference; + r:gives { + 2610 :numberToDigits (2 6 1 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2610 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2610 1000) math:remainder 610}] + [ a r:Fact; r:gives {(610 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(610 100) math:remainder 10}] + [ a r:Fact; r:gives {(10 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(10 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2610]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 610]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5007 a r:Inference; + r:gives { + 2611 :numberToDigits (2 6 1 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2611 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2611 1000) math:remainder 611}] + [ a r:Fact; r:gives {(611 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(611 100) math:remainder 11}] + [ a r:Fact; r:gives {(11 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(11 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2611]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 611]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 11]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5008 a r:Inference; + r:gives { + 2612 :numberToDigits (2 6 1 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2612 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2612 1000) math:remainder 612}] + [ a r:Fact; r:gives {(612 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(612 100) math:remainder 12}] + [ a r:Fact; r:gives {(12 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(12 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2612]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 612]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5009 a r:Inference; + r:gives { + 2613 :numberToDigits (2 6 1 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2613 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2613 1000) math:remainder 613}] + [ a r:Fact; r:gives {(613 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(613 100) math:remainder 13}] + [ a r:Fact; r:gives {(13 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(13 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2613]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 613]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 13]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5010 a r:Inference; + r:gives { + 2614 :numberToDigits (2 6 1 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2614 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2614 1000) math:remainder 614}] + [ a r:Fact; r:gives {(614 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(614 100) math:remainder 14}] + [ a r:Fact; r:gives {(14 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(14 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2614]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 614]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 14]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5011 a r:Inference; + r:gives { + 2615 :numberToDigits (2 6 1 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2615 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2615 1000) math:remainder 615}] + [ a r:Fact; r:gives {(615 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(615 100) math:remainder 15}] + [ a r:Fact; r:gives {(15 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(15 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2615]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 615]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 15]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5012 a r:Inference; + r:gives { + 2616 :numberToDigits (2 6 1 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2616 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2616 1000) math:remainder 616}] + [ a r:Fact; r:gives {(616 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(616 100) math:remainder 16}] + [ a r:Fact; r:gives {(16 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(16 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2616]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 616]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 16]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5013 a r:Inference; + r:gives { + 2617 :numberToDigits (2 6 1 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2617 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2617 1000) math:remainder 617}] + [ a r:Fact; r:gives {(617 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(617 100) math:remainder 17}] + [ a r:Fact; r:gives {(17 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(17 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2617]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 617]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 17]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5014 a r:Inference; + r:gives { + 2618 :numberToDigits (2 6 1 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2618 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2618 1000) math:remainder 618}] + [ a r:Fact; r:gives {(618 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(618 100) math:remainder 18}] + [ a r:Fact; r:gives {(18 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(18 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2618]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 618]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 18]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5015 a r:Inference; + r:gives { + 2619 :numberToDigits (2 6 1 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2619 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2619 1000) math:remainder 619}] + [ a r:Fact; r:gives {(619 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(619 100) math:remainder 19}] + [ a r:Fact; r:gives {(19 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(19 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2619]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 619]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 19]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5016 a r:Inference; + r:gives { + 2620 :numberToDigits (2 6 2 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2620 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2620 1000) math:remainder 620}] + [ a r:Fact; r:gives {(620 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(620 100) math:remainder 20}] + [ a r:Fact; r:gives {(20 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(20 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5017 a r:Inference; + r:gives { + 2621 :numberToDigits (2 6 2 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2621 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2621 1000) math:remainder 621}] + [ a r:Fact; r:gives {(621 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(621 100) math:remainder 21}] + [ a r:Fact; r:gives {(21 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(21 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 21]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5018 a r:Inference; + r:gives { + 2622 :numberToDigits (2 6 2 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2622 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2622 1000) math:remainder 622}] + [ a r:Fact; r:gives {(622 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(622 100) math:remainder 22}] + [ a r:Fact; r:gives {(22 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(22 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5019 a r:Inference; + r:gives { + 2623 :numberToDigits (2 6 2 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2623 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2623 1000) math:remainder 623}] + [ a r:Fact; r:gives {(623 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(623 100) math:remainder 23}] + [ a r:Fact; r:gives {(23 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(23 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2623]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 623]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5020 a r:Inference; + r:gives { + 2624 :numberToDigits (2 6 2 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2624 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2624 1000) math:remainder 624}] + [ a r:Fact; r:gives {(624 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(624 100) math:remainder 24}] + [ a r:Fact; r:gives {(24 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(24 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2624]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 624]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5021 a r:Inference; + r:gives { + 2625 :numberToDigits (2 6 2 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2625 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2625 1000) math:remainder 625}] + [ a r:Fact; r:gives {(625 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(625 100) math:remainder 25}] + [ a r:Fact; r:gives {(25 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(25 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2625]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 625]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5022 a r:Inference; + r:gives { + 2626 :numberToDigits (2 6 2 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2626 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2626 1000) math:remainder 626}] + [ a r:Fact; r:gives {(626 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(626 100) math:remainder 26}] + [ a r:Fact; r:gives {(26 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(26 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2626]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 626]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5023 a r:Inference; + r:gives { + 2627 :numberToDigits (2 6 2 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2627 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2627 1000) math:remainder 627}] + [ a r:Fact; r:gives {(627 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(627 100) math:remainder 27}] + [ a r:Fact; r:gives {(27 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(27 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2627]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 627]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5024 a r:Inference; + r:gives { + 2628 :numberToDigits (2 6 2 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2628 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2628 1000) math:remainder 628}] + [ a r:Fact; r:gives {(628 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(628 100) math:remainder 28}] + [ a r:Fact; r:gives {(28 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(28 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2628]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 628]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5025 a r:Inference; + r:gives { + 2629 :numberToDigits (2 6 2 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2629 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2629 1000) math:remainder 629}] + [ a r:Fact; r:gives {(629 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(629 100) math:remainder 29}] + [ a r:Fact; r:gives {(29 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(29 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2629]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 629]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5026 a r:Inference; + r:gives { + 2630 :numberToDigits (2 6 3 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2630 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2630 1000) math:remainder 630}] + [ a r:Fact; r:gives {(630 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(630 100) math:remainder 30}] + [ a r:Fact; r:gives {(30 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(30 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5027 a r:Inference; + r:gives { + 2631 :numberToDigits (2 6 3 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2631 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2631 1000) math:remainder 631}] + [ a r:Fact; r:gives {(631 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(631 100) math:remainder 31}] + [ a r:Fact; r:gives {(31 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(31 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 31]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5028 a r:Inference; + r:gives { + 2632 :numberToDigits (2 6 3 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2632 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2632 1000) math:remainder 632}] + [ a r:Fact; r:gives {(632 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(632 100) math:remainder 32}] + [ a r:Fact; r:gives {(32 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(32 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 32]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5029 a r:Inference; + r:gives { + 2633 :numberToDigits (2 6 3 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2633 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2633 1000) math:remainder 633}] + [ a r:Fact; r:gives {(633 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(633 100) math:remainder 33}] + [ a r:Fact; r:gives {(33 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(33 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 33]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5030 a r:Inference; + r:gives { + 2634 :numberToDigits (2 6 3 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2634 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2634 1000) math:remainder 634}] + [ a r:Fact; r:gives {(634 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(634 100) math:remainder 34}] + [ a r:Fact; r:gives {(34 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(34 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2634]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 634]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 34]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5031 a r:Inference; + r:gives { + 2635 :numberToDigits (2 6 3 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2635 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2635 1000) math:remainder 635}] + [ a r:Fact; r:gives {(635 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(635 100) math:remainder 35}] + [ a r:Fact; r:gives {(35 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(35 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2635]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 635]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 35]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5032 a r:Inference; + r:gives { + 2636 :numberToDigits (2 6 3 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2636 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2636 1000) math:remainder 636}] + [ a r:Fact; r:gives {(636 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(636 100) math:remainder 36}] + [ a r:Fact; r:gives {(36 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(36 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2636]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 636]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 36]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5033 a r:Inference; + r:gives { + 2637 :numberToDigits (2 6 3 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2637 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2637 1000) math:remainder 637}] + [ a r:Fact; r:gives {(637 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(637 100) math:remainder 37}] + [ a r:Fact; r:gives {(37 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(37 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2637]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 637]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 37]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5034 a r:Inference; + r:gives { + 2638 :numberToDigits (2 6 3 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2638 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2638 1000) math:remainder 638}] + [ a r:Fact; r:gives {(638 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(638 100) math:remainder 38}] + [ a r:Fact; r:gives {(38 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(38 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2638]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 638]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 38]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5035 a r:Inference; + r:gives { + 2639 :numberToDigits (2 6 3 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2639 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2639 1000) math:remainder 639}] + [ a r:Fact; r:gives {(639 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(639 100) math:remainder 39}] + [ a r:Fact; r:gives {(39 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(39 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2639]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 639]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 39]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5036 a r:Inference; + r:gives { + 2640 :numberToDigits (2 6 4 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2640 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2640 1000) math:remainder 640}] + [ a r:Fact; r:gives {(640 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(640 100) math:remainder 40}] + [ a r:Fact; r:gives {(40 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(40 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2640]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 640]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5037 a r:Inference; + r:gives { + 2641 :numberToDigits (2 6 4 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2641 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2641 1000) math:remainder 641}] + [ a r:Fact; r:gives {(641 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(641 100) math:remainder 41}] + [ a r:Fact; r:gives {(41 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(41 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2641]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 641]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 41]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5038 a r:Inference; + r:gives { + 2642 :numberToDigits (2 6 4 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2642 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2642 1000) math:remainder 642}] + [ a r:Fact; r:gives {(642 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(642 100) math:remainder 42}] + [ a r:Fact; r:gives {(42 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(42 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 42]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5039 a r:Inference; + r:gives { + 2643 :numberToDigits (2 6 4 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2643 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2643 1000) math:remainder 643}] + [ a r:Fact; r:gives {(643 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(643 100) math:remainder 43}] + [ a r:Fact; r:gives {(43 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(43 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 43]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5040 a r:Inference; + r:gives { + 2644 :numberToDigits (2 6 4 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2644 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2644 1000) math:remainder 644}] + [ a r:Fact; r:gives {(644 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(644 100) math:remainder 44}] + [ a r:Fact; r:gives {(44 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(44 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2644]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 644]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 44]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5041 a r:Inference; + r:gives { + 2645 :numberToDigits (2 6 4 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2645 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2645 1000) math:remainder 645}] + [ a r:Fact; r:gives {(645 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(645 100) math:remainder 45}] + [ a r:Fact; r:gives {(45 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(45 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2645]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 645]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 45]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5042 a r:Inference; + r:gives { + 2646 :numberToDigits (2 6 4 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2646 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2646 1000) math:remainder 646}] + [ a r:Fact; r:gives {(646 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(646 100) math:remainder 46}] + [ a r:Fact; r:gives {(46 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(46 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2646]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 646]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 46]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5043 a r:Inference; + r:gives { + 2647 :numberToDigits (2 6 4 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2647 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2647 1000) math:remainder 647}] + [ a r:Fact; r:gives {(647 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(647 100) math:remainder 47}] + [ a r:Fact; r:gives {(47 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(47 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2647]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 647]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 47]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5044 a r:Inference; + r:gives { + 2648 :numberToDigits (2 6 4 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2648 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2648 1000) math:remainder 648}] + [ a r:Fact; r:gives {(648 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(648 100) math:remainder 48}] + [ a r:Fact; r:gives {(48 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(48 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2648]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 648]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 48]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5045 a r:Inference; + r:gives { + 2649 :numberToDigits (2 6 4 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2649 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2649 1000) math:remainder 649}] + [ a r:Fact; r:gives {(649 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(649 100) math:remainder 49}] + [ a r:Fact; r:gives {(49 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(49 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2649]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 649]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 49]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5046 a r:Inference; + r:gives { + 2650 :numberToDigits (2 6 5 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2650 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2650 1000) math:remainder 650}] + [ a r:Fact; r:gives {(650 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(650 100) math:remainder 50}] + [ a r:Fact; r:gives {(50 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(50 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2650]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 650]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5047 a r:Inference; + r:gives { + 2651 :numberToDigits (2 6 5 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2651 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2651 1000) math:remainder 651}] + [ a r:Fact; r:gives {(651 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(651 100) math:remainder 51}] + [ a r:Fact; r:gives {(51 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(51 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2651]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 651]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 51]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5048 a r:Inference; + r:gives { + 2652 :numberToDigits (2 6 5 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2652 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2652 1000) math:remainder 652}] + [ a r:Fact; r:gives {(652 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(652 100) math:remainder 52}] + [ a r:Fact; r:gives {(52 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(52 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 52]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5049 a r:Inference; + r:gives { + 2653 :numberToDigits (2 6 5 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2653 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2653 1000) math:remainder 653}] + [ a r:Fact; r:gives {(653 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(653 100) math:remainder 53}] + [ a r:Fact; r:gives {(53 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(53 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 53]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5050 a r:Inference; + r:gives { + 2654 :numberToDigits (2 6 5 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2654 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2654 1000) math:remainder 654}] + [ a r:Fact; r:gives {(654 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(654 100) math:remainder 54}] + [ a r:Fact; r:gives {(54 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(54 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2654]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 654]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 54]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5051 a r:Inference; + r:gives { + 2655 :numberToDigits (2 6 5 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2655 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2655 1000) math:remainder 655}] + [ a r:Fact; r:gives {(655 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(655 100) math:remainder 55}] + [ a r:Fact; r:gives {(55 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(55 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2655]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 655]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 55]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5052 a r:Inference; + r:gives { + 2656 :numberToDigits (2 6 5 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2656 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2656 1000) math:remainder 656}] + [ a r:Fact; r:gives {(656 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(656 100) math:remainder 56}] + [ a r:Fact; r:gives {(56 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(56 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2656]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 656]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 56]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5053 a r:Inference; + r:gives { + 2657 :numberToDigits (2 6 5 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2657 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2657 1000) math:remainder 657}] + [ a r:Fact; r:gives {(657 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(657 100) math:remainder 57}] + [ a r:Fact; r:gives {(57 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(57 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2657]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 657]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 57]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5054 a r:Inference; + r:gives { + 2658 :numberToDigits (2 6 5 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2658 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2658 1000) math:remainder 658}] + [ a r:Fact; r:gives {(658 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(658 100) math:remainder 58}] + [ a r:Fact; r:gives {(58 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(58 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2658]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 658]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 58]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5055 a r:Inference; + r:gives { + 2659 :numberToDigits (2 6 5 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2659 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2659 1000) math:remainder 659}] + [ a r:Fact; r:gives {(659 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(659 100) math:remainder 59}] + [ a r:Fact; r:gives {(59 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(59 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2659]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 659]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 59]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5056 a r:Inference; + r:gives { + 2660 :numberToDigits (2 6 6 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2660 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2660 1000) math:remainder 660}] + [ a r:Fact; r:gives {(660 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(660 100) math:remainder 60}] + [ a r:Fact; r:gives {(60 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(60 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2660]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 660]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5057 a r:Inference; + r:gives { + 2661 :numberToDigits (2 6 6 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2661 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2661 1000) math:remainder 661}] + [ a r:Fact; r:gives {(661 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(661 100) math:remainder 61}] + [ a r:Fact; r:gives {(61 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(61 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2661]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 661]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 61]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5058 a r:Inference; + r:gives { + 2662 :numberToDigits (2 6 6 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2662 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2662 1000) math:remainder 662}] + [ a r:Fact; r:gives {(662 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(662 100) math:remainder 62}] + [ a r:Fact; r:gives {(62 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(62 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2662]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 662]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 62]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5059 a r:Inference; + r:gives { + 2663 :numberToDigits (2 6 6 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2663 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2663 1000) math:remainder 663}] + [ a r:Fact; r:gives {(663 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(663 100) math:remainder 63}] + [ a r:Fact; r:gives {(63 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(63 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2663]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 663]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 63]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5060 a r:Inference; + r:gives { + 2664 :numberToDigits (2 6 6 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2664 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2664 1000) math:remainder 664}] + [ a r:Fact; r:gives {(664 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(664 100) math:remainder 64}] + [ a r:Fact; r:gives {(64 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(64 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2664]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 664]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 64]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5061 a r:Inference; + r:gives { + 2665 :numberToDigits (2 6 6 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2665 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2665 1000) math:remainder 665}] + [ a r:Fact; r:gives {(665 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(665 100) math:remainder 65}] + [ a r:Fact; r:gives {(65 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(65 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2665]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 665]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 65]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5062 a r:Inference; + r:gives { + 2666 :numberToDigits (2 6 6 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2666 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2666 1000) math:remainder 666}] + [ a r:Fact; r:gives {(666 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(666 100) math:remainder 66}] + [ a r:Fact; r:gives {(66 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(66 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2666]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 666]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 66]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5063 a r:Inference; + r:gives { + (2 6 6 6) :digitsToNumber 2666 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(2000 600 60 6) math:sum 2666}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2666]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6764. + +skolem:lemma5064 a r:Inference; + r:gives { + (6 6 6 2) :digitsToNumber 6662 . + }; + r:evidence ( + [ a r:Fact; r:gives {(6 1000) math:product 6000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(6000 600 60 2) math:sum 6662}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6662]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma5065 a r:Inference; + r:gives { + 2667 :numberToDigits (2 6 6 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2667 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2667 1000) math:remainder 667}] + [ a r:Fact; r:gives {(667 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(667 100) math:remainder 67}] + [ a r:Fact; r:gives {(67 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(67 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2667]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 667]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 67]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5066 a r:Inference; + r:gives { + (2 6 6 7) :digitsToNumber 2667 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(2000 600 60 7) math:sum 2667}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2667]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma5067 a r:Inference; + r:gives { + (7 6 6 2) :digitsToNumber 7662 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(7000 600 60 2) math:sum 7662}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7662]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma5068 a r:Inference; + r:gives { + 2668 :numberToDigits (2 6 6 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2668 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2668 1000) math:remainder 668}] + [ a r:Fact; r:gives {(668 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(668 100) math:remainder 68}] + [ a r:Fact; r:gives {(68 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(68 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2668]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 668]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 68]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5069 a r:Inference; + r:gives { + (2 6 6 8) :digitsToNumber 2668 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(2000 600 60 8) math:sum 2668}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2668]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma5070 a r:Inference; + r:gives { + (8 6 6 2) :digitsToNumber 8662 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(8000 600 60 2) math:sum 8662}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8662]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma5071 a r:Inference; + r:gives { + 2669 :numberToDigits (2 6 6 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2669 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2669 1000) math:remainder 669}] + [ a r:Fact; r:gives {(669 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(669 100) math:remainder 69}] + [ a r:Fact; r:gives {(69 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(69 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2669]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 669]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 69]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5072 a r:Inference; + r:gives { + (2 6 6 9) :digitsToNumber 2669 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(2000 600 60 9) math:sum 2669}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2669]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma5073 a r:Inference; + r:gives { + (9 6 6 2) :digitsToNumber 9662 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(9000 600 60 2) math:sum 9662}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9662]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma5074 a r:Inference; + r:gives { + 2670 :numberToDigits (2 6 7 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2670 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2670 1000) math:remainder 670}] + [ a r:Fact; r:gives {(670 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(670 100) math:remainder 70}] + [ a r:Fact; r:gives {(70 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(70 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2670]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 670]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5075 a r:Inference; + r:gives { + 2671 :numberToDigits (2 6 7 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2671 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2671 1000) math:remainder 671}] + [ a r:Fact; r:gives {(671 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(671 100) math:remainder 71}] + [ a r:Fact; r:gives {(71 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(71 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2671]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 671]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 71]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5076 a r:Inference; + r:gives { + 2672 :numberToDigits (2 6 7 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2672 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2672 1000) math:remainder 672}] + [ a r:Fact; r:gives {(672 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(672 100) math:remainder 72}] + [ a r:Fact; r:gives {(72 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(72 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2672]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 672]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 72]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5077 a r:Inference; + r:gives { + 2673 :numberToDigits (2 6 7 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2673 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2673 1000) math:remainder 673}] + [ a r:Fact; r:gives {(673 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(673 100) math:remainder 73}] + [ a r:Fact; r:gives {(73 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(73 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2673]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 673]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 73]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5078 a r:Inference; + r:gives { + 2674 :numberToDigits (2 6 7 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2674 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2674 1000) math:remainder 674}] + [ a r:Fact; r:gives {(674 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(674 100) math:remainder 74}] + [ a r:Fact; r:gives {(74 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(74 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2674]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 674]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 74]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5079 a r:Inference; + r:gives { + 2675 :numberToDigits (2 6 7 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2675 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2675 1000) math:remainder 675}] + [ a r:Fact; r:gives {(675 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(675 100) math:remainder 75}] + [ a r:Fact; r:gives {(75 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(75 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2675]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 675]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 75]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5080 a r:Inference; + r:gives { + 2676 :numberToDigits (2 6 7 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2676 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2676 1000) math:remainder 676}] + [ a r:Fact; r:gives {(676 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(676 100) math:remainder 76}] + [ a r:Fact; r:gives {(76 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(76 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2676]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 676]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 76]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5081 a r:Inference; + r:gives { + 2677 :numberToDigits (2 6 7 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2677 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2677 1000) math:remainder 677}] + [ a r:Fact; r:gives {(677 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(677 100) math:remainder 77}] + [ a r:Fact; r:gives {(77 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(77 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2677]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 677]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 77]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5082 a r:Inference; + r:gives { + (2 6 7 7) :digitsToNumber 2677 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(2000 600 70 7) math:sum 2677}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2677]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma5083 a r:Inference; + r:gives { + (7 7 6 2) :digitsToNumber 7762 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(7000 700 60 2) math:sum 7762}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma5084 a r:Inference; + r:gives { + 2678 :numberToDigits (2 6 7 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2678 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2678 1000) math:remainder 678}] + [ a r:Fact; r:gives {(678 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(678 100) math:remainder 78}] + [ a r:Fact; r:gives {(78 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(78 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2678]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 678]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 78]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5085 a r:Inference; + r:gives { + (2 6 7 8) :digitsToNumber 2678 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(2000 600 70 8) math:sum 2678}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2678]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma5086 a r:Inference; + r:gives { + (8 7 6 2) :digitsToNumber 8762 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(8000 700 60 2) math:sum 8762}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma5087 a r:Inference; + r:gives { + 2679 :numberToDigits (2 6 7 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2679 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2679 1000) math:remainder 679}] + [ a r:Fact; r:gives {(679 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(679 100) math:remainder 79}] + [ a r:Fact; r:gives {(79 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(79 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2679]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 679]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 79]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5088 a r:Inference; + r:gives { + (2 6 7 9) :digitsToNumber 2679 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(2000 600 70 9) math:sum 2679}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2679]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma5089 a r:Inference; + r:gives { + (9 7 6 2) :digitsToNumber 9762 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(9000 700 60 2) math:sum 9762}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma5090 a r:Inference; + r:gives { + 2680 :numberToDigits (2 6 8 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2680 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2680 1000) math:remainder 680}] + [ a r:Fact; r:gives {(680 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(680 100) math:remainder 80}] + [ a r:Fact; r:gives {(80 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(80 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2680]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 680]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5091 a r:Inference; + r:gives { + 2681 :numberToDigits (2 6 8 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2681 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2681 1000) math:remainder 681}] + [ a r:Fact; r:gives {(681 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(681 100) math:remainder 81}] + [ a r:Fact; r:gives {(81 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(81 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2681]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 681]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 81]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5092 a r:Inference; + r:gives { + 2682 :numberToDigits (2 6 8 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2682 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2682 1000) math:remainder 682}] + [ a r:Fact; r:gives {(682 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(682 100) math:remainder 82}] + [ a r:Fact; r:gives {(82 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(82 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2682]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 682]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 82]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5093 a r:Inference; + r:gives { + 2683 :numberToDigits (2 6 8 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2683 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2683 1000) math:remainder 683}] + [ a r:Fact; r:gives {(683 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(683 100) math:remainder 83}] + [ a r:Fact; r:gives {(83 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(83 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2683]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 683]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 83]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5094 a r:Inference; + r:gives { + 2684 :numberToDigits (2 6 8 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2684 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2684 1000) math:remainder 684}] + [ a r:Fact; r:gives {(684 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(684 100) math:remainder 84}] + [ a r:Fact; r:gives {(84 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(84 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2684]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 684]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 84]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5095 a r:Inference; + r:gives { + 2685 :numberToDigits (2 6 8 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2685 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2685 1000) math:remainder 685}] + [ a r:Fact; r:gives {(685 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(685 100) math:remainder 85}] + [ a r:Fact; r:gives {(85 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(85 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2685]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 685]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 85]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5096 a r:Inference; + r:gives { + 2686 :numberToDigits (2 6 8 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2686 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2686 1000) math:remainder 686}] + [ a r:Fact; r:gives {(686 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(686 100) math:remainder 86}] + [ a r:Fact; r:gives {(86 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(86 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2686]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 686]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 86]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5097 a r:Inference; + r:gives { + 2687 :numberToDigits (2 6 8 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2687 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2687 1000) math:remainder 687}] + [ a r:Fact; r:gives {(687 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(687 100) math:remainder 87}] + [ a r:Fact; r:gives {(87 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(87 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2687]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 687]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 87]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5098 a r:Inference; + r:gives { + 2688 :numberToDigits (2 6 8 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2688 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2688 1000) math:remainder 688}] + [ a r:Fact; r:gives {(688 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(688 100) math:remainder 88}] + [ a r:Fact; r:gives {(88 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(88 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2688]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 688]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 88]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5099 a r:Inference; + r:gives { + (2 6 8 8) :digitsToNumber 2688 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(8 10) math:product 80}] + [ a r:Fact; r:gives {(2000 600 80 8) math:sum 2688}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2688]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma5100 a r:Inference; + r:gives { + (8 8 6 2) :digitsToNumber 8862 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(8 100) math:product 800}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(8000 800 60 2) math:sum 8862}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8862]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma5101 a r:Inference; + r:gives { + 2689 :numberToDigits (2 6 8 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2689 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2689 1000) math:remainder 689}] + [ a r:Fact; r:gives {(689 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(689 100) math:remainder 89}] + [ a r:Fact; r:gives {(89 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(89 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2689]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 689]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 89]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5102 a r:Inference; + r:gives { + (2 6 8 9) :digitsToNumber 2689 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(8 10) math:product 80}] + [ a r:Fact; r:gives {(2000 600 80 9) math:sum 2689}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2689]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma5103 a r:Inference; + r:gives { + (9 8 6 2) :digitsToNumber 9862 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(8 100) math:product 800}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(9000 800 60 2) math:sum 9862}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9862]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma5104 a r:Inference; + r:gives { + 2690 :numberToDigits (2 6 9 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2690 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2690 1000) math:remainder 690}] + [ a r:Fact; r:gives {(690 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(690 100) math:remainder 90}] + [ a r:Fact; r:gives {(90 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(90 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2690]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 690]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5105 a r:Inference; + r:gives { + 2691 :numberToDigits (2 6 9 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2691 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2691 1000) math:remainder 691}] + [ a r:Fact; r:gives {(691 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(691 100) math:remainder 91}] + [ a r:Fact; r:gives {(91 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(91 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2691]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 691]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 91]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5106 a r:Inference; + r:gives { + 2692 :numberToDigits (2 6 9 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2692 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2692 1000) math:remainder 692}] + [ a r:Fact; r:gives {(692 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(692 100) math:remainder 92}] + [ a r:Fact; r:gives {(92 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(92 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2692]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 692]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 92]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5107 a r:Inference; + r:gives { + 2693 :numberToDigits (2 6 9 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2693 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2693 1000) math:remainder 693}] + [ a r:Fact; r:gives {(693 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(693 100) math:remainder 93}] + [ a r:Fact; r:gives {(93 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(93 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2693]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 693]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 93]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5108 a r:Inference; + r:gives { + 2694 :numberToDigits (2 6 9 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2694 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2694 1000) math:remainder 694}] + [ a r:Fact; r:gives {(694 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(694 100) math:remainder 94}] + [ a r:Fact; r:gives {(94 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(94 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2694]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 694]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 94]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5109 a r:Inference; + r:gives { + 2695 :numberToDigits (2 6 9 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2695 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2695 1000) math:remainder 695}] + [ a r:Fact; r:gives {(695 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(695 100) math:remainder 95}] + [ a r:Fact; r:gives {(95 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(95 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2695]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 695]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 95]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5110 a r:Inference; + r:gives { + 2696 :numberToDigits (2 6 9 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2696 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2696 1000) math:remainder 696}] + [ a r:Fact; r:gives {(696 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(696 100) math:remainder 96}] + [ a r:Fact; r:gives {(96 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(96 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2696]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 696]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 96]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5111 a r:Inference; + r:gives { + 2697 :numberToDigits (2 6 9 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2697 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2697 1000) math:remainder 697}] + [ a r:Fact; r:gives {(697 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(697 100) math:remainder 97}] + [ a r:Fact; r:gives {(97 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(97 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2697]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 697]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 97]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5112 a r:Inference; + r:gives { + 2698 :numberToDigits (2 6 9 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2698 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2698 1000) math:remainder 698}] + [ a r:Fact; r:gives {(698 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(698 100) math:remainder 98}] + [ a r:Fact; r:gives {(98 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(98 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2698]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 698]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 98]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5113 a r:Inference; + r:gives { + 2699 :numberToDigits (2 6 9 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2699 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2699 1000) math:remainder 699}] + [ a r:Fact; r:gives {(699 100) math:integerQuotient 6}] + [ a r:Fact; r:gives {(699 100) math:remainder 99}] + [ a r:Fact; r:gives {(99 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(99 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2699]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 699]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 99]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5114 a r:Inference; + r:gives { + (2 6 9 9) :digitsToNumber 2699 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(6 100) math:product 600}] + [ a r:Fact; r:gives {(9 10) math:product 90}] + [ a r:Fact; r:gives {(2000 600 90 9) math:sum 2699}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2699]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma5115 a r:Inference; + r:gives { + (9 9 6 2) :digitsToNumber 9962 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(9 100) math:product 900}] + [ a r:Fact; r:gives {(6 10) math:product 60}] + [ a r:Fact; r:gives {(9000 900 60 2) math:sum 9962}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 900]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9962]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma5116 a r:Inference; + r:gives { + 2700 :numberToDigits (2 7 0 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2700 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2700 1000) math:remainder 700}] + [ a r:Fact; r:gives {(700 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(700 100) math:remainder 0}] + [ a r:Fact; r:gives {(0 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(0 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5117 a r:Inference; + r:gives { + 2701 :numberToDigits (2 7 0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2701 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2701 1000) math:remainder 701}] + [ a r:Fact; r:gives {(701 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(701 100) math:remainder 1}] + [ a r:Fact; r:gives {(1 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(1 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2701]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 701]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5118 a r:Inference; + r:gives { + 2702 :numberToDigits (2 7 0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2702 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2702 1000) math:remainder 702}] + [ a r:Fact; r:gives {(702 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(702 100) math:remainder 2}] + [ a r:Fact; r:gives {(2 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(2 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2702]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 702]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5119 a r:Inference; + r:gives { + 2703 :numberToDigits (2 7 0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2703 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2703 1000) math:remainder 703}] + [ a r:Fact; r:gives {(703 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(703 100) math:remainder 3}] + [ a r:Fact; r:gives {(3 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(3 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2703]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 703]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5120 a r:Inference; + r:gives { + 2704 :numberToDigits (2 7 0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2704 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2704 1000) math:remainder 704}] + [ a r:Fact; r:gives {(704 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(704 100) math:remainder 4}] + [ a r:Fact; r:gives {(4 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(4 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2704]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 704]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5121 a r:Inference; + r:gives { + 2705 :numberToDigits (2 7 0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2705 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2705 1000) math:remainder 705}] + [ a r:Fact; r:gives {(705 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(705 100) math:remainder 5}] + [ a r:Fact; r:gives {(5 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(5 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2705]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 705]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5122 a r:Inference; + r:gives { + 2706 :numberToDigits (2 7 0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2706 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2706 1000) math:remainder 706}] + [ a r:Fact; r:gives {(706 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(706 100) math:remainder 6}] + [ a r:Fact; r:gives {(6 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(6 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2706]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 706]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5123 a r:Inference; + r:gives { + 2707 :numberToDigits (2 7 0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2707 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2707 1000) math:remainder 707}] + [ a r:Fact; r:gives {(707 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(707 100) math:remainder 7}] + [ a r:Fact; r:gives {(7 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(7 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2707]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 707]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5124 a r:Inference; + r:gives { + 2708 :numberToDigits (2 7 0 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2708 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2708 1000) math:remainder 708}] + [ a r:Fact; r:gives {(708 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(708 100) math:remainder 8}] + [ a r:Fact; r:gives {(8 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(8 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2708]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 708]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5125 a r:Inference; + r:gives { + 2709 :numberToDigits (2 7 0 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2709 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2709 1000) math:remainder 709}] + [ a r:Fact; r:gives {(709 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(709 100) math:remainder 9}] + [ a r:Fact; r:gives {(9 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(9 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2709]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 709]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5126 a r:Inference; + r:gives { + 2710 :numberToDigits (2 7 1 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2710 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2710 1000) math:remainder 710}] + [ a r:Fact; r:gives {(710 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(710 100) math:remainder 10}] + [ a r:Fact; r:gives {(10 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(10 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2710]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 710]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5127 a r:Inference; + r:gives { + 2711 :numberToDigits (2 7 1 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2711 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2711 1000) math:remainder 711}] + [ a r:Fact; r:gives {(711 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(711 100) math:remainder 11}] + [ a r:Fact; r:gives {(11 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(11 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2711]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 711]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 11]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5128 a r:Inference; + r:gives { + 2712 :numberToDigits (2 7 1 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2712 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2712 1000) math:remainder 712}] + [ a r:Fact; r:gives {(712 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(712 100) math:remainder 12}] + [ a r:Fact; r:gives {(12 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(12 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2712]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 712]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5129 a r:Inference; + r:gives { + 2713 :numberToDigits (2 7 1 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2713 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2713 1000) math:remainder 713}] + [ a r:Fact; r:gives {(713 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(713 100) math:remainder 13}] + [ a r:Fact; r:gives {(13 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(13 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2713]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 713]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 13]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5130 a r:Inference; + r:gives { + 2714 :numberToDigits (2 7 1 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2714 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2714 1000) math:remainder 714}] + [ a r:Fact; r:gives {(714 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(714 100) math:remainder 14}] + [ a r:Fact; r:gives {(14 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(14 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2714]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 714]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 14]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5131 a r:Inference; + r:gives { + 2715 :numberToDigits (2 7 1 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2715 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2715 1000) math:remainder 715}] + [ a r:Fact; r:gives {(715 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(715 100) math:remainder 15}] + [ a r:Fact; r:gives {(15 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(15 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2715]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 715]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 15]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5132 a r:Inference; + r:gives { + 2716 :numberToDigits (2 7 1 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2716 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2716 1000) math:remainder 716}] + [ a r:Fact; r:gives {(716 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(716 100) math:remainder 16}] + [ a r:Fact; r:gives {(16 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(16 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2716]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 716]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 16]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5133 a r:Inference; + r:gives { + 2717 :numberToDigits (2 7 1 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2717 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2717 1000) math:remainder 717}] + [ a r:Fact; r:gives {(717 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(717 100) math:remainder 17}] + [ a r:Fact; r:gives {(17 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(17 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2717]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 717]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 17]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5134 a r:Inference; + r:gives { + 2718 :numberToDigits (2 7 1 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2718 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2718 1000) math:remainder 718}] + [ a r:Fact; r:gives {(718 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(718 100) math:remainder 18}] + [ a r:Fact; r:gives {(18 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(18 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2718]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 718]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 18]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5135 a r:Inference; + r:gives { + 2719 :numberToDigits (2 7 1 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2719 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2719 1000) math:remainder 719}] + [ a r:Fact; r:gives {(719 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(719 100) math:remainder 19}] + [ a r:Fact; r:gives {(19 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(19 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2719]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 719]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 19]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5136 a r:Inference; + r:gives { + 2720 :numberToDigits (2 7 2 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2720 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2720 1000) math:remainder 720}] + [ a r:Fact; r:gives {(720 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(720 100) math:remainder 20}] + [ a r:Fact; r:gives {(20 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(20 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5137 a r:Inference; + r:gives { + 2721 :numberToDigits (2 7 2 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2721 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2721 1000) math:remainder 721}] + [ a r:Fact; r:gives {(721 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(721 100) math:remainder 21}] + [ a r:Fact; r:gives {(21 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(21 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 21]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5138 a r:Inference; + r:gives { + 2722 :numberToDigits (2 7 2 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2722 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2722 1000) math:remainder 722}] + [ a r:Fact; r:gives {(722 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(722 100) math:remainder 22}] + [ a r:Fact; r:gives {(22 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(22 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5139 a r:Inference; + r:gives { + 2723 :numberToDigits (2 7 2 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2723 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2723 1000) math:remainder 723}] + [ a r:Fact; r:gives {(723 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(723 100) math:remainder 23}] + [ a r:Fact; r:gives {(23 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(23 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2723]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 723]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5140 a r:Inference; + r:gives { + 2724 :numberToDigits (2 7 2 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2724 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2724 1000) math:remainder 724}] + [ a r:Fact; r:gives {(724 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(724 100) math:remainder 24}] + [ a r:Fact; r:gives {(24 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(24 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2724]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 724]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5141 a r:Inference; + r:gives { + 2725 :numberToDigits (2 7 2 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2725 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2725 1000) math:remainder 725}] + [ a r:Fact; r:gives {(725 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(725 100) math:remainder 25}] + [ a r:Fact; r:gives {(25 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(25 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2725]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 725]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5142 a r:Inference; + r:gives { + 2726 :numberToDigits (2 7 2 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2726 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2726 1000) math:remainder 726}] + [ a r:Fact; r:gives {(726 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(726 100) math:remainder 26}] + [ a r:Fact; r:gives {(26 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(26 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2726]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 726]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5143 a r:Inference; + r:gives { + 2727 :numberToDigits (2 7 2 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2727 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2727 1000) math:remainder 727}] + [ a r:Fact; r:gives {(727 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(727 100) math:remainder 27}] + [ a r:Fact; r:gives {(27 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(27 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2727]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 727]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5144 a r:Inference; + r:gives { + 2728 :numberToDigits (2 7 2 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2728 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2728 1000) math:remainder 728}] + [ a r:Fact; r:gives {(728 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(728 100) math:remainder 28}] + [ a r:Fact; r:gives {(28 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(28 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2728]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 728]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5145 a r:Inference; + r:gives { + 2729 :numberToDigits (2 7 2 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2729 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2729 1000) math:remainder 729}] + [ a r:Fact; r:gives {(729 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(729 100) math:remainder 29}] + [ a r:Fact; r:gives {(29 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(29 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2729]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 729]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5146 a r:Inference; + r:gives { + 2730 :numberToDigits (2 7 3 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2730 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2730 1000) math:remainder 730}] + [ a r:Fact; r:gives {(730 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(730 100) math:remainder 30}] + [ a r:Fact; r:gives {(30 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(30 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5147 a r:Inference; + r:gives { + 2731 :numberToDigits (2 7 3 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2731 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2731 1000) math:remainder 731}] + [ a r:Fact; r:gives {(731 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(731 100) math:remainder 31}] + [ a r:Fact; r:gives {(31 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(31 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2731]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 731]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 31]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5148 a r:Inference; + r:gives { + 2732 :numberToDigits (2 7 3 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2732 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2732 1000) math:remainder 732}] + [ a r:Fact; r:gives {(732 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(732 100) math:remainder 32}] + [ a r:Fact; r:gives {(32 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(32 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 32]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5149 a r:Inference; + r:gives { + 2733 :numberToDigits (2 7 3 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2733 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2733 1000) math:remainder 733}] + [ a r:Fact; r:gives {(733 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(733 100) math:remainder 33}] + [ a r:Fact; r:gives {(33 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(33 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 33]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5150 a r:Inference; + r:gives { + 2734 :numberToDigits (2 7 3 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2734 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2734 1000) math:remainder 734}] + [ a r:Fact; r:gives {(734 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(734 100) math:remainder 34}] + [ a r:Fact; r:gives {(34 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(34 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2734]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 734]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 34]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5151 a r:Inference; + r:gives { + 2735 :numberToDigits (2 7 3 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2735 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2735 1000) math:remainder 735}] + [ a r:Fact; r:gives {(735 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(735 100) math:remainder 35}] + [ a r:Fact; r:gives {(35 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(35 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2735]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 735]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 35]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5152 a r:Inference; + r:gives { + 2736 :numberToDigits (2 7 3 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2736 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2736 1000) math:remainder 736}] + [ a r:Fact; r:gives {(736 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(736 100) math:remainder 36}] + [ a r:Fact; r:gives {(36 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(36 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2736]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 736]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 36]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5153 a r:Inference; + r:gives { + 2737 :numberToDigits (2 7 3 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2737 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2737 1000) math:remainder 737}] + [ a r:Fact; r:gives {(737 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(737 100) math:remainder 37}] + [ a r:Fact; r:gives {(37 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(37 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2737]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 737]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 37]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5154 a r:Inference; + r:gives { + 2738 :numberToDigits (2 7 3 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2738 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2738 1000) math:remainder 738}] + [ a r:Fact; r:gives {(738 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(738 100) math:remainder 38}] + [ a r:Fact; r:gives {(38 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(38 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2738]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 738]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 38]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5155 a r:Inference; + r:gives { + 2739 :numberToDigits (2 7 3 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2739 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2739 1000) math:remainder 739}] + [ a r:Fact; r:gives {(739 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(739 100) math:remainder 39}] + [ a r:Fact; r:gives {(39 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(39 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2739]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 739]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 39]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5156 a r:Inference; + r:gives { + 2740 :numberToDigits (2 7 4 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2740 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2740 1000) math:remainder 740}] + [ a r:Fact; r:gives {(740 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(740 100) math:remainder 40}] + [ a r:Fact; r:gives {(40 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(40 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2740]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 740]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5157 a r:Inference; + r:gives { + 2741 :numberToDigits (2 7 4 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2741 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2741 1000) math:remainder 741}] + [ a r:Fact; r:gives {(741 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(741 100) math:remainder 41}] + [ a r:Fact; r:gives {(41 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(41 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2741]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 741]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 41]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5158 a r:Inference; + r:gives { + 2742 :numberToDigits (2 7 4 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2742 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2742 1000) math:remainder 742}] + [ a r:Fact; r:gives {(742 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(742 100) math:remainder 42}] + [ a r:Fact; r:gives {(42 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(42 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 42]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5159 a r:Inference; + r:gives { + 2743 :numberToDigits (2 7 4 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2743 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2743 1000) math:remainder 743}] + [ a r:Fact; r:gives {(743 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(743 100) math:remainder 43}] + [ a r:Fact; r:gives {(43 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(43 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 43]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5160 a r:Inference; + r:gives { + 2744 :numberToDigits (2 7 4 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2744 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2744 1000) math:remainder 744}] + [ a r:Fact; r:gives {(744 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(744 100) math:remainder 44}] + [ a r:Fact; r:gives {(44 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(44 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2744]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 744]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 44]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5161 a r:Inference; + r:gives { + 2745 :numberToDigits (2 7 4 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2745 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2745 1000) math:remainder 745}] + [ a r:Fact; r:gives {(745 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(745 100) math:remainder 45}] + [ a r:Fact; r:gives {(45 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(45 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2745]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 745]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 45]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5162 a r:Inference; + r:gives { + 2746 :numberToDigits (2 7 4 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2746 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2746 1000) math:remainder 746}] + [ a r:Fact; r:gives {(746 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(746 100) math:remainder 46}] + [ a r:Fact; r:gives {(46 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(46 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2746]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 746]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 46]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5163 a r:Inference; + r:gives { + 2747 :numberToDigits (2 7 4 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2747 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2747 1000) math:remainder 747}] + [ a r:Fact; r:gives {(747 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(747 100) math:remainder 47}] + [ a r:Fact; r:gives {(47 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(47 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2747]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 747]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 47]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5164 a r:Inference; + r:gives { + 2748 :numberToDigits (2 7 4 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2748 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2748 1000) math:remainder 748}] + [ a r:Fact; r:gives {(748 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(748 100) math:remainder 48}] + [ a r:Fact; r:gives {(48 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(48 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2748]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 748]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 48]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5165 a r:Inference; + r:gives { + 2749 :numberToDigits (2 7 4 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2749 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2749 1000) math:remainder 749}] + [ a r:Fact; r:gives {(749 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(749 100) math:remainder 49}] + [ a r:Fact; r:gives {(49 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(49 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2749]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 749]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 49]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5166 a r:Inference; + r:gives { + 2750 :numberToDigits (2 7 5 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2750 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2750 1000) math:remainder 750}] + [ a r:Fact; r:gives {(750 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(750 100) math:remainder 50}] + [ a r:Fact; r:gives {(50 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(50 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2750]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 750]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5167 a r:Inference; + r:gives { + 2751 :numberToDigits (2 7 5 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2751 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2751 1000) math:remainder 751}] + [ a r:Fact; r:gives {(751 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(751 100) math:remainder 51}] + [ a r:Fact; r:gives {(51 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(51 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2751]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 751]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 51]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5168 a r:Inference; + r:gives { + 2752 :numberToDigits (2 7 5 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2752 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2752 1000) math:remainder 752}] + [ a r:Fact; r:gives {(752 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(752 100) math:remainder 52}] + [ a r:Fact; r:gives {(52 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(52 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 52]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5169 a r:Inference; + r:gives { + 2753 :numberToDigits (2 7 5 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2753 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2753 1000) math:remainder 753}] + [ a r:Fact; r:gives {(753 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(753 100) math:remainder 53}] + [ a r:Fact; r:gives {(53 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(53 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 53]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5170 a r:Inference; + r:gives { + 2754 :numberToDigits (2 7 5 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2754 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2754 1000) math:remainder 754}] + [ a r:Fact; r:gives {(754 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(754 100) math:remainder 54}] + [ a r:Fact; r:gives {(54 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(54 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2754]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 754]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 54]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5171 a r:Inference; + r:gives { + 2755 :numberToDigits (2 7 5 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2755 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2755 1000) math:remainder 755}] + [ a r:Fact; r:gives {(755 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(755 100) math:remainder 55}] + [ a r:Fact; r:gives {(55 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(55 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2755]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 755]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 55]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5172 a r:Inference; + r:gives { + 2756 :numberToDigits (2 7 5 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2756 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2756 1000) math:remainder 756}] + [ a r:Fact; r:gives {(756 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(756 100) math:remainder 56}] + [ a r:Fact; r:gives {(56 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(56 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2756]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 756]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 56]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5173 a r:Inference; + r:gives { + 2757 :numberToDigits (2 7 5 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2757 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2757 1000) math:remainder 757}] + [ a r:Fact; r:gives {(757 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(757 100) math:remainder 57}] + [ a r:Fact; r:gives {(57 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(57 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2757]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 757]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 57]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5174 a r:Inference; + r:gives { + 2758 :numberToDigits (2 7 5 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2758 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2758 1000) math:remainder 758}] + [ a r:Fact; r:gives {(758 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(758 100) math:remainder 58}] + [ a r:Fact; r:gives {(58 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(58 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2758]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 758]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 58]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5175 a r:Inference; + r:gives { + 2759 :numberToDigits (2 7 5 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2759 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2759 1000) math:remainder 759}] + [ a r:Fact; r:gives {(759 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(759 100) math:remainder 59}] + [ a r:Fact; r:gives {(59 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(59 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2759]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 759]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 59]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5176 a r:Inference; + r:gives { + 2760 :numberToDigits (2 7 6 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2760 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2760 1000) math:remainder 760}] + [ a r:Fact; r:gives {(760 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(760 100) math:remainder 60}] + [ a r:Fact; r:gives {(60 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(60 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2760]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 760]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5177 a r:Inference; + r:gives { + 2761 :numberToDigits (2 7 6 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2761 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2761 1000) math:remainder 761}] + [ a r:Fact; r:gives {(761 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(761 100) math:remainder 61}] + [ a r:Fact; r:gives {(61 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(61 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2761]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 761]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 61]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5178 a r:Inference; + r:gives { + 2762 :numberToDigits (2 7 6 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2762 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2762 1000) math:remainder 762}] + [ a r:Fact; r:gives {(762 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(762 100) math:remainder 62}] + [ a r:Fact; r:gives {(62 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(62 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 62]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5179 a r:Inference; + r:gives { + 2763 :numberToDigits (2 7 6 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2763 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2763 1000) math:remainder 763}] + [ a r:Fact; r:gives {(763 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(763 100) math:remainder 63}] + [ a r:Fact; r:gives {(63 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(63 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 63]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5180 a r:Inference; + r:gives { + 2764 :numberToDigits (2 7 6 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2764 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2764 1000) math:remainder 764}] + [ a r:Fact; r:gives {(764 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(764 100) math:remainder 64}] + [ a r:Fact; r:gives {(64 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(64 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2764]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 764]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 64]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5181 a r:Inference; + r:gives { + 2765 :numberToDigits (2 7 6 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2765 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2765 1000) math:remainder 765}] + [ a r:Fact; r:gives {(765 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(765 100) math:remainder 65}] + [ a r:Fact; r:gives {(65 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(65 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2765]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 765]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 65]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5182 a r:Inference; + r:gives { + 2766 :numberToDigits (2 7 6 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2766 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2766 1000) math:remainder 766}] + [ a r:Fact; r:gives {(766 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(766 100) math:remainder 66}] + [ a r:Fact; r:gives {(66 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(66 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2766]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 766]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 66]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5183 a r:Inference; + r:gives { + 2767 :numberToDigits (2 7 6 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2767 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2767 1000) math:remainder 767}] + [ a r:Fact; r:gives {(767 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(767 100) math:remainder 67}] + [ a r:Fact; r:gives {(67 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(67 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2767]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 767]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 67]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5184 a r:Inference; + r:gives { + 2768 :numberToDigits (2 7 6 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2768 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2768 1000) math:remainder 768}] + [ a r:Fact; r:gives {(768 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(768 100) math:remainder 68}] + [ a r:Fact; r:gives {(68 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(68 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2768]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 768]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 68]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5185 a r:Inference; + r:gives { + 2769 :numberToDigits (2 7 6 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2769 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2769 1000) math:remainder 769}] + [ a r:Fact; r:gives {(769 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(769 100) math:remainder 69}] + [ a r:Fact; r:gives {(69 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(69 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2769]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 769]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 69]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5186 a r:Inference; + r:gives { + 2770 :numberToDigits (2 7 7 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2770 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2770 1000) math:remainder 770}] + [ a r:Fact; r:gives {(770 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(770 100) math:remainder 70}] + [ a r:Fact; r:gives {(70 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(70 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2770]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 770]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5187 a r:Inference; + r:gives { + 2771 :numberToDigits (2 7 7 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2771 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2771 1000) math:remainder 771}] + [ a r:Fact; r:gives {(771 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(771 100) math:remainder 71}] + [ a r:Fact; r:gives {(71 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(71 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2771]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 771]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 71]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5188 a r:Inference; + r:gives { + 2772 :numberToDigits (2 7 7 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2772 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2772 1000) math:remainder 772}] + [ a r:Fact; r:gives {(772 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(772 100) math:remainder 72}] + [ a r:Fact; r:gives {(72 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(72 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2772]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 772]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 72]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5189 a r:Inference; + r:gives { + 2773 :numberToDigits (2 7 7 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2773 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2773 1000) math:remainder 773}] + [ a r:Fact; r:gives {(773 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(773 100) math:remainder 73}] + [ a r:Fact; r:gives {(73 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(73 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2773]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 773]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 73]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5190 a r:Inference; + r:gives { + 2774 :numberToDigits (2 7 7 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2774 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2774 1000) math:remainder 774}] + [ a r:Fact; r:gives {(774 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(774 100) math:remainder 74}] + [ a r:Fact; r:gives {(74 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(74 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2774]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 774]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 74]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5191 a r:Inference; + r:gives { + 2775 :numberToDigits (2 7 7 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2775 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2775 1000) math:remainder 775}] + [ a r:Fact; r:gives {(775 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(775 100) math:remainder 75}] + [ a r:Fact; r:gives {(75 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(75 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2775]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 775]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 75]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5192 a r:Inference; + r:gives { + 2776 :numberToDigits (2 7 7 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2776 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2776 1000) math:remainder 776}] + [ a r:Fact; r:gives {(776 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(776 100) math:remainder 76}] + [ a r:Fact; r:gives {(76 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(76 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2776]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 776]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 76]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5193 a r:Inference; + r:gives { + 2777 :numberToDigits (2 7 7 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2777 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2777 1000) math:remainder 777}] + [ a r:Fact; r:gives {(777 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(777 100) math:remainder 77}] + [ a r:Fact; r:gives {(77 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(77 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2777]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 777]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 77]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5194 a r:Inference; + r:gives { + (2 7 7 7) :digitsToNumber 2777 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(2000 700 70 7) math:sum 2777}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2777]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6764. + +skolem:lemma5195 a r:Inference; + r:gives { + (7 7 7 2) :digitsToNumber 7772 . + }; + r:evidence ( + [ a r:Fact; r:gives {(7 1000) math:product 7000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(7000 700 70 2) math:sum 7772}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7772]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma5196 a r:Inference; + r:gives { + 2778 :numberToDigits (2 7 7 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2778 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2778 1000) math:remainder 778}] + [ a r:Fact; r:gives {(778 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(778 100) math:remainder 78}] + [ a r:Fact; r:gives {(78 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(78 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2778]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 778]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 78]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5197 a r:Inference; + r:gives { + (2 7 7 8) :digitsToNumber 2778 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(2000 700 70 8) math:sum 2778}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2778]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma5198 a r:Inference; + r:gives { + (8 7 7 2) :digitsToNumber 8772 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(8000 700 70 2) math:sum 8772}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8772]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma5199 a r:Inference; + r:gives { + 2779 :numberToDigits (2 7 7 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2779 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2779 1000) math:remainder 779}] + [ a r:Fact; r:gives {(779 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(779 100) math:remainder 79}] + [ a r:Fact; r:gives {(79 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(79 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2779]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 779]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 79]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5200 a r:Inference; + r:gives { + (2 7 7 9) :digitsToNumber 2779 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(2000 700 70 9) math:sum 2779}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2779]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma5201 a r:Inference; + r:gives { + (9 7 7 2) :digitsToNumber 9772 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(9000 700 70 2) math:sum 9772}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9772]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma5202 a r:Inference; + r:gives { + 2780 :numberToDigits (2 7 8 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2780 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2780 1000) math:remainder 780}] + [ a r:Fact; r:gives {(780 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(780 100) math:remainder 80}] + [ a r:Fact; r:gives {(80 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(80 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2780]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 780]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5203 a r:Inference; + r:gives { + 2781 :numberToDigits (2 7 8 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2781 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2781 1000) math:remainder 781}] + [ a r:Fact; r:gives {(781 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(781 100) math:remainder 81}] + [ a r:Fact; r:gives {(81 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(81 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2781]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 781]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 81]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5204 a r:Inference; + r:gives { + 2782 :numberToDigits (2 7 8 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2782 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2782 1000) math:remainder 782}] + [ a r:Fact; r:gives {(782 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(782 100) math:remainder 82}] + [ a r:Fact; r:gives {(82 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(82 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2782]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 782]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 82]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5205 a r:Inference; + r:gives { + 2783 :numberToDigits (2 7 8 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2783 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2783 1000) math:remainder 783}] + [ a r:Fact; r:gives {(783 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(783 100) math:remainder 83}] + [ a r:Fact; r:gives {(83 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(83 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2783]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 783]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 83]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5206 a r:Inference; + r:gives { + 2784 :numberToDigits (2 7 8 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2784 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2784 1000) math:remainder 784}] + [ a r:Fact; r:gives {(784 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(784 100) math:remainder 84}] + [ a r:Fact; r:gives {(84 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(84 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2784]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 784]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 84]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5207 a r:Inference; + r:gives { + 2785 :numberToDigits (2 7 8 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2785 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2785 1000) math:remainder 785}] + [ a r:Fact; r:gives {(785 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(785 100) math:remainder 85}] + [ a r:Fact; r:gives {(85 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(85 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2785]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 785]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 85]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5208 a r:Inference; + r:gives { + 2786 :numberToDigits (2 7 8 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2786 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2786 1000) math:remainder 786}] + [ a r:Fact; r:gives {(786 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(786 100) math:remainder 86}] + [ a r:Fact; r:gives {(86 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(86 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2786]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 786]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 86]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5209 a r:Inference; + r:gives { + 2787 :numberToDigits (2 7 8 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2787 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2787 1000) math:remainder 787}] + [ a r:Fact; r:gives {(787 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(787 100) math:remainder 87}] + [ a r:Fact; r:gives {(87 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(87 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2787]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 787]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 87]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5210 a r:Inference; + r:gives { + 2788 :numberToDigits (2 7 8 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2788 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2788 1000) math:remainder 788}] + [ a r:Fact; r:gives {(788 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(788 100) math:remainder 88}] + [ a r:Fact; r:gives {(88 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(88 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2788]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 788]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 88]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5211 a r:Inference; + r:gives { + (2 7 8 8) :digitsToNumber 2788 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(8 10) math:product 80}] + [ a r:Fact; r:gives {(2000 700 80 8) math:sum 2788}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2788]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma5212 a r:Inference; + r:gives { + (8 8 7 2) :digitsToNumber 8872 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(8 100) math:product 800}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(8000 800 70 2) math:sum 8872}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8872]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma5213 a r:Inference; + r:gives { + 2789 :numberToDigits (2 7 8 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2789 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2789 1000) math:remainder 789}] + [ a r:Fact; r:gives {(789 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(789 100) math:remainder 89}] + [ a r:Fact; r:gives {(89 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(89 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2789]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 789]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 89]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5214 a r:Inference; + r:gives { + (2 7 8 9) :digitsToNumber 2789 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(8 10) math:product 80}] + [ a r:Fact; r:gives {(2000 700 80 9) math:sum 2789}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2789]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma5215 a r:Inference; + r:gives { + (9 8 7 2) :digitsToNumber 9872 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(8 100) math:product 800}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(9000 800 70 2) math:sum 9872}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9872]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma5216 a r:Inference; + r:gives { + 2790 :numberToDigits (2 7 9 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2790 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2790 1000) math:remainder 790}] + [ a r:Fact; r:gives {(790 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(790 100) math:remainder 90}] + [ a r:Fact; r:gives {(90 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(90 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2790]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 790]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5217 a r:Inference; + r:gives { + 2791 :numberToDigits (2 7 9 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2791 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2791 1000) math:remainder 791}] + [ a r:Fact; r:gives {(791 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(791 100) math:remainder 91}] + [ a r:Fact; r:gives {(91 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(91 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2791]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 791]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 91]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5218 a r:Inference; + r:gives { + 2792 :numberToDigits (2 7 9 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2792 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2792 1000) math:remainder 792}] + [ a r:Fact; r:gives {(792 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(792 100) math:remainder 92}] + [ a r:Fact; r:gives {(92 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(92 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2792]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 792]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 92]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5219 a r:Inference; + r:gives { + 2793 :numberToDigits (2 7 9 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2793 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2793 1000) math:remainder 793}] + [ a r:Fact; r:gives {(793 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(793 100) math:remainder 93}] + [ a r:Fact; r:gives {(93 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(93 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2793]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 793]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 93]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5220 a r:Inference; + r:gives { + 2794 :numberToDigits (2 7 9 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2794 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2794 1000) math:remainder 794}] + [ a r:Fact; r:gives {(794 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(794 100) math:remainder 94}] + [ a r:Fact; r:gives {(94 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(94 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2794]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 794]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 94]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5221 a r:Inference; + r:gives { + 2795 :numberToDigits (2 7 9 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2795 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2795 1000) math:remainder 795}] + [ a r:Fact; r:gives {(795 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(795 100) math:remainder 95}] + [ a r:Fact; r:gives {(95 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(95 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2795]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 795]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 95]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5222 a r:Inference; + r:gives { + 2796 :numberToDigits (2 7 9 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2796 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2796 1000) math:remainder 796}] + [ a r:Fact; r:gives {(796 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(796 100) math:remainder 96}] + [ a r:Fact; r:gives {(96 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(96 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2796]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 796]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 96]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5223 a r:Inference; + r:gives { + 2797 :numberToDigits (2 7 9 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2797 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2797 1000) math:remainder 797}] + [ a r:Fact; r:gives {(797 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(797 100) math:remainder 97}] + [ a r:Fact; r:gives {(97 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(97 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2797]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 797]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 97]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5224 a r:Inference; + r:gives { + 2798 :numberToDigits (2 7 9 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2798 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2798 1000) math:remainder 798}] + [ a r:Fact; r:gives {(798 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(798 100) math:remainder 98}] + [ a r:Fact; r:gives {(98 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(98 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2798]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 798]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 98]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5225 a r:Inference; + r:gives { + 2799 :numberToDigits (2 7 9 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2799 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2799 1000) math:remainder 799}] + [ a r:Fact; r:gives {(799 100) math:integerQuotient 7}] + [ a r:Fact; r:gives {(799 100) math:remainder 99}] + [ a r:Fact; r:gives {(99 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(99 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2799]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 799]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 99]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5226 a r:Inference; + r:gives { + (2 7 9 9) :digitsToNumber 2799 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(7 100) math:product 700}] + [ a r:Fact; r:gives {(9 10) math:product 90}] + [ a r:Fact; r:gives {(2000 700 90 9) math:sum 2799}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2799]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma5227 a r:Inference; + r:gives { + (9 9 7 2) :digitsToNumber 9972 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(9 100) math:product 900}] + [ a r:Fact; r:gives {(7 10) math:product 70}] + [ a r:Fact; r:gives {(9000 900 70 2) math:sum 9972}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 900]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9972]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma5228 a r:Inference; + r:gives { + 2800 :numberToDigits (2 8 0 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2800 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2800 1000) math:remainder 800}] + [ a r:Fact; r:gives {(800 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(800 100) math:remainder 0}] + [ a r:Fact; r:gives {(0 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(0 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5229 a r:Inference; + r:gives { + 2801 :numberToDigits (2 8 0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2801 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2801 1000) math:remainder 801}] + [ a r:Fact; r:gives {(801 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(801 100) math:remainder 1}] + [ a r:Fact; r:gives {(1 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(1 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2801]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 801]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5230 a r:Inference; + r:gives { + 2802 :numberToDigits (2 8 0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2802 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2802 1000) math:remainder 802}] + [ a r:Fact; r:gives {(802 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(802 100) math:remainder 2}] + [ a r:Fact; r:gives {(2 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(2 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2802]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 802]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5231 a r:Inference; + r:gives { + 2803 :numberToDigits (2 8 0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2803 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2803 1000) math:remainder 803}] + [ a r:Fact; r:gives {(803 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(803 100) math:remainder 3}] + [ a r:Fact; r:gives {(3 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(3 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2803]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 803]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5232 a r:Inference; + r:gives { + 2804 :numberToDigits (2 8 0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2804 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2804 1000) math:remainder 804}] + [ a r:Fact; r:gives {(804 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(804 100) math:remainder 4}] + [ a r:Fact; r:gives {(4 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(4 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2804]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 804]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5233 a r:Inference; + r:gives { + 2805 :numberToDigits (2 8 0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2805 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2805 1000) math:remainder 805}] + [ a r:Fact; r:gives {(805 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(805 100) math:remainder 5}] + [ a r:Fact; r:gives {(5 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(5 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2805]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 805]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5234 a r:Inference; + r:gives { + 2806 :numberToDigits (2 8 0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2806 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2806 1000) math:remainder 806}] + [ a r:Fact; r:gives {(806 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(806 100) math:remainder 6}] + [ a r:Fact; r:gives {(6 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(6 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2806]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 806]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5235 a r:Inference; + r:gives { + 2807 :numberToDigits (2 8 0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2807 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2807 1000) math:remainder 807}] + [ a r:Fact; r:gives {(807 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(807 100) math:remainder 7}] + [ a r:Fact; r:gives {(7 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(7 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2807]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 807]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5236 a r:Inference; + r:gives { + 2808 :numberToDigits (2 8 0 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2808 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2808 1000) math:remainder 808}] + [ a r:Fact; r:gives {(808 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(808 100) math:remainder 8}] + [ a r:Fact; r:gives {(8 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(8 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2808]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 808]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5237 a r:Inference; + r:gives { + 2809 :numberToDigits (2 8 0 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2809 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2809 1000) math:remainder 809}] + [ a r:Fact; r:gives {(809 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(809 100) math:remainder 9}] + [ a r:Fact; r:gives {(9 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(9 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2809]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 809]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5238 a r:Inference; + r:gives { + 2810 :numberToDigits (2 8 1 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2810 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2810 1000) math:remainder 810}] + [ a r:Fact; r:gives {(810 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(810 100) math:remainder 10}] + [ a r:Fact; r:gives {(10 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(10 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2810]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 810]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5239 a r:Inference; + r:gives { + 2811 :numberToDigits (2 8 1 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2811 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2811 1000) math:remainder 811}] + [ a r:Fact; r:gives {(811 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(811 100) math:remainder 11}] + [ a r:Fact; r:gives {(11 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(11 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2811]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 811]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 11]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5240 a r:Inference; + r:gives { + 2812 :numberToDigits (2 8 1 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2812 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2812 1000) math:remainder 812}] + [ a r:Fact; r:gives {(812 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(812 100) math:remainder 12}] + [ a r:Fact; r:gives {(12 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(12 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2812]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 812]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5241 a r:Inference; + r:gives { + 2813 :numberToDigits (2 8 1 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2813 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2813 1000) math:remainder 813}] + [ a r:Fact; r:gives {(813 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(813 100) math:remainder 13}] + [ a r:Fact; r:gives {(13 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(13 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2813]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 813]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 13]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5242 a r:Inference; + r:gives { + 2814 :numberToDigits (2 8 1 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2814 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2814 1000) math:remainder 814}] + [ a r:Fact; r:gives {(814 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(814 100) math:remainder 14}] + [ a r:Fact; r:gives {(14 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(14 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2814]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 814]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 14]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5243 a r:Inference; + r:gives { + 2815 :numberToDigits (2 8 1 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2815 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2815 1000) math:remainder 815}] + [ a r:Fact; r:gives {(815 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(815 100) math:remainder 15}] + [ a r:Fact; r:gives {(15 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(15 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2815]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 815]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 15]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5244 a r:Inference; + r:gives { + 2816 :numberToDigits (2 8 1 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2816 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2816 1000) math:remainder 816}] + [ a r:Fact; r:gives {(816 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(816 100) math:remainder 16}] + [ a r:Fact; r:gives {(16 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(16 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2816]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 816]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 16]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5245 a r:Inference; + r:gives { + 2817 :numberToDigits (2 8 1 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2817 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2817 1000) math:remainder 817}] + [ a r:Fact; r:gives {(817 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(817 100) math:remainder 17}] + [ a r:Fact; r:gives {(17 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(17 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2817]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 817]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 17]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5246 a r:Inference; + r:gives { + 2818 :numberToDigits (2 8 1 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2818 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2818 1000) math:remainder 818}] + [ a r:Fact; r:gives {(818 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(818 100) math:remainder 18}] + [ a r:Fact; r:gives {(18 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(18 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2818]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 818]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 18]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5247 a r:Inference; + r:gives { + 2819 :numberToDigits (2 8 1 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2819 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2819 1000) math:remainder 819}] + [ a r:Fact; r:gives {(819 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(819 100) math:remainder 19}] + [ a r:Fact; r:gives {(19 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(19 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2819]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 819]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 19]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5248 a r:Inference; + r:gives { + 2820 :numberToDigits (2 8 2 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2820 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2820 1000) math:remainder 820}] + [ a r:Fact; r:gives {(820 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(820 100) math:remainder 20}] + [ a r:Fact; r:gives {(20 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(20 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2820]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 820]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5249 a r:Inference; + r:gives { + 2821 :numberToDigits (2 8 2 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2821 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2821 1000) math:remainder 821}] + [ a r:Fact; r:gives {(821 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(821 100) math:remainder 21}] + [ a r:Fact; r:gives {(21 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(21 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2821]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 821]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 21]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5250 a r:Inference; + r:gives { + 2822 :numberToDigits (2 8 2 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2822 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2822 1000) math:remainder 822}] + [ a r:Fact; r:gives {(822 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(822 100) math:remainder 22}] + [ a r:Fact; r:gives {(22 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(22 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2822]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 822]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5251 a r:Inference; + r:gives { + 2823 :numberToDigits (2 8 2 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2823 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2823 1000) math:remainder 823}] + [ a r:Fact; r:gives {(823 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(823 100) math:remainder 23}] + [ a r:Fact; r:gives {(23 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(23 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2823]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 823]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5252 a r:Inference; + r:gives { + 2824 :numberToDigits (2 8 2 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2824 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2824 1000) math:remainder 824}] + [ a r:Fact; r:gives {(824 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(824 100) math:remainder 24}] + [ a r:Fact; r:gives {(24 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(24 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2824]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 824]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5253 a r:Inference; + r:gives { + 2825 :numberToDigits (2 8 2 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2825 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2825 1000) math:remainder 825}] + [ a r:Fact; r:gives {(825 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(825 100) math:remainder 25}] + [ a r:Fact; r:gives {(25 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(25 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2825]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 825]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5254 a r:Inference; + r:gives { + 2826 :numberToDigits (2 8 2 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2826 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2826 1000) math:remainder 826}] + [ a r:Fact; r:gives {(826 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(826 100) math:remainder 26}] + [ a r:Fact; r:gives {(26 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(26 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2826]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 826]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5255 a r:Inference; + r:gives { + 2827 :numberToDigits (2 8 2 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2827 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2827 1000) math:remainder 827}] + [ a r:Fact; r:gives {(827 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(827 100) math:remainder 27}] + [ a r:Fact; r:gives {(27 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(27 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2827]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 827]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5256 a r:Inference; + r:gives { + 2828 :numberToDigits (2 8 2 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2828 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2828 1000) math:remainder 828}] + [ a r:Fact; r:gives {(828 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(828 100) math:remainder 28}] + [ a r:Fact; r:gives {(28 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(28 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2828]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 828]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5257 a r:Inference; + r:gives { + 2829 :numberToDigits (2 8 2 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2829 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2829 1000) math:remainder 829}] + [ a r:Fact; r:gives {(829 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(829 100) math:remainder 29}] + [ a r:Fact; r:gives {(29 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(29 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2829]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 829]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5258 a r:Inference; + r:gives { + 2830 :numberToDigits (2 8 3 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2830 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2830 1000) math:remainder 830}] + [ a r:Fact; r:gives {(830 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(830 100) math:remainder 30}] + [ a r:Fact; r:gives {(30 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(30 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2830]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 830]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5259 a r:Inference; + r:gives { + 2831 :numberToDigits (2 8 3 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2831 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2831 1000) math:remainder 831}] + [ a r:Fact; r:gives {(831 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(831 100) math:remainder 31}] + [ a r:Fact; r:gives {(31 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(31 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2831]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 831]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 31]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5260 a r:Inference; + r:gives { + 2832 :numberToDigits (2 8 3 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2832 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2832 1000) math:remainder 832}] + [ a r:Fact; r:gives {(832 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(832 100) math:remainder 32}] + [ a r:Fact; r:gives {(32 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(32 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 32]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5261 a r:Inference; + r:gives { + 2833 :numberToDigits (2 8 3 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2833 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2833 1000) math:remainder 833}] + [ a r:Fact; r:gives {(833 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(833 100) math:remainder 33}] + [ a r:Fact; r:gives {(33 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(33 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2833]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 833]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 33]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5262 a r:Inference; + r:gives { + 2834 :numberToDigits (2 8 3 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2834 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2834 1000) math:remainder 834}] + [ a r:Fact; r:gives {(834 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(834 100) math:remainder 34}] + [ a r:Fact; r:gives {(34 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(34 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2834]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 834]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 34]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5263 a r:Inference; + r:gives { + 2835 :numberToDigits (2 8 3 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2835 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2835 1000) math:remainder 835}] + [ a r:Fact; r:gives {(835 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(835 100) math:remainder 35}] + [ a r:Fact; r:gives {(35 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(35 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2835]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 835]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 35]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5264 a r:Inference; + r:gives { + 2836 :numberToDigits (2 8 3 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2836 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2836 1000) math:remainder 836}] + [ a r:Fact; r:gives {(836 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(836 100) math:remainder 36}] + [ a r:Fact; r:gives {(36 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(36 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2836]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 836]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 36]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5265 a r:Inference; + r:gives { + 2837 :numberToDigits (2 8 3 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2837 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2837 1000) math:remainder 837}] + [ a r:Fact; r:gives {(837 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(837 100) math:remainder 37}] + [ a r:Fact; r:gives {(37 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(37 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2837]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 837]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 37]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5266 a r:Inference; + r:gives { + 2838 :numberToDigits (2 8 3 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2838 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2838 1000) math:remainder 838}] + [ a r:Fact; r:gives {(838 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(838 100) math:remainder 38}] + [ a r:Fact; r:gives {(38 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(38 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2838]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 838]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 38]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5267 a r:Inference; + r:gives { + 2839 :numberToDigits (2 8 3 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2839 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2839 1000) math:remainder 839}] + [ a r:Fact; r:gives {(839 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(839 100) math:remainder 39}] + [ a r:Fact; r:gives {(39 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(39 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2839]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 839]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 39]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5268 a r:Inference; + r:gives { + 2840 :numberToDigits (2 8 4 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2840 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2840 1000) math:remainder 840}] + [ a r:Fact; r:gives {(840 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(840 100) math:remainder 40}] + [ a r:Fact; r:gives {(40 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(40 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2840]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 840]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5269 a r:Inference; + r:gives { + 2841 :numberToDigits (2 8 4 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2841 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2841 1000) math:remainder 841}] + [ a r:Fact; r:gives {(841 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(841 100) math:remainder 41}] + [ a r:Fact; r:gives {(41 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(41 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2841]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 841]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 41]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5270 a r:Inference; + r:gives { + 2842 :numberToDigits (2 8 4 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2842 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2842 1000) math:remainder 842}] + [ a r:Fact; r:gives {(842 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(842 100) math:remainder 42}] + [ a r:Fact; r:gives {(42 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(42 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2842]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 842]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 42]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5271 a r:Inference; + r:gives { + 2843 :numberToDigits (2 8 4 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2843 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2843 1000) math:remainder 843}] + [ a r:Fact; r:gives {(843 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(843 100) math:remainder 43}] + [ a r:Fact; r:gives {(43 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(43 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2843]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 843]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 43]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5272 a r:Inference; + r:gives { + 2844 :numberToDigits (2 8 4 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2844 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2844 1000) math:remainder 844}] + [ a r:Fact; r:gives {(844 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(844 100) math:remainder 44}] + [ a r:Fact; r:gives {(44 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(44 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2844]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 844]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 44]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5273 a r:Inference; + r:gives { + 2845 :numberToDigits (2 8 4 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2845 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2845 1000) math:remainder 845}] + [ a r:Fact; r:gives {(845 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(845 100) math:remainder 45}] + [ a r:Fact; r:gives {(45 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(45 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2845]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 845]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 45]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5274 a r:Inference; + r:gives { + 2846 :numberToDigits (2 8 4 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2846 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2846 1000) math:remainder 846}] + [ a r:Fact; r:gives {(846 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(846 100) math:remainder 46}] + [ a r:Fact; r:gives {(46 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(46 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2846]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 846]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 46]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5275 a r:Inference; + r:gives { + 2847 :numberToDigits (2 8 4 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2847 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2847 1000) math:remainder 847}] + [ a r:Fact; r:gives {(847 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(847 100) math:remainder 47}] + [ a r:Fact; r:gives {(47 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(47 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2847]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 847]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 47]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5276 a r:Inference; + r:gives { + 2848 :numberToDigits (2 8 4 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2848 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2848 1000) math:remainder 848}] + [ a r:Fact; r:gives {(848 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(848 100) math:remainder 48}] + [ a r:Fact; r:gives {(48 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(48 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2848]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 848]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 48]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5277 a r:Inference; + r:gives { + 2849 :numberToDigits (2 8 4 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2849 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2849 1000) math:remainder 849}] + [ a r:Fact; r:gives {(849 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(849 100) math:remainder 49}] + [ a r:Fact; r:gives {(49 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(49 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2849]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 849]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 49]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5278 a r:Inference; + r:gives { + 2850 :numberToDigits (2 8 5 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2850 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2850 1000) math:remainder 850}] + [ a r:Fact; r:gives {(850 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(850 100) math:remainder 50}] + [ a r:Fact; r:gives {(50 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(50 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2850]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 850]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5279 a r:Inference; + r:gives { + 2851 :numberToDigits (2 8 5 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2851 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2851 1000) math:remainder 851}] + [ a r:Fact; r:gives {(851 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(851 100) math:remainder 51}] + [ a r:Fact; r:gives {(51 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(51 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2851]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 851]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 51]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5280 a r:Inference; + r:gives { + 2852 :numberToDigits (2 8 5 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2852 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2852 1000) math:remainder 852}] + [ a r:Fact; r:gives {(852 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(852 100) math:remainder 52}] + [ a r:Fact; r:gives {(52 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(52 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2852]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 852]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 52]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5281 a r:Inference; + r:gives { + 2853 :numberToDigits (2 8 5 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2853 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2853 1000) math:remainder 853}] + [ a r:Fact; r:gives {(853 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(853 100) math:remainder 53}] + [ a r:Fact; r:gives {(53 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(53 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2853]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 853]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 53]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5282 a r:Inference; + r:gives { + 2854 :numberToDigits (2 8 5 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2854 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2854 1000) math:remainder 854}] + [ a r:Fact; r:gives {(854 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(854 100) math:remainder 54}] + [ a r:Fact; r:gives {(54 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(54 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2854]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 854]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 54]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5283 a r:Inference; + r:gives { + 2855 :numberToDigits (2 8 5 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2855 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2855 1000) math:remainder 855}] + [ a r:Fact; r:gives {(855 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(855 100) math:remainder 55}] + [ a r:Fact; r:gives {(55 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(55 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2855]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 855]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 55]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5284 a r:Inference; + r:gives { + 2856 :numberToDigits (2 8 5 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2856 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2856 1000) math:remainder 856}] + [ a r:Fact; r:gives {(856 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(856 100) math:remainder 56}] + [ a r:Fact; r:gives {(56 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(56 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2856]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 856]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 56]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5285 a r:Inference; + r:gives { + 2857 :numberToDigits (2 8 5 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2857 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2857 1000) math:remainder 857}] + [ a r:Fact; r:gives {(857 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(857 100) math:remainder 57}] + [ a r:Fact; r:gives {(57 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(57 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2857]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 857]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 57]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5286 a r:Inference; + r:gives { + 2858 :numberToDigits (2 8 5 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2858 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2858 1000) math:remainder 858}] + [ a r:Fact; r:gives {(858 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(858 100) math:remainder 58}] + [ a r:Fact; r:gives {(58 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(58 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2858]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 858]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 58]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5287 a r:Inference; + r:gives { + 2859 :numberToDigits (2 8 5 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2859 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2859 1000) math:remainder 859}] + [ a r:Fact; r:gives {(859 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(859 100) math:remainder 59}] + [ a r:Fact; r:gives {(59 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(59 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2859]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 859]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 59]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5288 a r:Inference; + r:gives { + 2860 :numberToDigits (2 8 6 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2860 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2860 1000) math:remainder 860}] + [ a r:Fact; r:gives {(860 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(860 100) math:remainder 60}] + [ a r:Fact; r:gives {(60 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(60 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2860]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 860]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5289 a r:Inference; + r:gives { + 2861 :numberToDigits (2 8 6 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2861 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2861 1000) math:remainder 861}] + [ a r:Fact; r:gives {(861 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(861 100) math:remainder 61}] + [ a r:Fact; r:gives {(61 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(61 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2861]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 861]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 61]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5290 a r:Inference; + r:gives { + 2862 :numberToDigits (2 8 6 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2862 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2862 1000) math:remainder 862}] + [ a r:Fact; r:gives {(862 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(862 100) math:remainder 62}] + [ a r:Fact; r:gives {(62 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(62 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2862]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 862]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 62]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5291 a r:Inference; + r:gives { + 2863 :numberToDigits (2 8 6 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2863 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2863 1000) math:remainder 863}] + [ a r:Fact; r:gives {(863 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(863 100) math:remainder 63}] + [ a r:Fact; r:gives {(63 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(63 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2863]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 863]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 63]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5292 a r:Inference; + r:gives { + 2864 :numberToDigits (2 8 6 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2864 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2864 1000) math:remainder 864}] + [ a r:Fact; r:gives {(864 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(864 100) math:remainder 64}] + [ a r:Fact; r:gives {(64 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(64 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2864]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 864]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 64]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5293 a r:Inference; + r:gives { + 2865 :numberToDigits (2 8 6 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2865 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2865 1000) math:remainder 865}] + [ a r:Fact; r:gives {(865 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(865 100) math:remainder 65}] + [ a r:Fact; r:gives {(65 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(65 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2865]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 865]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 65]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5294 a r:Inference; + r:gives { + 2866 :numberToDigits (2 8 6 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2866 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2866 1000) math:remainder 866}] + [ a r:Fact; r:gives {(866 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(866 100) math:remainder 66}] + [ a r:Fact; r:gives {(66 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(66 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2866]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 866]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 66]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5295 a r:Inference; + r:gives { + 2867 :numberToDigits (2 8 6 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2867 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2867 1000) math:remainder 867}] + [ a r:Fact; r:gives {(867 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(867 100) math:remainder 67}] + [ a r:Fact; r:gives {(67 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(67 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2867]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 867]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 67]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5296 a r:Inference; + r:gives { + 2868 :numberToDigits (2 8 6 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2868 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2868 1000) math:remainder 868}] + [ a r:Fact; r:gives {(868 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(868 100) math:remainder 68}] + [ a r:Fact; r:gives {(68 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(68 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2868]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 868]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 68]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5297 a r:Inference; + r:gives { + 2869 :numberToDigits (2 8 6 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2869 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2869 1000) math:remainder 869}] + [ a r:Fact; r:gives {(869 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(869 100) math:remainder 69}] + [ a r:Fact; r:gives {(69 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(69 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2869]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 869]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 69]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5298 a r:Inference; + r:gives { + 2870 :numberToDigits (2 8 7 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2870 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2870 1000) math:remainder 870}] + [ a r:Fact; r:gives {(870 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(870 100) math:remainder 70}] + [ a r:Fact; r:gives {(70 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(70 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2870]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 870]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5299 a r:Inference; + r:gives { + 2871 :numberToDigits (2 8 7 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2871 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2871 1000) math:remainder 871}] + [ a r:Fact; r:gives {(871 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(871 100) math:remainder 71}] + [ a r:Fact; r:gives {(71 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(71 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2871]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 871]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 71]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5300 a r:Inference; + r:gives { + 2872 :numberToDigits (2 8 7 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2872 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2872 1000) math:remainder 872}] + [ a r:Fact; r:gives {(872 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(872 100) math:remainder 72}] + [ a r:Fact; r:gives {(72 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(72 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2872]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 872]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 72]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5301 a r:Inference; + r:gives { + 2873 :numberToDigits (2 8 7 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2873 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2873 1000) math:remainder 873}] + [ a r:Fact; r:gives {(873 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(873 100) math:remainder 73}] + [ a r:Fact; r:gives {(73 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(73 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2873]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 873]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 73]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5302 a r:Inference; + r:gives { + 2874 :numberToDigits (2 8 7 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2874 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2874 1000) math:remainder 874}] + [ a r:Fact; r:gives {(874 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(874 100) math:remainder 74}] + [ a r:Fact; r:gives {(74 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(74 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2874]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 874]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 74]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5303 a r:Inference; + r:gives { + 2875 :numberToDigits (2 8 7 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2875 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2875 1000) math:remainder 875}] + [ a r:Fact; r:gives {(875 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(875 100) math:remainder 75}] + [ a r:Fact; r:gives {(75 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(75 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2875]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 875]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 75]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5304 a r:Inference; + r:gives { + 2876 :numberToDigits (2 8 7 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2876 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2876 1000) math:remainder 876}] + [ a r:Fact; r:gives {(876 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(876 100) math:remainder 76}] + [ a r:Fact; r:gives {(76 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(76 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2876]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 876]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 76]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5305 a r:Inference; + r:gives { + 2877 :numberToDigits (2 8 7 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2877 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2877 1000) math:remainder 877}] + [ a r:Fact; r:gives {(877 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(877 100) math:remainder 77}] + [ a r:Fact; r:gives {(77 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(77 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2877]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 877]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 77]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5306 a r:Inference; + r:gives { + 2878 :numberToDigits (2 8 7 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2878 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2878 1000) math:remainder 878}] + [ a r:Fact; r:gives {(878 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(878 100) math:remainder 78}] + [ a r:Fact; r:gives {(78 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(78 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2878]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 878]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 78]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5307 a r:Inference; + r:gives { + 2879 :numberToDigits (2 8 7 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2879 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2879 1000) math:remainder 879}] + [ a r:Fact; r:gives {(879 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(879 100) math:remainder 79}] + [ a r:Fact; r:gives {(79 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(79 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2879]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 879]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 79]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5308 a r:Inference; + r:gives { + 2880 :numberToDigits (2 8 8 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2880 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2880 1000) math:remainder 880}] + [ a r:Fact; r:gives {(880 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(880 100) math:remainder 80}] + [ a r:Fact; r:gives {(80 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(80 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2880]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 880]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5309 a r:Inference; + r:gives { + 2881 :numberToDigits (2 8 8 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2881 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2881 1000) math:remainder 881}] + [ a r:Fact; r:gives {(881 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(881 100) math:remainder 81}] + [ a r:Fact; r:gives {(81 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(81 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2881]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 881]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 81]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5310 a r:Inference; + r:gives { + 2882 :numberToDigits (2 8 8 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2882 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2882 1000) math:remainder 882}] + [ a r:Fact; r:gives {(882 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(882 100) math:remainder 82}] + [ a r:Fact; r:gives {(82 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(82 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2882]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 882]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 82]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5311 a r:Inference; + r:gives { + 2883 :numberToDigits (2 8 8 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2883 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2883 1000) math:remainder 883}] + [ a r:Fact; r:gives {(883 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(883 100) math:remainder 83}] + [ a r:Fact; r:gives {(83 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(83 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2883]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 883]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 83]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5312 a r:Inference; + r:gives { + 2884 :numberToDigits (2 8 8 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2884 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2884 1000) math:remainder 884}] + [ a r:Fact; r:gives {(884 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(884 100) math:remainder 84}] + [ a r:Fact; r:gives {(84 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(84 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2884]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 884]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 84]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5313 a r:Inference; + r:gives { + 2885 :numberToDigits (2 8 8 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2885 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2885 1000) math:remainder 885}] + [ a r:Fact; r:gives {(885 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(885 100) math:remainder 85}] + [ a r:Fact; r:gives {(85 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(85 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2885]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 885]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 85]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5314 a r:Inference; + r:gives { + 2886 :numberToDigits (2 8 8 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2886 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2886 1000) math:remainder 886}] + [ a r:Fact; r:gives {(886 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(886 100) math:remainder 86}] + [ a r:Fact; r:gives {(86 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(86 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2886]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 886]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 86]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5315 a r:Inference; + r:gives { + 2887 :numberToDigits (2 8 8 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2887 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2887 1000) math:remainder 887}] + [ a r:Fact; r:gives {(887 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(887 100) math:remainder 87}] + [ a r:Fact; r:gives {(87 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(87 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2887]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 887]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 87]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5316 a r:Inference; + r:gives { + 2888 :numberToDigits (2 8 8 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2888 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2888 1000) math:remainder 888}] + [ a r:Fact; r:gives {(888 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(888 100) math:remainder 88}] + [ a r:Fact; r:gives {(88 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(88 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2888]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 888]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 88]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5317 a r:Inference; + r:gives { + (2 8 8 8) :digitsToNumber 2888 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(8 100) math:product 800}] + [ a r:Fact; r:gives {(8 10) math:product 80}] + [ a r:Fact; r:gives {(2000 800 80 8) math:sum 2888}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2888]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6764. + +skolem:lemma5318 a r:Inference; + r:gives { + (8 8 8 2) :digitsToNumber 8882 . + }; + r:evidence ( + [ a r:Fact; r:gives {(8 1000) math:product 8000}] + [ a r:Fact; r:gives {(8 100) math:product 800}] + [ a r:Fact; r:gives {(8 10) math:product 80}] + [ a r:Fact; r:gives {(8000 800 80 2) math:sum 8882}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8882]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma5319 a r:Inference; + r:gives { + 2889 :numberToDigits (2 8 8 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2889 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2889 1000) math:remainder 889}] + [ a r:Fact; r:gives {(889 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(889 100) math:remainder 89}] + [ a r:Fact; r:gives {(89 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(89 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2889]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 889]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 89]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5320 a r:Inference; + r:gives { + (2 8 8 9) :digitsToNumber 2889 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(8 100) math:product 800}] + [ a r:Fact; r:gives {(8 10) math:product 80}] + [ a r:Fact; r:gives {(2000 800 80 9) math:sum 2889}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2889]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma5321 a r:Inference; + r:gives { + (9 8 8 2) :digitsToNumber 9882 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(8 100) math:product 800}] + [ a r:Fact; r:gives {(8 10) math:product 80}] + [ a r:Fact; r:gives {(9000 800 80 2) math:sum 9882}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9882]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma5322 a r:Inference; + r:gives { + 2890 :numberToDigits (2 8 9 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2890 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2890 1000) math:remainder 890}] + [ a r:Fact; r:gives {(890 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(890 100) math:remainder 90}] + [ a r:Fact; r:gives {(90 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(90 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2890]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 890]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5323 a r:Inference; + r:gives { + 2891 :numberToDigits (2 8 9 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2891 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2891 1000) math:remainder 891}] + [ a r:Fact; r:gives {(891 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(891 100) math:remainder 91}] + [ a r:Fact; r:gives {(91 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(91 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2891]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 891]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 91]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5324 a r:Inference; + r:gives { + 2892 :numberToDigits (2 8 9 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2892 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2892 1000) math:remainder 892}] + [ a r:Fact; r:gives {(892 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(892 100) math:remainder 92}] + [ a r:Fact; r:gives {(92 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(92 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2892]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 892]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 92]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5325 a r:Inference; + r:gives { + 2893 :numberToDigits (2 8 9 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2893 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2893 1000) math:remainder 893}] + [ a r:Fact; r:gives {(893 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(893 100) math:remainder 93}] + [ a r:Fact; r:gives {(93 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(93 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2893]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 893]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 93]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5326 a r:Inference; + r:gives { + 2894 :numberToDigits (2 8 9 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2894 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2894 1000) math:remainder 894}] + [ a r:Fact; r:gives {(894 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(894 100) math:remainder 94}] + [ a r:Fact; r:gives {(94 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(94 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2894]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 894]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 94]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5327 a r:Inference; + r:gives { + 2895 :numberToDigits (2 8 9 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2895 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2895 1000) math:remainder 895}] + [ a r:Fact; r:gives {(895 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(895 100) math:remainder 95}] + [ a r:Fact; r:gives {(95 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(95 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2895]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 895]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 95]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5328 a r:Inference; + r:gives { + 2896 :numberToDigits (2 8 9 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2896 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2896 1000) math:remainder 896}] + [ a r:Fact; r:gives {(896 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(896 100) math:remainder 96}] + [ a r:Fact; r:gives {(96 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(96 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2896]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 896]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 96]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5329 a r:Inference; + r:gives { + 2897 :numberToDigits (2 8 9 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2897 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2897 1000) math:remainder 897}] + [ a r:Fact; r:gives {(897 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(897 100) math:remainder 97}] + [ a r:Fact; r:gives {(97 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(97 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2897]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 897]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 97]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5330 a r:Inference; + r:gives { + 2898 :numberToDigits (2 8 9 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2898 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2898 1000) math:remainder 898}] + [ a r:Fact; r:gives {(898 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(898 100) math:remainder 98}] + [ a r:Fact; r:gives {(98 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(98 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2898]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 898]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 98]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5331 a r:Inference; + r:gives { + 2899 :numberToDigits (2 8 9 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2899 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2899 1000) math:remainder 899}] + [ a r:Fact; r:gives {(899 100) math:integerQuotient 8}] + [ a r:Fact; r:gives {(899 100) math:remainder 99}] + [ a r:Fact; r:gives {(99 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(99 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2899]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 899]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 99]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5332 a r:Inference; + r:gives { + (2 8 9 9) :digitsToNumber 2899 . + }; + r:evidence ( + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(8 100) math:product 800}] + [ a r:Fact; r:gives {(9 10) math:product 90}] + [ a r:Fact; r:gives {(2000 800 90 9) math:sum 2899}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2899]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. + +skolem:lemma5333 a r:Inference; + r:gives { + (9 9 8 2) :digitsToNumber 9982 . + }; + r:evidence ( + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(9 100) math:product 900}] + [ a r:Fact; r:gives {(8 10) math:product 80}] + [ a r:Fact; r:gives {(9000 900 80 2) math:sum 9982}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 900]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9982]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. + +skolem:lemma5334 a r:Inference; + r:gives { + 2900 :numberToDigits (2 9 0 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2900 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2900 1000) math:remainder 900}] + [ a r:Fact; r:gives {(900 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(900 100) math:remainder 0}] + [ a r:Fact; r:gives {(0 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(0 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2900]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 900]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5335 a r:Inference; + r:gives { + 2901 :numberToDigits (2 9 0 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2901 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2901 1000) math:remainder 901}] + [ a r:Fact; r:gives {(901 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(901 100) math:remainder 1}] + [ a r:Fact; r:gives {(1 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(1 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2901]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 901]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5336 a r:Inference; + r:gives { + 2902 :numberToDigits (2 9 0 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2902 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2902 1000) math:remainder 902}] + [ a r:Fact; r:gives {(902 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(902 100) math:remainder 2}] + [ a r:Fact; r:gives {(2 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(2 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2902]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 902]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5337 a r:Inference; + r:gives { + 2903 :numberToDigits (2 9 0 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2903 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2903 1000) math:remainder 903}] + [ a r:Fact; r:gives {(903 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(903 100) math:remainder 3}] + [ a r:Fact; r:gives {(3 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(3 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2903]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 903]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5338 a r:Inference; + r:gives { + 2904 :numberToDigits (2 9 0 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2904 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2904 1000) math:remainder 904}] + [ a r:Fact; r:gives {(904 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(904 100) math:remainder 4}] + [ a r:Fact; r:gives {(4 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(4 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2904]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 904]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5339 a r:Inference; + r:gives { + 2905 :numberToDigits (2 9 0 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2905 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2905 1000) math:remainder 905}] + [ a r:Fact; r:gives {(905 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(905 100) math:remainder 5}] + [ a r:Fact; r:gives {(5 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(5 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2905]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 905]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5340 a r:Inference; + r:gives { + 2906 :numberToDigits (2 9 0 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2906 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2906 1000) math:remainder 906}] + [ a r:Fact; r:gives {(906 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(906 100) math:remainder 6}] + [ a r:Fact; r:gives {(6 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(6 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2906]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 906]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5341 a r:Inference; + r:gives { + 2907 :numberToDigits (2 9 0 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2907 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2907 1000) math:remainder 907}] + [ a r:Fact; r:gives {(907 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(907 100) math:remainder 7}] + [ a r:Fact; r:gives {(7 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(7 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2907]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 907]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5342 a r:Inference; + r:gives { + 2908 :numberToDigits (2 9 0 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2908 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2908 1000) math:remainder 908}] + [ a r:Fact; r:gives {(908 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(908 100) math:remainder 8}] + [ a r:Fact; r:gives {(8 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(8 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2908]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 908]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5343 a r:Inference; + r:gives { + 2909 :numberToDigits (2 9 0 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2909 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2909 1000) math:remainder 909}] + [ a r:Fact; r:gives {(909 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(909 100) math:remainder 9}] + [ a r:Fact; r:gives {(9 10) math:integerQuotient 0}] + [ a r:Fact; r:gives {(9 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2909]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 909]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5344 a r:Inference; + r:gives { + 2910 :numberToDigits (2 9 1 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2910 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2910 1000) math:remainder 910}] + [ a r:Fact; r:gives {(910 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(910 100) math:remainder 10}] + [ a r:Fact; r:gives {(10 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(10 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2910]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 910]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 10]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5345 a r:Inference; + r:gives { + 2911 :numberToDigits (2 9 1 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2911 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2911 1000) math:remainder 911}] + [ a r:Fact; r:gives {(911 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(911 100) math:remainder 11}] + [ a r:Fact; r:gives {(11 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(11 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2911]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 911]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 11]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5346 a r:Inference; + r:gives { + 2912 :numberToDigits (2 9 1 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2912 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2912 1000) math:remainder 912}] + [ a r:Fact; r:gives {(912 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(912 100) math:remainder 12}] + [ a r:Fact; r:gives {(12 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(12 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2912]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 912]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5347 a r:Inference; + r:gives { + 2913 :numberToDigits (2 9 1 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2913 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2913 1000) math:remainder 913}] + [ a r:Fact; r:gives {(913 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(913 100) math:remainder 13}] + [ a r:Fact; r:gives {(13 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(13 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2913]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 913]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 13]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5348 a r:Inference; + r:gives { + 2914 :numberToDigits (2 9 1 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2914 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2914 1000) math:remainder 914}] + [ a r:Fact; r:gives {(914 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(914 100) math:remainder 14}] + [ a r:Fact; r:gives {(14 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(14 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2914]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 914]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 14]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5349 a r:Inference; + r:gives { + 2915 :numberToDigits (2 9 1 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2915 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2915 1000) math:remainder 915}] + [ a r:Fact; r:gives {(915 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(915 100) math:remainder 15}] + [ a r:Fact; r:gives {(15 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(15 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2915]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 915]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 15]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5350 a r:Inference; + r:gives { + 2916 :numberToDigits (2 9 1 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2916 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2916 1000) math:remainder 916}] + [ a r:Fact; r:gives {(916 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(916 100) math:remainder 16}] + [ a r:Fact; r:gives {(16 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(16 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2916]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 916]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 16]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5351 a r:Inference; + r:gives { + 2917 :numberToDigits (2 9 1 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2917 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2917 1000) math:remainder 917}] + [ a r:Fact; r:gives {(917 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(917 100) math:remainder 17}] + [ a r:Fact; r:gives {(17 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(17 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2917]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 917]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 17]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5352 a r:Inference; + r:gives { + 2918 :numberToDigits (2 9 1 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2918 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2918 1000) math:remainder 918}] + [ a r:Fact; r:gives {(918 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(918 100) math:remainder 18}] + [ a r:Fact; r:gives {(18 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(18 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2918]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 918]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 18]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5353 a r:Inference; + r:gives { + 2919 :numberToDigits (2 9 1 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2919 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2919 1000) math:remainder 919}] + [ a r:Fact; r:gives {(919 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(919 100) math:remainder 19}] + [ a r:Fact; r:gives {(19 10) math:integerQuotient 1}] + [ a r:Fact; r:gives {(19 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2919]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 919]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 19]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5354 a r:Inference; + r:gives { + 2920 :numberToDigits (2 9 2 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2920 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2920 1000) math:remainder 920}] + [ a r:Fact; r:gives {(920 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(920 100) math:remainder 20}] + [ a r:Fact; r:gives {(20 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(20 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2920]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 920]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 20]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5355 a r:Inference; + r:gives { + 2921 :numberToDigits (2 9 2 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2921 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2921 1000) math:remainder 921}] + [ a r:Fact; r:gives {(921 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(921 100) math:remainder 21}] + [ a r:Fact; r:gives {(21 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(21 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2921]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 921]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 21]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5356 a r:Inference; + r:gives { + 2922 :numberToDigits (2 9 2 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2922 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2922 1000) math:remainder 922}] + [ a r:Fact; r:gives {(922 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(922 100) math:remainder 22}] + [ a r:Fact; r:gives {(22 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(22 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2922]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 922]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5357 a r:Inference; + r:gives { + 2923 :numberToDigits (2 9 2 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2923 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2923 1000) math:remainder 923}] + [ a r:Fact; r:gives {(923 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(923 100) math:remainder 23}] + [ a r:Fact; r:gives {(23 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(23 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2923]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 923]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5358 a r:Inference; + r:gives { + 2924 :numberToDigits (2 9 2 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2924 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2924 1000) math:remainder 924}] + [ a r:Fact; r:gives {(924 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(924 100) math:remainder 24}] + [ a r:Fact; r:gives {(24 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(24 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2924]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 924]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5359 a r:Inference; + r:gives { + 2925 :numberToDigits (2 9 2 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2925 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2925 1000) math:remainder 925}] + [ a r:Fact; r:gives {(925 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(925 100) math:remainder 25}] + [ a r:Fact; r:gives {(25 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(25 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2925]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 925]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5360 a r:Inference; + r:gives { + 2926 :numberToDigits (2 9 2 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2926 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2926 1000) math:remainder 926}] + [ a r:Fact; r:gives {(926 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(926 100) math:remainder 26}] + [ a r:Fact; r:gives {(26 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(26 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2926]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 926]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5361 a r:Inference; + r:gives { + 2927 :numberToDigits (2 9 2 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2927 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2927 1000) math:remainder 927}] + [ a r:Fact; r:gives {(927 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(927 100) math:remainder 27}] + [ a r:Fact; r:gives {(27 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(27 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2927]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 927]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5362 a r:Inference; + r:gives { + 2928 :numberToDigits (2 9 2 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2928 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2928 1000) math:remainder 928}] + [ a r:Fact; r:gives {(928 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(928 100) math:remainder 28}] + [ a r:Fact; r:gives {(28 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(28 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2928]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 928]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5363 a r:Inference; + r:gives { + 2929 :numberToDigits (2 9 2 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2929 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2929 1000) math:remainder 929}] + [ a r:Fact; r:gives {(929 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(929 100) math:remainder 29}] + [ a r:Fact; r:gives {(29 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(29 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2929]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 929]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5364 a r:Inference; + r:gives { + 2930 :numberToDigits (2 9 3 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2930 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2930 1000) math:remainder 930}] + [ a r:Fact; r:gives {(930 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(930 100) math:remainder 30}] + [ a r:Fact; r:gives {(30 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(30 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2930]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 930]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5365 a r:Inference; + r:gives { + 2931 :numberToDigits (2 9 3 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2931 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2931 1000) math:remainder 931}] + [ a r:Fact; r:gives {(931 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(931 100) math:remainder 31}] + [ a r:Fact; r:gives {(31 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(31 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2931]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 931]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 31]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5366 a r:Inference; + r:gives { + 2932 :numberToDigits (2 9 3 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2932 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2932 1000) math:remainder 932}] + [ a r:Fact; r:gives {(932 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(932 100) math:remainder 32}] + [ a r:Fact; r:gives {(32 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(32 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2932]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 932]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 32]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5367 a r:Inference; + r:gives { + 2933 :numberToDigits (2 9 3 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2933 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2933 1000) math:remainder 933}] + [ a r:Fact; r:gives {(933 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(933 100) math:remainder 33}] + [ a r:Fact; r:gives {(33 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(33 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2933]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 933]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 33]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5368 a r:Inference; + r:gives { + 2934 :numberToDigits (2 9 3 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2934 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2934 1000) math:remainder 934}] + [ a r:Fact; r:gives {(934 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(934 100) math:remainder 34}] + [ a r:Fact; r:gives {(34 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(34 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2934]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 934]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 34]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5369 a r:Inference; + r:gives { + 2935 :numberToDigits (2 9 3 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2935 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2935 1000) math:remainder 935}] + [ a r:Fact; r:gives {(935 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(935 100) math:remainder 35}] + [ a r:Fact; r:gives {(35 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(35 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2935]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 935]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 35]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5370 a r:Inference; + r:gives { + 2936 :numberToDigits (2 9 3 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2936 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2936 1000) math:remainder 936}] + [ a r:Fact; r:gives {(936 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(936 100) math:remainder 36}] + [ a r:Fact; r:gives {(36 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(36 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2936]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 936]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 36]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5371 a r:Inference; + r:gives { + 2937 :numberToDigits (2 9 3 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2937 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2937 1000) math:remainder 937}] + [ a r:Fact; r:gives {(937 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(937 100) math:remainder 37}] + [ a r:Fact; r:gives {(37 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(37 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2937]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 937]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 37]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5372 a r:Inference; + r:gives { + 2938 :numberToDigits (2 9 3 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2938 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2938 1000) math:remainder 938}] + [ a r:Fact; r:gives {(938 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(938 100) math:remainder 38}] + [ a r:Fact; r:gives {(38 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(38 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2938]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 938]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 38]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5373 a r:Inference; + r:gives { + 2939 :numberToDigits (2 9 3 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2939 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2939 1000) math:remainder 939}] + [ a r:Fact; r:gives {(939 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(939 100) math:remainder 39}] + [ a r:Fact; r:gives {(39 10) math:integerQuotient 3}] + [ a r:Fact; r:gives {(39 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2939]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 939]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 39]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5374 a r:Inference; + r:gives { + 2940 :numberToDigits (2 9 4 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2940 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2940 1000) math:remainder 940}] + [ a r:Fact; r:gives {(940 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(940 100) math:remainder 40}] + [ a r:Fact; r:gives {(40 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(40 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2940]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 940]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 40]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5375 a r:Inference; + r:gives { + 2941 :numberToDigits (2 9 4 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2941 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2941 1000) math:remainder 941}] + [ a r:Fact; r:gives {(941 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(941 100) math:remainder 41}] + [ a r:Fact; r:gives {(41 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(41 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2941]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 941]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 41]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5376 a r:Inference; + r:gives { + 2942 :numberToDigits (2 9 4 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2942 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2942 1000) math:remainder 942}] + [ a r:Fact; r:gives {(942 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(942 100) math:remainder 42}] + [ a r:Fact; r:gives {(42 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(42 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2942]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 942]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 42]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5377 a r:Inference; + r:gives { + 2943 :numberToDigits (2 9 4 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2943 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2943 1000) math:remainder 943}] + [ a r:Fact; r:gives {(943 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(943 100) math:remainder 43}] + [ a r:Fact; r:gives {(43 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(43 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2943]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 943]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 43]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5378 a r:Inference; + r:gives { + 2944 :numberToDigits (2 9 4 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2944 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2944 1000) math:remainder 944}] + [ a r:Fact; r:gives {(944 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(944 100) math:remainder 44}] + [ a r:Fact; r:gives {(44 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(44 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2944]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 944]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 44]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5379 a r:Inference; + r:gives { + 2945 :numberToDigits (2 9 4 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2945 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2945 1000) math:remainder 945}] + [ a r:Fact; r:gives {(945 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(945 100) math:remainder 45}] + [ a r:Fact; r:gives {(45 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(45 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2945]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 945]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 45]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5380 a r:Inference; + r:gives { + 2946 :numberToDigits (2 9 4 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2946 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2946 1000) math:remainder 946}] + [ a r:Fact; r:gives {(946 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(946 100) math:remainder 46}] + [ a r:Fact; r:gives {(46 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(46 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2946]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 946]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 46]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5381 a r:Inference; + r:gives { + 2947 :numberToDigits (2 9 4 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2947 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2947 1000) math:remainder 947}] + [ a r:Fact; r:gives {(947 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(947 100) math:remainder 47}] + [ a r:Fact; r:gives {(47 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(47 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2947]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 947]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 47]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5382 a r:Inference; + r:gives { + 2948 :numberToDigits (2 9 4 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2948 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2948 1000) math:remainder 948}] + [ a r:Fact; r:gives {(948 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(948 100) math:remainder 48}] + [ a r:Fact; r:gives {(48 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(48 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2948]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 948]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 48]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5383 a r:Inference; + r:gives { + 2949 :numberToDigits (2 9 4 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2949 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2949 1000) math:remainder 949}] + [ a r:Fact; r:gives {(949 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(949 100) math:remainder 49}] + [ a r:Fact; r:gives {(49 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(49 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2949]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 949]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 49]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5384 a r:Inference; + r:gives { + 2950 :numberToDigits (2 9 5 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2950 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2950 1000) math:remainder 950}] + [ a r:Fact; r:gives {(950 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(950 100) math:remainder 50}] + [ a r:Fact; r:gives {(50 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(50 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2950]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 950]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 50]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5385 a r:Inference; + r:gives { + 2951 :numberToDigits (2 9 5 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2951 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2951 1000) math:remainder 951}] + [ a r:Fact; r:gives {(951 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(951 100) math:remainder 51}] + [ a r:Fact; r:gives {(51 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(51 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2951]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 951]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 51]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5386 a r:Inference; + r:gives { + 2952 :numberToDigits (2 9 5 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2952 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2952 1000) math:remainder 952}] + [ a r:Fact; r:gives {(952 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(952 100) math:remainder 52}] + [ a r:Fact; r:gives {(52 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(52 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2952]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 952]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 52]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5387 a r:Inference; + r:gives { + 2953 :numberToDigits (2 9 5 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2953 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2953 1000) math:remainder 953}] + [ a r:Fact; r:gives {(953 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(953 100) math:remainder 53}] + [ a r:Fact; r:gives {(53 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(53 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2953]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 953]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 53]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5388 a r:Inference; + r:gives { + 2954 :numberToDigits (2 9 5 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2954 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2954 1000) math:remainder 954}] + [ a r:Fact; r:gives {(954 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(954 100) math:remainder 54}] + [ a r:Fact; r:gives {(54 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(54 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2954]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 954]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 54]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5389 a r:Inference; + r:gives { + 2955 :numberToDigits (2 9 5 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2955 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2955 1000) math:remainder 955}] + [ a r:Fact; r:gives {(955 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(955 100) math:remainder 55}] + [ a r:Fact; r:gives {(55 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(55 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2955]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 955]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 55]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5390 a r:Inference; + r:gives { + 2956 :numberToDigits (2 9 5 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2956 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2956 1000) math:remainder 956}] + [ a r:Fact; r:gives {(956 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(956 100) math:remainder 56}] + [ a r:Fact; r:gives {(56 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(56 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2956]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 956]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 56]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5391 a r:Inference; + r:gives { + 2957 :numberToDigits (2 9 5 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2957 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2957 1000) math:remainder 957}] + [ a r:Fact; r:gives {(957 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(957 100) math:remainder 57}] + [ a r:Fact; r:gives {(57 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(57 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2957]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 957]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 57]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5392 a r:Inference; + r:gives { + 2958 :numberToDigits (2 9 5 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2958 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2958 1000) math:remainder 958}] + [ a r:Fact; r:gives {(958 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(958 100) math:remainder 58}] + [ a r:Fact; r:gives {(58 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(58 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2958]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 958]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 58]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5393 a r:Inference; + r:gives { + 2959 :numberToDigits (2 9 5 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2959 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2959 1000) math:remainder 959}] + [ a r:Fact; r:gives {(959 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(959 100) math:remainder 59}] + [ a r:Fact; r:gives {(59 10) math:integerQuotient 5}] + [ a r:Fact; r:gives {(59 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2959]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 959]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 59]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5394 a r:Inference; + r:gives { + 2960 :numberToDigits (2 9 6 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2960 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2960 1000) math:remainder 960}] + [ a r:Fact; r:gives {(960 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(960 100) math:remainder 60}] + [ a r:Fact; r:gives {(60 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(60 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2960]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 960]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 60]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5395 a r:Inference; + r:gives { + 2961 :numberToDigits (2 9 6 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2961 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2961 1000) math:remainder 961}] + [ a r:Fact; r:gives {(961 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(961 100) math:remainder 61}] + [ a r:Fact; r:gives {(61 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(61 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2961]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 961]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 61]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5396 a r:Inference; + r:gives { + 2962 :numberToDigits (2 9 6 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2962 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2962 1000) math:remainder 962}] + [ a r:Fact; r:gives {(962 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(962 100) math:remainder 62}] + [ a r:Fact; r:gives {(62 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(62 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2962]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 962]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 62]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5397 a r:Inference; + r:gives { + 2963 :numberToDigits (2 9 6 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2963 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2963 1000) math:remainder 963}] + [ a r:Fact; r:gives {(963 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(963 100) math:remainder 63}] + [ a r:Fact; r:gives {(63 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(63 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2963]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 963]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 63]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5398 a r:Inference; + r:gives { + 2964 :numberToDigits (2 9 6 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2964 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2964 1000) math:remainder 964}] + [ a r:Fact; r:gives {(964 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(964 100) math:remainder 64}] + [ a r:Fact; r:gives {(64 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(64 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2964]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 964]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 64]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5399 a r:Inference; + r:gives { + 2965 :numberToDigits (2 9 6 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2965 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2965 1000) math:remainder 965}] + [ a r:Fact; r:gives {(965 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(965 100) math:remainder 65}] + [ a r:Fact; r:gives {(65 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(65 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2965]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 965]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 65]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5400 a r:Inference; + r:gives { + 2966 :numberToDigits (2 9 6 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2966 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2966 1000) math:remainder 966}] + [ a r:Fact; r:gives {(966 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(966 100) math:remainder 66}] + [ a r:Fact; r:gives {(66 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(66 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2966]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 966]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 66]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5401 a r:Inference; + r:gives { + 2967 :numberToDigits (2 9 6 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2967 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2967 1000) math:remainder 967}] + [ a r:Fact; r:gives {(967 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(967 100) math:remainder 67}] + [ a r:Fact; r:gives {(67 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(67 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2967]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 967]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 67]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5402 a r:Inference; + r:gives { + 2968 :numberToDigits (2 9 6 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2968 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2968 1000) math:remainder 968}] + [ a r:Fact; r:gives {(968 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(968 100) math:remainder 68}] + [ a r:Fact; r:gives {(68 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(68 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2968]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 968]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 68]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5403 a r:Inference; + r:gives { + 2969 :numberToDigits (2 9 6 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2969 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2969 1000) math:remainder 969}] + [ a r:Fact; r:gives {(969 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(969 100) math:remainder 69}] + [ a r:Fact; r:gives {(69 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(69 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2969]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 969]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 69]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5404 a r:Inference; + r:gives { + 2970 :numberToDigits (2 9 7 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2970 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2970 1000) math:remainder 970}] + [ a r:Fact; r:gives {(970 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(970 100) math:remainder 70}] + [ a r:Fact; r:gives {(70 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(70 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2970]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 970]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 70]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5405 a r:Inference; + r:gives { + 2971 :numberToDigits (2 9 7 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2971 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2971 1000) math:remainder 971}] + [ a r:Fact; r:gives {(971 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(971 100) math:remainder 71}] + [ a r:Fact; r:gives {(71 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(71 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2971]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 971]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 71]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5406 a r:Inference; + r:gives { + 2972 :numberToDigits (2 9 7 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2972 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2972 1000) math:remainder 972}] + [ a r:Fact; r:gives {(972 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(972 100) math:remainder 72}] + [ a r:Fact; r:gives {(72 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(72 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2972]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 972]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 72]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5407 a r:Inference; + r:gives { + 2973 :numberToDigits (2 9 7 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2973 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2973 1000) math:remainder 973}] + [ a r:Fact; r:gives {(973 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(973 100) math:remainder 73}] + [ a r:Fact; r:gives {(73 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(73 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2973]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 973]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 73]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5408 a r:Inference; + r:gives { + 2974 :numberToDigits (2 9 7 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2974 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2974 1000) math:remainder 974}] + [ a r:Fact; r:gives {(974 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(974 100) math:remainder 74}] + [ a r:Fact; r:gives {(74 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(74 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2974]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 974]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 74]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5409 a r:Inference; + r:gives { + 2975 :numberToDigits (2 9 7 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2975 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2975 1000) math:remainder 975}] + [ a r:Fact; r:gives {(975 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(975 100) math:remainder 75}] + [ a r:Fact; r:gives {(75 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(75 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2975]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 975]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 75]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5410 a r:Inference; + r:gives { + 2976 :numberToDigits (2 9 7 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2976 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2976 1000) math:remainder 976}] + [ a r:Fact; r:gives {(976 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(976 100) math:remainder 76}] + [ a r:Fact; r:gives {(76 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(76 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2976]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 976]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 76]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5411 a r:Inference; + r:gives { + 2977 :numberToDigits (2 9 7 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2977 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2977 1000) math:remainder 977}] + [ a r:Fact; r:gives {(977 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(977 100) math:remainder 77}] + [ a r:Fact; r:gives {(77 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(77 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2977]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 977]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 77]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5412 a r:Inference; + r:gives { + 2978 :numberToDigits (2 9 7 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2978 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2978 1000) math:remainder 978}] + [ a r:Fact; r:gives {(978 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(978 100) math:remainder 78}] + [ a r:Fact; r:gives {(78 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(78 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2978]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 978]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 78]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5413 a r:Inference; + r:gives { + 2979 :numberToDigits (2 9 7 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2979 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2979 1000) math:remainder 979}] + [ a r:Fact; r:gives {(979 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(979 100) math:remainder 79}] + [ a r:Fact; r:gives {(79 10) math:integerQuotient 7}] + [ a r:Fact; r:gives {(79 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2979]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 979]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 79]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5414 a r:Inference; + r:gives { + 2980 :numberToDigits (2 9 8 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2980 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2980 1000) math:remainder 980}] + [ a r:Fact; r:gives {(980 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(980 100) math:remainder 80}] + [ a r:Fact; r:gives {(80 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(80 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2980]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 980]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 80]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5415 a r:Inference; + r:gives { + 2981 :numberToDigits (2 9 8 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2981 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2981 1000) math:remainder 981}] + [ a r:Fact; r:gives {(981 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(981 100) math:remainder 81}] + [ a r:Fact; r:gives {(81 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(81 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2981]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 981]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 81]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5416 a r:Inference; + r:gives { + 2982 :numberToDigits (2 9 8 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2982 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2982 1000) math:remainder 982}] + [ a r:Fact; r:gives {(982 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(982 100) math:remainder 82}] + [ a r:Fact; r:gives {(82 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(82 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2982]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 982]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 82]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5417 a r:Inference; + r:gives { + 2983 :numberToDigits (2 9 8 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2983 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2983 1000) math:remainder 983}] + [ a r:Fact; r:gives {(983 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(983 100) math:remainder 83}] + [ a r:Fact; r:gives {(83 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(83 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2983]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 983]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 83]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5418 a r:Inference; + r:gives { + 2984 :numberToDigits (2 9 8 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2984 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2984 1000) math:remainder 984}] + [ a r:Fact; r:gives {(984 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(984 100) math:remainder 84}] + [ a r:Fact; r:gives {(84 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(84 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2984]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 984]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 84]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5419 a r:Inference; + r:gives { + 2985 :numberToDigits (2 9 8 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2985 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2985 1000) math:remainder 985}] + [ a r:Fact; r:gives {(985 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(985 100) math:remainder 85}] + [ a r:Fact; r:gives {(85 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(85 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2985]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 985]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 85]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5420 a r:Inference; + r:gives { + 2986 :numberToDigits (2 9 8 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2986 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2986 1000) math:remainder 986}] + [ a r:Fact; r:gives {(986 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(986 100) math:remainder 86}] + [ a r:Fact; r:gives {(86 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(86 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2986]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 986]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 86]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5421 a r:Inference; + r:gives { + 2987 :numberToDigits (2 9 8 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2987 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2987 1000) math:remainder 987}] + [ a r:Fact; r:gives {(987 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(987 100) math:remainder 87}] + [ a r:Fact; r:gives {(87 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(87 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2987]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 987]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 87]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5422 a r:Inference; + r:gives { + 2988 :numberToDigits (2 9 8 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2988 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2988 1000) math:remainder 988}] + [ a r:Fact; r:gives {(988 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(988 100) math:remainder 88}] + [ a r:Fact; r:gives {(88 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(88 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2988]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 988]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 88]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5423 a r:Inference; + r:gives { + 2989 :numberToDigits (2 9 8 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2989 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2989 1000) math:remainder 989}] + [ a r:Fact; r:gives {(989 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(989 100) math:remainder 89}] + [ a r:Fact; r:gives {(89 10) math:integerQuotient 8}] + [ a r:Fact; r:gives {(89 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2989]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 989]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 89]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5424 a r:Inference; + r:gives { + 2990 :numberToDigits (2 9 9 0). + }; + r:evidence ( + [ a r:Fact; r:gives {(2990 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2990 1000) math:remainder 990}] + [ a r:Fact; r:gives {(990 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(990 100) math:remainder 90}] + [ a r:Fact; r:gives {(90 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(90 10) math:remainder 0}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2990]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 990]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; + r:rule skolem:lemma6763. + +skolem:lemma5425 a r:Inference; + r:gives { + 2991 :numberToDigits (2 9 9 1). + }; + r:evidence ( + [ a r:Fact; r:gives {(2991 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2991 1000) math:remainder 991}] + [ a r:Fact; r:gives {(991 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(991 100) math:remainder 91}] + [ a r:Fact; r:gives {(91 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(91 10) math:remainder 1}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2991]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 991]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 91]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; + r:rule skolem:lemma6763. + +skolem:lemma5426 a r:Inference; + r:gives { + 2992 :numberToDigits (2 9 9 2). + }; + r:evidence ( + [ a r:Fact; r:gives {(2992 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2992 1000) math:remainder 992}] + [ a r:Fact; r:gives {(992 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(992 100) math:remainder 92}] + [ a r:Fact; r:gives {(92 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(92 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 92]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5427 a r:Inference; + r:gives { + 2993 :numberToDigits (2 9 9 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(2993 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2993 1000) math:remainder 993}] + [ a r:Fact; r:gives {(993 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(993 100) math:remainder 93}] + [ a r:Fact; r:gives {(93 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(93 10) math:remainder 3}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 93]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6763. + +skolem:lemma5428 a r:Inference; + r:gives { + 2994 :numberToDigits (2 9 9 4). + }; + r:evidence ( + [ a r:Fact; r:gives {(2994 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2994 1000) math:remainder 994}] + [ a r:Fact; r:gives {(994 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(994 100) math:remainder 94}] + [ a r:Fact; r:gives {(94 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(94 10) math:remainder 4}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 94]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; + r:rule skolem:lemma6763. + +skolem:lemma5429 a r:Inference; + r:gives { + 2995 :numberToDigits (2 9 9 5). + }; + r:evidence ( + [ a r:Fact; r:gives {(2995 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2995 1000) math:remainder 995}] + [ a r:Fact; r:gives {(995 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(995 100) math:remainder 95}] + [ a r:Fact; r:gives {(95 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(95 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 95]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. + +skolem:lemma5430 a r:Inference; + r:gives { + 2996 :numberToDigits (2 9 9 6). + }; + r:evidence ( + [ a r:Fact; r:gives {(2996 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2996 1000) math:remainder 996}] + [ a r:Fact; r:gives {(996 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(996 100) math:remainder 96}] + [ a r:Fact; r:gives {(96 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(96 10) math:remainder 6}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 96]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. + +skolem:lemma5431 a r:Inference; + r:gives { + 2997 :numberToDigits (2 9 9 7). + }; + r:evidence ( + [ a r:Fact; r:gives {(2997 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2997 1000) math:remainder 997}] + [ a r:Fact; r:gives {(997 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(997 100) math:remainder 97}] + [ a r:Fact; r:gives {(97 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(97 10) math:remainder 7}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 97]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. + +skolem:lemma5432 a r:Inference; + r:gives { + 2998 :numberToDigits (2 9 9 8). + }; + r:evidence ( + [ a r:Fact; r:gives {(2998 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2998 1000) math:remainder 998}] + [ a r:Fact; r:gives {(998 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(998 100) math:remainder 98}] + [ a r:Fact; r:gives {(98 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(98 10) math:remainder 8}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 98]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. + +skolem:lemma5433 a r:Inference; + r:gives { + 2999 :numberToDigits (2 9 9 9). + }; + r:evidence ( + [ a r:Fact; r:gives {(2999 1000) math:integerQuotient 2}] + [ a r:Fact; r:gives {(2999 1000) math:remainder 999}] + [ a r:Fact; r:gives {(999 100) math:integerQuotient 9}] + [ a r:Fact; r:gives {(999 100) math:remainder 99}] + [ a r:Fact; r:gives {(99 10) math:integerQuotient 9}] + [ a r:Fact; r:gives {(99 10) math:remainder 9}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 99]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. + +skolem:lemma5434 a r:Inference; + r:gives { + (2 9 9 9) :digitsToNumber 2999 . }; r:evidence ( - [ a r:Fact; r:gives {2998 math:notEqualTo 0}] - skolem:lemma3434 - [ a r:Fact; r:gives {((2 9 9 8) "=<") list:sort (2 8 9 9)}] - [ a r:Fact; r:gives {((2 9 9 8) ">=") list:sort (9 9 8 2)}] - skolem:lemma3334 - skolem:lemma3335 - [ a r:Fact; r:gives {(9982 2899) math:difference 7083}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 7083 math:equalTo 6174. - } { - 3 log:equalTo 1. - } { - 7083 :kaprekar (1 3). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(9 100) math:product 900}] + [ a r:Fact; r:gives {(9 10) math:product 90}] + [ a r:Fact; r:gives {(2000 900 90 9) math:sum 2999}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2998]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 9 8)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 8 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 8 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2899]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9982]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7083]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 3]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 900]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6764. -skolem:lemma1999 a r:Inference; +skolem:lemma5435 a r:Inference; r:gives { - 2999 :kaprekar (0 4). + (9 9 9 2) :digitsToNumber 9992 . }; r:evidence ( - [ a r:Fact; r:gives {2999 math:notEqualTo 0}] - skolem:lemma3435 - [ a r:Fact; r:gives {((2 9 9 9) "=<") list:sort (2 9 9 9)}] - [ a r:Fact; r:gives {((2 9 9 9) ">=") list:sort (9 9 9 2)}] - skolem:lemma3436 - skolem:lemma3437 - [ a r:Fact; r:gives {(9992 2999) math:difference 6993}] - [ a r:Fact; r:gives {(0 1) math:sum 1}] - [ a r:Fact; r:gives {({ - 6993 math:equalTo 6174. - } { - 4 log:equalTo 1. - } { - 6993 :kaprekar (1 4). - }) log:ifThenElseIn (() 1)}] + [ a r:Fact; r:gives {(9 1000) math:product 9000}] + [ a r:Fact; r:gives {(9 100) math:product 900}] + [ a r:Fact; r:gives {(9 10) math:product 90}] + [ a r:Fact; r:gives {(9000 900 90 2) math:sum 9992}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2999]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo (2 9 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo (2 9 9 9)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo (9 9 9 2)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2999]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6993]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_8"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_10"]; r:boundTo (() 1)]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_9"]; r:boundTo 4]; - r:rule skolem:lemma2003. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 900]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 90]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6764. -skolem:lemma2000 a r:Inference; +skolem:lemma5436 a r:Inference; r:gives { - 2000 :numberToDigits (2 0 0 0). + 3000 :numberToDigits (3 0 0 0). }; r:evidence ( - [ a r:Fact; r:gives {(2000 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2000 1000) math:remainder 0}] + [ a r:Fact; r:gives {(3000 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3000 1000) math:remainder 0}] [ a r:Fact; r:gives {(0 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(0 100) math:remainder 0}] [ a r:Fact; r:gives {(0 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(0 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2001 a r:Inference; +skolem:lemma5437 a r:Inference; r:gives { - (0 0 0 2) :digitsToNumber 2 . + (0 0 0 3) :digitsToNumber 3 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] [ a r:Fact; r:gives {(0 100) math:product 0}] [ a r:Fact; r:gives {(0 10) math:product 0}] - [ a r:Fact; r:gives {(0 0 0 2) math:sum 2}] + [ a r:Fact; r:gives {(0 0 0 3) math:sum 3}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; @@ -50010,84 +129723,60 @@ skolem:lemma2001 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2002 a r:Inference; +skolem:lemma5438 a r:Inference; r:gives { - (2 0 0 0) :digitsToNumber 2000 . + (3 0 0 0) :digitsToNumber 3000 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(0 100) math:product 0}] [ a r:Fact; r:gives {(0 10) math:product 0}] - [ a r:Fact; r:gives {(2000 0 0 0) math:sum 2000}] + [ a r:Fact; r:gives {(3000 0 0 0) math:sum 3000}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. - -skolem:lemma2003 a r:Extraction; - r:gives { - @forAll var:x_0, var:x_1, var:x_2, var:x_3, var:x_4, var:x_5, var:x_6, var:x_7, var:x_8, var:x_9, var:x_10. { - var:x_0 :kaprekar (var:x_7 var:x_9). - } <= { - var:x_0 math:notEqualTo 0 . - var:x_0 :numberToDigits var:x_1. - (var:x_1 "=<") list:sort var:x_2. - (var:x_1 ">=") list:sort var:x_3. - var:x_2 :digitsToNumber var:x_4. - var:x_3 :digitsToNumber var:x_5. - (var:x_5 var:x_4) math:difference var:x_6. - (var:x_7 1) math:sum var:x_8. - ({ - var:x_6 math:equalTo 6174. - } { - var:x_9 log:equalTo var:x_8. - } { - var:x_6 :kaprekar (var:x_8 var:x_9). - }) log:ifThenElseIn var:x_10. - }. - }; - r:because [ a r:Parsing; r:source ]. + r:rule skolem:lemma6764. -skolem:lemma2004 a r:Inference; +skolem:lemma5439 a r:Inference; r:gives { - 2001 :numberToDigits (2 0 0 1). + 3001 :numberToDigits (3 0 0 1). }; r:evidence ( - [ a r:Fact; r:gives {(2001 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2001 1000) math:remainder 1}] + [ a r:Fact; r:gives {(3001 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3001 1000) math:remainder 1}] [ a r:Fact; r:gives {(1 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(1 100) math:remainder 1}] [ a r:Fact; r:gives {(1 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(1 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2001]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3001]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2005 a r:Inference; +skolem:lemma5440 a r:Inference; r:gives { - (0 0 1 2) :digitsToNumber 12 . + (0 0 1 3) :digitsToNumber 13 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] [ a r:Fact; r:gives {(0 100) math:product 0}] [ a r:Fact; r:gives {(1 10) math:product 10}] - [ a r:Fact; r:gives {(0 0 10 2) math:sum 12}] + [ a r:Fact; r:gives {(0 0 10 3) math:sum 13}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; @@ -50095,569 +129784,529 @@ skolem:lemma2005 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 12]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 13]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2006 a r:Inference; +skolem:lemma5441 a r:Inference; r:gives { - (2 1 0 0) :digitsToNumber 2100 . + (3 1 0 0) :digitsToNumber 3100 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(1 100) math:product 100}] [ a r:Fact; r:gives {(0 10) math:product 0}] - [ a r:Fact; r:gives {(2000 100 0 0) math:sum 2100}] + [ a r:Fact; r:gives {(3000 100 0 0) math:sum 3100}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3100]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2007 a r:Inference; +skolem:lemma5442 a r:Inference; r:gives { - 2002 :numberToDigits (2 0 0 2). + 3002 :numberToDigits (3 0 0 2). }; r:evidence ( - [ a r:Fact; r:gives {(2002 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2002 1000) math:remainder 2}] + [ a r:Fact; r:gives {(3002 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3002 1000) math:remainder 2}] [ a r:Fact; r:gives {(2 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(2 100) math:remainder 2}] [ a r:Fact; r:gives {(2 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(2 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2002]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3002]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. - -skolem:lemma2008 a r:Inference; - r:gives { - (0 0 2 2) :digitsToNumber 22 . - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(0 100) math:product 0}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 0 20 2) math:sum 22}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 22]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. - -skolem:lemma2009 a r:Inference; - r:gives { - (2 2 0 0) :digitsToNumber 2200 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(0 10) math:product 0}] - [ a r:Fact; r:gives {(2000 200 0 0) math:sum 2200}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2010 a r:Inference; +skolem:lemma5443 a r:Inference; r:gives { - 2003 :numberToDigits (2 0 0 3). + 3003 :numberToDigits (3 0 0 3). }; r:evidence ( - [ a r:Fact; r:gives {(2003 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2003 1000) math:remainder 3}] + [ a r:Fact; r:gives {(3003 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3003 1000) math:remainder 3}] [ a r:Fact; r:gives {(3 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(3 100) math:remainder 3}] [ a r:Fact; r:gives {(3 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(3 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2003]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3003]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2011 a r:Inference; +skolem:lemma5444 a r:Inference; r:gives { - (0 0 2 3) :digitsToNumber 23 . + (0 0 3 3) :digitsToNumber 33 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] [ a r:Fact; r:gives {(0 100) math:product 0}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 0 20 3) math:sum 23}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(0 0 30 3) math:sum 33}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 23]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 33]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2012 a r:Inference; +skolem:lemma5445 a r:Inference; r:gives { - (3 2 0 0) :digitsToNumber 3200 . + (3 3 0 0) :digitsToNumber 3300 . }; r:evidence ( [ a r:Fact; r:gives {(3 1000) math:product 3000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(0 10) math:product 0}] - [ a r:Fact; r:gives {(3000 200 0 0) math:sum 3200}] + [ a r:Fact; r:gives {(3000 300 0 0) math:sum 3300}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2013 a r:Inference; +skolem:lemma5446 a r:Inference; r:gives { - 2004 :numberToDigits (2 0 0 4). + 3004 :numberToDigits (3 0 0 4). }; r:evidence ( - [ a r:Fact; r:gives {(2004 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2004 1000) math:remainder 4}] + [ a r:Fact; r:gives {(3004 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3004 1000) math:remainder 4}] [ a r:Fact; r:gives {(4 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(4 100) math:remainder 4}] [ a r:Fact; r:gives {(4 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(4 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2004]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3004]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2014 a r:Inference; +skolem:lemma5447 a r:Inference; r:gives { - (0 0 2 4) :digitsToNumber 24 . + (0 0 3 4) :digitsToNumber 34 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] [ a r:Fact; r:gives {(0 100) math:product 0}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 0 20 4) math:sum 24}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(0 0 30 4) math:sum 34}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 24]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 34]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2015 a r:Inference; +skolem:lemma5448 a r:Inference; r:gives { - (4 2 0 0) :digitsToNumber 4200 . + (4 3 0 0) :digitsToNumber 4300 . }; r:evidence ( [ a r:Fact; r:gives {(4 1000) math:product 4000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(0 10) math:product 0}] - [ a r:Fact; r:gives {(4000 200 0 0) math:sum 4200}] + [ a r:Fact; r:gives {(4000 300 0 0) math:sum 4300}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2016 a r:Inference; +skolem:lemma5449 a r:Inference; r:gives { - 2005 :numberToDigits (2 0 0 5). + 3005 :numberToDigits (3 0 0 5). }; r:evidence ( - [ a r:Fact; r:gives {(2005 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2005 1000) math:remainder 5}] + [ a r:Fact; r:gives {(3005 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3005 1000) math:remainder 5}] [ a r:Fact; r:gives {(5 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(5 100) math:remainder 5}] [ a r:Fact; r:gives {(5 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(5 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2005]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3005]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2017 a r:Inference; +skolem:lemma5450 a r:Inference; r:gives { - (0 0 2 5) :digitsToNumber 25 . + (0 0 3 5) :digitsToNumber 35 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] [ a r:Fact; r:gives {(0 100) math:product 0}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 0 20 5) math:sum 25}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(0 0 30 5) math:sum 35}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 25]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 35]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2018 a r:Inference; +skolem:lemma5451 a r:Inference; r:gives { - (5 2 0 0) :digitsToNumber 5200 . + (5 3 0 0) :digitsToNumber 5300 . }; r:evidence ( [ a r:Fact; r:gives {(5 1000) math:product 5000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(0 10) math:product 0}] - [ a r:Fact; r:gives {(5000 200 0 0) math:sum 5200}] + [ a r:Fact; r:gives {(5000 300 0 0) math:sum 5300}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2019 a r:Inference; +skolem:lemma5452 a r:Inference; r:gives { - 2006 :numberToDigits (2 0 0 6). + 3006 :numberToDigits (3 0 0 6). }; r:evidence ( - [ a r:Fact; r:gives {(2006 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2006 1000) math:remainder 6}] + [ a r:Fact; r:gives {(3006 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3006 1000) math:remainder 6}] [ a r:Fact; r:gives {(6 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(6 100) math:remainder 6}] [ a r:Fact; r:gives {(6 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(6 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2006]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3006]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2020 a r:Inference; +skolem:lemma5453 a r:Inference; r:gives { - (0 0 2 6) :digitsToNumber 26 . + (0 0 3 6) :digitsToNumber 36 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] [ a r:Fact; r:gives {(0 100) math:product 0}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 0 20 6) math:sum 26}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(0 0 30 6) math:sum 36}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 26]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 36]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2021 a r:Inference; +skolem:lemma5454 a r:Inference; r:gives { - (6 2 0 0) :digitsToNumber 6200 . + (6 3 0 0) :digitsToNumber 6300 . }; r:evidence ( [ a r:Fact; r:gives {(6 1000) math:product 6000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(0 10) math:product 0}] - [ a r:Fact; r:gives {(6000 200 0 0) math:sum 6200}] + [ a r:Fact; r:gives {(6000 300 0 0) math:sum 6300}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2022 a r:Inference; +skolem:lemma5455 a r:Inference; r:gives { - 2007 :numberToDigits (2 0 0 7). + 3007 :numberToDigits (3 0 0 7). }; r:evidence ( - [ a r:Fact; r:gives {(2007 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2007 1000) math:remainder 7}] + [ a r:Fact; r:gives {(3007 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3007 1000) math:remainder 7}] [ a r:Fact; r:gives {(7 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(7 100) math:remainder 7}] [ a r:Fact; r:gives {(7 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(7 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2007]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3007]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2023 a r:Inference; +skolem:lemma5456 a r:Inference; r:gives { - (0 0 2 7) :digitsToNumber 27 . + (0 0 3 7) :digitsToNumber 37 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] [ a r:Fact; r:gives {(0 100) math:product 0}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 0 20 7) math:sum 27}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(0 0 30 7) math:sum 37}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 27]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 37]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2024 a r:Inference; +skolem:lemma5457 a r:Inference; r:gives { - (7 2 0 0) :digitsToNumber 7200 . + (7 3 0 0) :digitsToNumber 7300 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(0 10) math:product 0}] - [ a r:Fact; r:gives {(7000 200 0 0) math:sum 7200}] + [ a r:Fact; r:gives {(7000 300 0 0) math:sum 7300}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2025 a r:Inference; +skolem:lemma5458 a r:Inference; r:gives { - 2008 :numberToDigits (2 0 0 8). + 3008 :numberToDigits (3 0 0 8). }; r:evidence ( - [ a r:Fact; r:gives {(2008 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2008 1000) math:remainder 8}] + [ a r:Fact; r:gives {(3008 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3008 1000) math:remainder 8}] [ a r:Fact; r:gives {(8 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(8 100) math:remainder 8}] [ a r:Fact; r:gives {(8 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(8 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2008]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3008]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2026 a r:Inference; +skolem:lemma5459 a r:Inference; r:gives { - (0 0 2 8) :digitsToNumber 28 . + (0 0 3 8) :digitsToNumber 38 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] [ a r:Fact; r:gives {(0 100) math:product 0}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 0 20 8) math:sum 28}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(0 0 30 8) math:sum 38}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 28]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 38]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2027 a r:Inference; +skolem:lemma5460 a r:Inference; r:gives { - (8 2 0 0) :digitsToNumber 8200 . + (8 3 0 0) :digitsToNumber 8300 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(0 10) math:product 0}] - [ a r:Fact; r:gives {(8000 200 0 0) math:sum 8200}] + [ a r:Fact; r:gives {(8000 300 0 0) math:sum 8300}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2028 a r:Inference; +skolem:lemma5461 a r:Inference; r:gives { - 2009 :numberToDigits (2 0 0 9). + 3009 :numberToDigits (3 0 0 9). }; r:evidence ( - [ a r:Fact; r:gives {(2009 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2009 1000) math:remainder 9}] + [ a r:Fact; r:gives {(3009 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3009 1000) math:remainder 9}] [ a r:Fact; r:gives {(9 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(9 100) math:remainder 9}] [ a r:Fact; r:gives {(9 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(9 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2009]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3009]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2029 a r:Inference; +skolem:lemma5462 a r:Inference; r:gives { - (0 0 2 9) :digitsToNumber 29 . + (0 0 3 9) :digitsToNumber 39 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] [ a r:Fact; r:gives {(0 100) math:product 0}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 0 20 9) math:sum 29}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(0 0 30 9) math:sum 39}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 29]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 39]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2030 a r:Inference; +skolem:lemma5463 a r:Inference; r:gives { - (9 2 0 0) :digitsToNumber 9200 . + (9 3 0 0) :digitsToNumber 9300 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(0 10) math:product 0}] - [ a r:Fact; r:gives {(9000 200 0 0) math:sum 9200}] + [ a r:Fact; r:gives {(9000 300 0 0) math:sum 9300}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2031 a r:Inference; +skolem:lemma5464 a r:Inference; r:gives { - 2010 :numberToDigits (2 0 1 0). + 3010 :numberToDigits (3 0 1 0). }; r:evidence ( - [ a r:Fact; r:gives {(2010 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2010 1000) math:remainder 10}] + [ a r:Fact; r:gives {(3010 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3010 1000) math:remainder 10}] [ a r:Fact; r:gives {(10 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(10 100) math:remainder 10}] [ a r:Fact; r:gives {(10 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(10 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2010]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3010]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2032 a r:Inference; +skolem:lemma5465 a r:Inference; r:gives { - 2011 :numberToDigits (2 0 1 1). + 3011 :numberToDigits (3 0 1 1). }; r:evidence ( - [ a r:Fact; r:gives {(2011 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2011 1000) math:remainder 11}] + [ a r:Fact; r:gives {(3011 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3011 1000) math:remainder 11}] [ a r:Fact; r:gives {(11 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(11 100) math:remainder 11}] [ a r:Fact; r:gives {(11 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(11 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2011]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3011]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 11]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 11]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2033 a r:Inference; +skolem:lemma5466 a r:Inference; r:gives { - (0 1 1 2) :digitsToNumber 112 . + (0 1 1 3) :digitsToNumber 113 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] [ a r:Fact; r:gives {(1 100) math:product 100}] [ a r:Fact; r:gives {(1 10) math:product 10}] - [ a r:Fact; r:gives {(0 100 10 2) math:sum 112}] + [ a r:Fact; r:gives {(0 100 10 3) math:sum 113}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; @@ -50665,3899 +130314,3539 @@ skolem:lemma2033 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 112]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 113]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2034 a r:Inference; +skolem:lemma5467 a r:Inference; r:gives { - (2 1 1 0) :digitsToNumber 2110 . + (3 1 1 0) :digitsToNumber 3110 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(1 100) math:product 100}] [ a r:Fact; r:gives {(1 10) math:product 10}] - [ a r:Fact; r:gives {(2000 100 10 0) math:sum 2110}] + [ a r:Fact; r:gives {(3000 100 10 0) math:sum 3110}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2110]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3110]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2035 a r:Inference; +skolem:lemma5468 a r:Inference; r:gives { - 2012 :numberToDigits (2 0 1 2). + 3012 :numberToDigits (3 0 1 2). }; r:evidence ( - [ a r:Fact; r:gives {(2012 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2012 1000) math:remainder 12}] + [ a r:Fact; r:gives {(3012 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3012 1000) math:remainder 12}] [ a r:Fact; r:gives {(12 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(12 100) math:remainder 12}] [ a r:Fact; r:gives {(12 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(12 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2012]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3012]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 12]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. - -skolem:lemma2036 a r:Inference; - r:gives { - (0 1 2 2) :digitsToNumber 122 . - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(1 100) math:product 100}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 100 20 2) math:sum 122}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 122]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. - -skolem:lemma2037 a r:Inference; - r:gives { - (2 2 1 0) :digitsToNumber 2210 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(1 10) math:product 10}] - [ a r:Fact; r:gives {(2000 200 10 0) math:sum 2210}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2210]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2038 a r:Inference; +skolem:lemma5469 a r:Inference; r:gives { - 2013 :numberToDigits (2 0 1 3). + 3013 :numberToDigits (3 0 1 3). }; r:evidence ( - [ a r:Fact; r:gives {(2013 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2013 1000) math:remainder 13}] + [ a r:Fact; r:gives {(3013 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3013 1000) math:remainder 13}] [ a r:Fact; r:gives {(13 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(13 100) math:remainder 13}] [ a r:Fact; r:gives {(13 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(13 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2013]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3013]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 13]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 13]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2039 a r:Inference; +skolem:lemma5470 a r:Inference; r:gives { - (0 1 2 3) :digitsToNumber 123 . + (0 1 3 3) :digitsToNumber 133 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] [ a r:Fact; r:gives {(1 100) math:product 100}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 100 20 3) math:sum 123}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(0 100 30 3) math:sum 133}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 133]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2040 a r:Inference; +skolem:lemma5471 a r:Inference; r:gives { - (3 2 1 0) :digitsToNumber 3210 . + (3 3 1 0) :digitsToNumber 3310 . }; r:evidence ( [ a r:Fact; r:gives {(3 1000) math:product 3000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(1 10) math:product 10}] - [ a r:Fact; r:gives {(3000 200 10 0) math:sum 3210}] + [ a r:Fact; r:gives {(3000 300 10 0) math:sum 3310}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3310]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2041 a r:Inference; +skolem:lemma5472 a r:Inference; r:gives { - 2014 :numberToDigits (2 0 1 4). + 3014 :numberToDigits (3 0 1 4). }; r:evidence ( - [ a r:Fact; r:gives {(2014 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2014 1000) math:remainder 14}] + [ a r:Fact; r:gives {(3014 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3014 1000) math:remainder 14}] [ a r:Fact; r:gives {(14 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(14 100) math:remainder 14}] [ a r:Fact; r:gives {(14 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(14 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2014]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3014]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 14]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 14]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2042 a r:Inference; +skolem:lemma5473 a r:Inference; r:gives { - (0 1 2 4) :digitsToNumber 124 . + (0 1 3 4) :digitsToNumber 134 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] [ a r:Fact; r:gives {(1 100) math:product 100}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 100 20 4) math:sum 124}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(0 100 30 4) math:sum 134}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 134]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2043 a r:Inference; +skolem:lemma5474 a r:Inference; r:gives { - (4 2 1 0) :digitsToNumber 4210 . + (4 3 1 0) :digitsToNumber 4310 . }; r:evidence ( [ a r:Fact; r:gives {(4 1000) math:product 4000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(1 10) math:product 10}] - [ a r:Fact; r:gives {(4000 200 10 0) math:sum 4210}] + [ a r:Fact; r:gives {(4000 300 10 0) math:sum 4310}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4310]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2044 a r:Inference; +skolem:lemma5475 a r:Inference; r:gives { - 2015 :numberToDigits (2 0 1 5). + 3015 :numberToDigits (3 0 1 5). }; r:evidence ( - [ a r:Fact; r:gives {(2015 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2015 1000) math:remainder 15}] + [ a r:Fact; r:gives {(3015 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3015 1000) math:remainder 15}] [ a r:Fact; r:gives {(15 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(15 100) math:remainder 15}] [ a r:Fact; r:gives {(15 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(15 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2015]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3015]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 15]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 15]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2045 a r:Inference; +skolem:lemma5476 a r:Inference; r:gives { - (0 1 2 5) :digitsToNumber 125 . + (0 1 3 5) :digitsToNumber 135 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] [ a r:Fact; r:gives {(1 100) math:product 100}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 100 20 5) math:sum 125}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(0 100 30 5) math:sum 135}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 135]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2046 a r:Inference; +skolem:lemma5477 a r:Inference; r:gives { - (5 2 1 0) :digitsToNumber 5210 . + (5 3 1 0) :digitsToNumber 5310 . }; r:evidence ( [ a r:Fact; r:gives {(5 1000) math:product 5000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(1 10) math:product 10}] - [ a r:Fact; r:gives {(5000 200 10 0) math:sum 5210}] + [ a r:Fact; r:gives {(5000 300 10 0) math:sum 5310}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5310]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2047 a r:Inference; +skolem:lemma5478 a r:Inference; r:gives { - 2016 :numberToDigits (2 0 1 6). + 3016 :numberToDigits (3 0 1 6). }; r:evidence ( - [ a r:Fact; r:gives {(2016 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2016 1000) math:remainder 16}] + [ a r:Fact; r:gives {(3016 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3016 1000) math:remainder 16}] [ a r:Fact; r:gives {(16 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(16 100) math:remainder 16}] [ a r:Fact; r:gives {(16 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(16 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2016]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3016]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 16]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 16]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2048 a r:Inference; +skolem:lemma5479 a r:Inference; r:gives { - (0 1 2 6) :digitsToNumber 126 . + (0 1 3 6) :digitsToNumber 136 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] [ a r:Fact; r:gives {(1 100) math:product 100}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 100 20 6) math:sum 126}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(0 100 30 6) math:sum 136}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 136]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2049 a r:Inference; +skolem:lemma5480 a r:Inference; r:gives { - (6 2 1 0) :digitsToNumber 6210 . + (6 3 1 0) :digitsToNumber 6310 . }; r:evidence ( [ a r:Fact; r:gives {(6 1000) math:product 6000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(1 10) math:product 10}] - [ a r:Fact; r:gives {(6000 200 10 0) math:sum 6210}] + [ a r:Fact; r:gives {(6000 300 10 0) math:sum 6310}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6310]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2050 a r:Inference; +skolem:lemma5481 a r:Inference; r:gives { - 2017 :numberToDigits (2 0 1 7). + 3017 :numberToDigits (3 0 1 7). }; r:evidence ( - [ a r:Fact; r:gives {(2017 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2017 1000) math:remainder 17}] + [ a r:Fact; r:gives {(3017 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3017 1000) math:remainder 17}] [ a r:Fact; r:gives {(17 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(17 100) math:remainder 17}] [ a r:Fact; r:gives {(17 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(17 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2017]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3017]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 17]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 17]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2051 a r:Inference; +skolem:lemma5482 a r:Inference; r:gives { - (0 1 2 7) :digitsToNumber 127 . + (0 1 3 7) :digitsToNumber 137 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] [ a r:Fact; r:gives {(1 100) math:product 100}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 100 20 7) math:sum 127}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(0 100 30 7) math:sum 137}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 137]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2052 a r:Inference; +skolem:lemma5483 a r:Inference; r:gives { - (7 2 1 0) :digitsToNumber 7210 . + (7 3 1 0) :digitsToNumber 7310 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(1 10) math:product 10}] - [ a r:Fact; r:gives {(7000 200 10 0) math:sum 7210}] + [ a r:Fact; r:gives {(7000 300 10 0) math:sum 7310}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7310]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2053 a r:Inference; +skolem:lemma5484 a r:Inference; r:gives { - 2018 :numberToDigits (2 0 1 8). + 3018 :numberToDigits (3 0 1 8). }; r:evidence ( - [ a r:Fact; r:gives {(2018 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2018 1000) math:remainder 18}] + [ a r:Fact; r:gives {(3018 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3018 1000) math:remainder 18}] [ a r:Fact; r:gives {(18 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(18 100) math:remainder 18}] [ a r:Fact; r:gives {(18 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(18 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2018]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3018]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 18]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 18]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2054 a r:Inference; +skolem:lemma5485 a r:Inference; r:gives { - (0 1 2 8) :digitsToNumber 128 . + (0 1 3 8) :digitsToNumber 138 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] [ a r:Fact; r:gives {(1 100) math:product 100}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 100 20 8) math:sum 128}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(0 100 30 8) math:sum 138}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 138]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2055 a r:Inference; +skolem:lemma5486 a r:Inference; r:gives { - (8 2 1 0) :digitsToNumber 8210 . + (8 3 1 0) :digitsToNumber 8310 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(1 10) math:product 10}] - [ a r:Fact; r:gives {(8000 200 10 0) math:sum 8210}] + [ a r:Fact; r:gives {(8000 300 10 0) math:sum 8310}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8310]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2056 a r:Inference; +skolem:lemma5487 a r:Inference; r:gives { - 2019 :numberToDigits (2 0 1 9). + 3019 :numberToDigits (3 0 1 9). }; r:evidence ( - [ a r:Fact; r:gives {(2019 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2019 1000) math:remainder 19}] + [ a r:Fact; r:gives {(3019 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3019 1000) math:remainder 19}] [ a r:Fact; r:gives {(19 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(19 100) math:remainder 19}] [ a r:Fact; r:gives {(19 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(19 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2019]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3019]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 19]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 19]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2057 a r:Inference; +skolem:lemma5488 a r:Inference; r:gives { - (0 1 2 9) :digitsToNumber 129 . + (0 1 3 9) :digitsToNumber 139 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] [ a r:Fact; r:gives {(1 100) math:product 100}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 100 20 9) math:sum 129}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(0 100 30 9) math:sum 139}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 139]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2058 a r:Inference; +skolem:lemma5489 a r:Inference; r:gives { - (9 2 1 0) :digitsToNumber 9210 . + (9 3 1 0) :digitsToNumber 9310 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(1 10) math:product 10}] - [ a r:Fact; r:gives {(9000 200 10 0) math:sum 9210}] + [ a r:Fact; r:gives {(9000 300 10 0) math:sum 9310}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9310]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2059 a r:Inference; +skolem:lemma5490 a r:Inference; r:gives { - 2020 :numberToDigits (2 0 2 0). + 3020 :numberToDigits (3 0 2 0). }; r:evidence ( - [ a r:Fact; r:gives {(2020 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2020 1000) math:remainder 20}] + [ a r:Fact; r:gives {(3020 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3020 1000) math:remainder 20}] [ a r:Fact; r:gives {(20 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(20 100) math:remainder 20}] [ a r:Fact; r:gives {(20 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(20 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2020]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3020]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 20]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 20]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2060 a r:Inference; +skolem:lemma5491 a r:Inference; r:gives { - 2021 :numberToDigits (2 0 2 1). + 3021 :numberToDigits (3 0 2 1). }; r:evidence ( - [ a r:Fact; r:gives {(2021 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2021 1000) math:remainder 21}] + [ a r:Fact; r:gives {(3021 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3021 1000) math:remainder 21}] [ a r:Fact; r:gives {(21 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(21 100) math:remainder 21}] [ a r:Fact; r:gives {(21 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(21 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2021]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3021]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 21]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 21]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2061 a r:Inference; +skolem:lemma5492 a r:Inference; r:gives { - 2022 :numberToDigits (2 0 2 2). + 3022 :numberToDigits (3 0 2 2). }; r:evidence ( - [ a r:Fact; r:gives {(2022 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2022 1000) math:remainder 22}] + [ a r:Fact; r:gives {(3022 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3022 1000) math:remainder 22}] [ a r:Fact; r:gives {(22 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(22 100) math:remainder 22}] [ a r:Fact; r:gives {(22 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(22 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2022]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3022]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 22]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. - -skolem:lemma2062 a r:Inference; - r:gives { - (0 2 2 2) :digitsToNumber 222 . - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 200 20 2) math:sum 222}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. - -skolem:lemma2063 a r:Inference; - r:gives { - (2 2 2 0) :digitsToNumber 2220 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(2000 200 20 0) math:sum 2220}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2064 a r:Inference; +skolem:lemma5493 a r:Inference; r:gives { - 2023 :numberToDigits (2 0 2 3). + 3023 :numberToDigits (3 0 2 3). }; r:evidence ( - [ a r:Fact; r:gives {(2023 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2023 1000) math:remainder 23}] + [ a r:Fact; r:gives {(3023 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3023 1000) math:remainder 23}] [ a r:Fact; r:gives {(23 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(23 100) math:remainder 23}] [ a r:Fact; r:gives {(23 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(23 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2023]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3023]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 23]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. - -skolem:lemma2065 a r:Inference; - r:gives { - (0 2 2 3) :digitsToNumber 223 . - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 200 20 3) math:sum 223}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 223]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3439. - -skolem:lemma2066 a r:Inference; - r:gives { - (3 2 2 0) :digitsToNumber 3220 . - }; - r:evidence ( - [ a r:Fact; r:gives {(3 1000) math:product 3000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(3000 200 20 0) math:sum 3220}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2067 a r:Inference; +skolem:lemma5494 a r:Inference; r:gives { - 2024 :numberToDigits (2 0 2 4). + 3024 :numberToDigits (3 0 2 4). }; r:evidence ( - [ a r:Fact; r:gives {(2024 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2024 1000) math:remainder 24}] + [ a r:Fact; r:gives {(3024 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3024 1000) math:remainder 24}] [ a r:Fact; r:gives {(24 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(24 100) math:remainder 24}] [ a r:Fact; r:gives {(24 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(24 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2024]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3024]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 24]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. - -skolem:lemma2068 a r:Inference; - r:gives { - (0 2 2 4) :digitsToNumber 224 . - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 200 20 4) math:sum 224}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 224]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3439. - -skolem:lemma2069 a r:Inference; - r:gives { - (4 2 2 0) :digitsToNumber 4220 . - }; - r:evidence ( - [ a r:Fact; r:gives {(4 1000) math:product 4000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(4000 200 20 0) math:sum 4220}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2070 a r:Inference; +skolem:lemma5495 a r:Inference; r:gives { - 2025 :numberToDigits (2 0 2 5). + 3025 :numberToDigits (3 0 2 5). }; r:evidence ( - [ a r:Fact; r:gives {(2025 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2025 1000) math:remainder 25}] + [ a r:Fact; r:gives {(3025 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3025 1000) math:remainder 25}] [ a r:Fact; r:gives {(25 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(25 100) math:remainder 25}] [ a r:Fact; r:gives {(25 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(25 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2025]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3025]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 25]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. - -skolem:lemma2071 a r:Inference; - r:gives { - (0 2 2 5) :digitsToNumber 225 . - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 200 20 5) math:sum 225}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 225]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3439. - -skolem:lemma2072 a r:Inference; - r:gives { - (5 2 2 0) :digitsToNumber 5220 . - }; - r:evidence ( - [ a r:Fact; r:gives {(5 1000) math:product 5000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(5000 200 20 0) math:sum 5220}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2073 a r:Inference; +skolem:lemma5496 a r:Inference; r:gives { - 2026 :numberToDigits (2 0 2 6). + 3026 :numberToDigits (3 0 2 6). }; r:evidence ( - [ a r:Fact; r:gives {(2026 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2026 1000) math:remainder 26}] + [ a r:Fact; r:gives {(3026 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3026 1000) math:remainder 26}] [ a r:Fact; r:gives {(26 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(26 100) math:remainder 26}] [ a r:Fact; r:gives {(26 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(26 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2026]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3026]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 26]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. - -skolem:lemma2074 a r:Inference; - r:gives { - (0 2 2 6) :digitsToNumber 226 . - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 200 20 6) math:sum 226}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 226]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. - -skolem:lemma2075 a r:Inference; - r:gives { - (6 2 2 0) :digitsToNumber 6220 . - }; - r:evidence ( - [ a r:Fact; r:gives {(6 1000) math:product 6000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(6000 200 20 0) math:sum 6220}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2076 a r:Inference; +skolem:lemma5497 a r:Inference; r:gives { - 2027 :numberToDigits (2 0 2 7). + 3027 :numberToDigits (3 0 2 7). }; r:evidence ( - [ a r:Fact; r:gives {(2027 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2027 1000) math:remainder 27}] + [ a r:Fact; r:gives {(3027 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3027 1000) math:remainder 27}] [ a r:Fact; r:gives {(27 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(27 100) math:remainder 27}] [ a r:Fact; r:gives {(27 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(27 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2027]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3027]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 27]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. - -skolem:lemma2077 a r:Inference; - r:gives { - (0 2 2 7) :digitsToNumber 227 . - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 200 20 7) math:sum 227}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 227]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. - -skolem:lemma2078 a r:Inference; - r:gives { - (7 2 2 0) :digitsToNumber 7220 . - }; - r:evidence ( - [ a r:Fact; r:gives {(7 1000) math:product 7000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(7000 200 20 0) math:sum 7220}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2079 a r:Inference; +skolem:lemma5498 a r:Inference; r:gives { - 2028 :numberToDigits (2 0 2 8). + 3028 :numberToDigits (3 0 2 8). }; r:evidence ( - [ a r:Fact; r:gives {(2028 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2028 1000) math:remainder 28}] + [ a r:Fact; r:gives {(3028 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3028 1000) math:remainder 28}] [ a r:Fact; r:gives {(28 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(28 100) math:remainder 28}] [ a r:Fact; r:gives {(28 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(28 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2028]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3028]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 28]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. - -skolem:lemma2080 a r:Inference; - r:gives { - (0 2 2 8) :digitsToNumber 228 . - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 200 20 8) math:sum 228}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 228]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. - -skolem:lemma2081 a r:Inference; - r:gives { - (8 2 2 0) :digitsToNumber 8220 . - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1000) math:product 8000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(8000 200 20 0) math:sum 8220}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2082 a r:Inference; +skolem:lemma5499 a r:Inference; r:gives { - 2029 :numberToDigits (2 0 2 9). + 3029 :numberToDigits (3 0 2 9). }; r:evidence ( - [ a r:Fact; r:gives {(2029 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2029 1000) math:remainder 29}] + [ a r:Fact; r:gives {(3029 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3029 1000) math:remainder 29}] [ a r:Fact; r:gives {(29 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(29 100) math:remainder 29}] [ a r:Fact; r:gives {(29 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(29 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2029]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3029]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 29]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. - -skolem:lemma2083 a r:Inference; - r:gives { - (0 2 2 9) :digitsToNumber 229 . - }; - r:evidence ( - [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(0 200 20 9) math:sum 229}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 229]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. - -skolem:lemma2084 a r:Inference; - r:gives { - (9 2 2 0) :digitsToNumber 9220 . - }; - r:evidence ( - [ a r:Fact; r:gives {(9 1000) math:product 9000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 200 20 0) math:sum 9220}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9220]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2085 a r:Inference; +skolem:lemma5500 a r:Inference; r:gives { - 2030 :numberToDigits (2 0 3 0). + 3030 :numberToDigits (3 0 3 0). }; r:evidence ( - [ a r:Fact; r:gives {(2030 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2030 1000) math:remainder 30}] + [ a r:Fact; r:gives {(3030 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3030 1000) math:remainder 30}] [ a r:Fact; r:gives {(30 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(30 100) math:remainder 30}] [ a r:Fact; r:gives {(30 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(30 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2030]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3030]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2086 a r:Inference; +skolem:lemma5501 a r:Inference; r:gives { - 2031 :numberToDigits (2 0 3 1). + 3031 :numberToDigits (3 0 3 1). }; r:evidence ( - [ a r:Fact; r:gives {(2031 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2031 1000) math:remainder 31}] + [ a r:Fact; r:gives {(3031 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3031 1000) math:remainder 31}] [ a r:Fact; r:gives {(31 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(31 100) math:remainder 31}] [ a r:Fact; r:gives {(31 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(31 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2031]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3031]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 31]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 31]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2087 a r:Inference; +skolem:lemma5502 a r:Inference; r:gives { - 2032 :numberToDigits (2 0 3 2). + 3032 :numberToDigits (3 0 3 2). }; r:evidence ( - [ a r:Fact; r:gives {(2032 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2032 1000) math:remainder 32}] + [ a r:Fact; r:gives {(3032 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3032 1000) math:remainder 32}] [ a r:Fact; r:gives {(32 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(32 100) math:remainder 32}] [ a r:Fact; r:gives {(32 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(32 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2032]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3032]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 32]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 32]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2088 a r:Inference; +skolem:lemma5503 a r:Inference; r:gives { - 2033 :numberToDigits (2 0 3 3). + 3033 :numberToDigits (3 0 3 3). }; r:evidence ( - [ a r:Fact; r:gives {(2033 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2033 1000) math:remainder 33}] + [ a r:Fact; r:gives {(3033 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3033 1000) math:remainder 33}] [ a r:Fact; r:gives {(33 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(33 100) math:remainder 33}] [ a r:Fact; r:gives {(33 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(33 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2033]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3033]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 33]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 33]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2089 a r:Inference; +skolem:lemma5504 a r:Inference; r:gives { - (0 2 3 3) :digitsToNumber 233 . + (0 3 3 3) :digitsToNumber 333 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(0 200 30 3) math:sum 233}] + [ a r:Fact; r:gives {(0 300 30 3) math:sum 333}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 333]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2090 a r:Inference; +skolem:lemma5505 a r:Inference; r:gives { - (3 3 2 0) :digitsToNumber 3320 . + (3 3 3 0) :digitsToNumber 3330 . }; r:evidence ( [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(3000 300 20 0) math:sum 3320}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(3000 300 30 0) math:sum 3330}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3330]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2091 a r:Inference; +skolem:lemma5506 a r:Inference; r:gives { - 2034 :numberToDigits (2 0 3 4). + 3034 :numberToDigits (3 0 3 4). }; r:evidence ( - [ a r:Fact; r:gives {(2034 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2034 1000) math:remainder 34}] + [ a r:Fact; r:gives {(3034 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3034 1000) math:remainder 34}] [ a r:Fact; r:gives {(34 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(34 100) math:remainder 34}] [ a r:Fact; r:gives {(34 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(34 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2034]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3034]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 34]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 34]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2092 a r:Inference; +skolem:lemma5507 a r:Inference; r:gives { - (0 2 3 4) :digitsToNumber 234 . + (0 3 3 4) :digitsToNumber 334 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(0 200 30 4) math:sum 234}] + [ a r:Fact; r:gives {(0 300 30 4) math:sum 334}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 334]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2093 a r:Inference; +skolem:lemma5508 a r:Inference; r:gives { - (4 3 2 0) :digitsToNumber 4320 . + (4 3 3 0) :digitsToNumber 4330 . }; r:evidence ( [ a r:Fact; r:gives {(4 1000) math:product 4000}] [ a r:Fact; r:gives {(3 100) math:product 300}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(4000 300 20 0) math:sum 4320}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(4000 300 30 0) math:sum 4330}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4330]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2094 a r:Inference; +skolem:lemma5509 a r:Inference; r:gives { - 2035 :numberToDigits (2 0 3 5). + 3035 :numberToDigits (3 0 3 5). }; r:evidence ( - [ a r:Fact; r:gives {(2035 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2035 1000) math:remainder 35}] + [ a r:Fact; r:gives {(3035 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3035 1000) math:remainder 35}] [ a r:Fact; r:gives {(35 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(35 100) math:remainder 35}] [ a r:Fact; r:gives {(35 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(35 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2035]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3035]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 35]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 35]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2095 a r:Inference; +skolem:lemma5510 a r:Inference; r:gives { - (0 2 3 5) :digitsToNumber 235 . + (0 3 3 5) :digitsToNumber 335 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(0 200 30 5) math:sum 235}] + [ a r:Fact; r:gives {(0 300 30 5) math:sum 335}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 335]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2096 a r:Inference; +skolem:lemma5511 a r:Inference; r:gives { - (5 3 2 0) :digitsToNumber 5320 . + (5 3 3 0) :digitsToNumber 5330 . }; r:evidence ( [ a r:Fact; r:gives {(5 1000) math:product 5000}] [ a r:Fact; r:gives {(3 100) math:product 300}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(5000 300 20 0) math:sum 5320}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(5000 300 30 0) math:sum 5330}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5330]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2097 a r:Inference; +skolem:lemma5512 a r:Inference; r:gives { - 2036 :numberToDigits (2 0 3 6). + 3036 :numberToDigits (3 0 3 6). }; r:evidence ( - [ a r:Fact; r:gives {(2036 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2036 1000) math:remainder 36}] + [ a r:Fact; r:gives {(3036 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3036 1000) math:remainder 36}] [ a r:Fact; r:gives {(36 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(36 100) math:remainder 36}] [ a r:Fact; r:gives {(36 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(36 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2036]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3036]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 36]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 36]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2098 a r:Inference; +skolem:lemma5513 a r:Inference; r:gives { - (0 2 3 6) :digitsToNumber 236 . + (0 3 3 6) :digitsToNumber 336 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(0 200 30 6) math:sum 236}] + [ a r:Fact; r:gives {(0 300 30 6) math:sum 336}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 336]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2099 a r:Inference; +skolem:lemma5514 a r:Inference; r:gives { - (6 3 2 0) :digitsToNumber 6320 . + (6 3 3 0) :digitsToNumber 6330 . }; r:evidence ( [ a r:Fact; r:gives {(6 1000) math:product 6000}] [ a r:Fact; r:gives {(3 100) math:product 300}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(6000 300 20 0) math:sum 6320}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(6000 300 30 0) math:sum 6330}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6330]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2100 a r:Inference; +skolem:lemma5515 a r:Inference; r:gives { - 2037 :numberToDigits (2 0 3 7). + 3037 :numberToDigits (3 0 3 7). }; r:evidence ( - [ a r:Fact; r:gives {(2037 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2037 1000) math:remainder 37}] + [ a r:Fact; r:gives {(3037 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3037 1000) math:remainder 37}] [ a r:Fact; r:gives {(37 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(37 100) math:remainder 37}] [ a r:Fact; r:gives {(37 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(37 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2037]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3037]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 37]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 37]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2101 a r:Inference; +skolem:lemma5516 a r:Inference; r:gives { - (0 2 3 7) :digitsToNumber 237 . + (0 3 3 7) :digitsToNumber 337 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(0 200 30 7) math:sum 237}] + [ a r:Fact; r:gives {(0 300 30 7) math:sum 337}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 337]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2102 a r:Inference; +skolem:lemma5517 a r:Inference; r:gives { - (7 3 2 0) :digitsToNumber 7320 . + (7 3 3 0) :digitsToNumber 7330 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(3 100) math:product 300}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(7000 300 20 0) math:sum 7320}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(7000 300 30 0) math:sum 7330}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7330]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2103 a r:Inference; +skolem:lemma5518 a r:Inference; r:gives { - 2038 :numberToDigits (2 0 3 8). + 3038 :numberToDigits (3 0 3 8). }; r:evidence ( - [ a r:Fact; r:gives {(2038 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2038 1000) math:remainder 38}] + [ a r:Fact; r:gives {(3038 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3038 1000) math:remainder 38}] [ a r:Fact; r:gives {(38 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(38 100) math:remainder 38}] [ a r:Fact; r:gives {(38 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(38 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2038]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3038]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 38]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 38]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2104 a r:Inference; +skolem:lemma5519 a r:Inference; r:gives { - (0 2 3 8) :digitsToNumber 238 . + (0 3 3 8) :digitsToNumber 338 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(0 200 30 8) math:sum 238}] + [ a r:Fact; r:gives {(0 300 30 8) math:sum 338}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 338]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2105 a r:Inference; +skolem:lemma5520 a r:Inference; r:gives { - (8 3 2 0) :digitsToNumber 8320 . + (8 3 3 0) :digitsToNumber 8330 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(3 100) math:product 300}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(8000 300 20 0) math:sum 8320}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(8000 300 30 0) math:sum 8330}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8330]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2106 a r:Inference; +skolem:lemma5521 a r:Inference; r:gives { - 2039 :numberToDigits (2 0 3 9). + 3039 :numberToDigits (3 0 3 9). }; r:evidence ( - [ a r:Fact; r:gives {(2039 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2039 1000) math:remainder 39}] + [ a r:Fact; r:gives {(3039 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3039 1000) math:remainder 39}] [ a r:Fact; r:gives {(39 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(39 100) math:remainder 39}] [ a r:Fact; r:gives {(39 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(39 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2039]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3039]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 39]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 39]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2107 a r:Inference; +skolem:lemma5522 a r:Inference; r:gives { - (0 2 3 9) :digitsToNumber 239 . + (0 3 3 9) :digitsToNumber 339 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(0 200 30 9) math:sum 239}] + [ a r:Fact; r:gives {(0 300 30 9) math:sum 339}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 339]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2108 a r:Inference; +skolem:lemma5523 a r:Inference; r:gives { - (9 3 2 0) :digitsToNumber 9320 . + (9 3 3 0) :digitsToNumber 9330 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(3 100) math:product 300}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 300 20 0) math:sum 9320}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(9000 300 30 0) math:sum 9330}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9330]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2109 a r:Inference; +skolem:lemma5524 a r:Inference; r:gives { - 2040 :numberToDigits (2 0 4 0). + 3040 :numberToDigits (3 0 4 0). }; r:evidence ( - [ a r:Fact; r:gives {(2040 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2040 1000) math:remainder 40}] + [ a r:Fact; r:gives {(3040 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3040 1000) math:remainder 40}] [ a r:Fact; r:gives {(40 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(40 100) math:remainder 40}] [ a r:Fact; r:gives {(40 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(40 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2040]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3040]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2110 a r:Inference; +skolem:lemma5525 a r:Inference; r:gives { - 2041 :numberToDigits (2 0 4 1). + 3041 :numberToDigits (3 0 4 1). }; r:evidence ( - [ a r:Fact; r:gives {(2041 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2041 1000) math:remainder 41}] + [ a r:Fact; r:gives {(3041 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3041 1000) math:remainder 41}] [ a r:Fact; r:gives {(41 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(41 100) math:remainder 41}] [ a r:Fact; r:gives {(41 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(41 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2041]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3041]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 41]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 41]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2111 a r:Inference; +skolem:lemma5526 a r:Inference; r:gives { - 2042 :numberToDigits (2 0 4 2). + 3042 :numberToDigits (3 0 4 2). }; r:evidence ( - [ a r:Fact; r:gives {(2042 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2042 1000) math:remainder 42}] + [ a r:Fact; r:gives {(3042 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3042 1000) math:remainder 42}] [ a r:Fact; r:gives {(42 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(42 100) math:remainder 42}] [ a r:Fact; r:gives {(42 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(42 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2042]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3042]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 42]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 42]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2112 a r:Inference; +skolem:lemma5527 a r:Inference; r:gives { - 2043 :numberToDigits (2 0 4 3). + 3043 :numberToDigits (3 0 4 3). }; r:evidence ( - [ a r:Fact; r:gives {(2043 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2043 1000) math:remainder 43}] + [ a r:Fact; r:gives {(3043 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3043 1000) math:remainder 43}] [ a r:Fact; r:gives {(43 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(43 100) math:remainder 43}] [ a r:Fact; r:gives {(43 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(43 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2043]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3043]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 43]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 43]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2113 a r:Inference; +skolem:lemma5528 a r:Inference; r:gives { - 2044 :numberToDigits (2 0 4 4). + 3044 :numberToDigits (3 0 4 4). }; r:evidence ( - [ a r:Fact; r:gives {(2044 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2044 1000) math:remainder 44}] + [ a r:Fact; r:gives {(3044 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3044 1000) math:remainder 44}] [ a r:Fact; r:gives {(44 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(44 100) math:remainder 44}] [ a r:Fact; r:gives {(44 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(44 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2044]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3044]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 44]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 44]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2114 a r:Inference; +skolem:lemma5529 a r:Inference; r:gives { - (0 2 4 4) :digitsToNumber 244 . + (0 3 4 4) :digitsToNumber 344 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(0 200 40 4) math:sum 244}] + [ a r:Fact; r:gives {(0 300 40 4) math:sum 344}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 344]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2115 a r:Inference; +skolem:lemma5530 a r:Inference; r:gives { - (4 4 2 0) :digitsToNumber 4420 . + (4 4 3 0) :digitsToNumber 4430 . }; r:evidence ( [ a r:Fact; r:gives {(4 1000) math:product 4000}] [ a r:Fact; r:gives {(4 100) math:product 400}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(4000 400 20 0) math:sum 4420}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(4000 400 30 0) math:sum 4430}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4430]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2116 a r:Inference; +skolem:lemma5531 a r:Inference; r:gives { - 2045 :numberToDigits (2 0 4 5). + 3045 :numberToDigits (3 0 4 5). }; r:evidence ( - [ a r:Fact; r:gives {(2045 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2045 1000) math:remainder 45}] + [ a r:Fact; r:gives {(3045 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3045 1000) math:remainder 45}] [ a r:Fact; r:gives {(45 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(45 100) math:remainder 45}] [ a r:Fact; r:gives {(45 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(45 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2045]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3045]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 45]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 45]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2117 a r:Inference; +skolem:lemma5532 a r:Inference; r:gives { - (0 2 4 5) :digitsToNumber 245 . + (0 3 4 5) :digitsToNumber 345 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(0 200 40 5) math:sum 245}] + [ a r:Fact; r:gives {(0 300 40 5) math:sum 345}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 345]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2118 a r:Inference; +skolem:lemma5533 a r:Inference; r:gives { - (5 4 2 0) :digitsToNumber 5420 . + (5 4 3 0) :digitsToNumber 5430 . }; r:evidence ( [ a r:Fact; r:gives {(5 1000) math:product 5000}] [ a r:Fact; r:gives {(4 100) math:product 400}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(5000 400 20 0) math:sum 5420}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(5000 400 30 0) math:sum 5430}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5430]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2119 a r:Inference; +skolem:lemma5534 a r:Inference; r:gives { - 2046 :numberToDigits (2 0 4 6). + 3046 :numberToDigits (3 0 4 6). }; r:evidence ( - [ a r:Fact; r:gives {(2046 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2046 1000) math:remainder 46}] + [ a r:Fact; r:gives {(3046 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3046 1000) math:remainder 46}] [ a r:Fact; r:gives {(46 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(46 100) math:remainder 46}] [ a r:Fact; r:gives {(46 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(46 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2046]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3046]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 46]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 46]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2120 a r:Inference; +skolem:lemma5535 a r:Inference; r:gives { - (0 2 4 6) :digitsToNumber 246 . + (0 3 4 6) :digitsToNumber 346 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(0 200 40 6) math:sum 246}] + [ a r:Fact; r:gives {(0 300 40 6) math:sum 346}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 346]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2121 a r:Inference; +skolem:lemma5536 a r:Inference; r:gives { - (6 4 2 0) :digitsToNumber 6420 . + (6 4 3 0) :digitsToNumber 6430 . }; r:evidence ( [ a r:Fact; r:gives {(6 1000) math:product 6000}] [ a r:Fact; r:gives {(4 100) math:product 400}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(6000 400 20 0) math:sum 6420}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(6000 400 30 0) math:sum 6430}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6430]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2122 a r:Inference; +skolem:lemma5537 a r:Inference; r:gives { - 2047 :numberToDigits (2 0 4 7). + 3047 :numberToDigits (3 0 4 7). }; r:evidence ( - [ a r:Fact; r:gives {(2047 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2047 1000) math:remainder 47}] + [ a r:Fact; r:gives {(3047 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3047 1000) math:remainder 47}] [ a r:Fact; r:gives {(47 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(47 100) math:remainder 47}] [ a r:Fact; r:gives {(47 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(47 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2047]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3047]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 47]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 47]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2123 a r:Inference; +skolem:lemma5538 a r:Inference; r:gives { - (0 2 4 7) :digitsToNumber 247 . + (0 3 4 7) :digitsToNumber 347 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(0 200 40 7) math:sum 247}] + [ a r:Fact; r:gives {(0 300 40 7) math:sum 347}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 347]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2124 a r:Inference; +skolem:lemma5539 a r:Inference; r:gives { - (7 4 2 0) :digitsToNumber 7420 . + (7 4 3 0) :digitsToNumber 7430 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(4 100) math:product 400}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(7000 400 20 0) math:sum 7420}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(7000 400 30 0) math:sum 7430}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7430]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2125 a r:Inference; +skolem:lemma5540 a r:Inference; r:gives { - 2048 :numberToDigits (2 0 4 8). + 3048 :numberToDigits (3 0 4 8). }; r:evidence ( - [ a r:Fact; r:gives {(2048 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2048 1000) math:remainder 48}] + [ a r:Fact; r:gives {(3048 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3048 1000) math:remainder 48}] [ a r:Fact; r:gives {(48 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(48 100) math:remainder 48}] [ a r:Fact; r:gives {(48 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(48 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2048]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3048]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 48]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 48]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2126 a r:Inference; +skolem:lemma5541 a r:Inference; r:gives { - (0 2 4 8) :digitsToNumber 248 . + (0 3 4 8) :digitsToNumber 348 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(0 200 40 8) math:sum 248}] + [ a r:Fact; r:gives {(0 300 40 8) math:sum 348}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 348]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2127 a r:Inference; +skolem:lemma5542 a r:Inference; r:gives { - (8 4 2 0) :digitsToNumber 8420 . + (8 4 3 0) :digitsToNumber 8430 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(4 100) math:product 400}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(8000 400 20 0) math:sum 8420}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(8000 400 30 0) math:sum 8430}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8430]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2128 a r:Inference; +skolem:lemma5543 a r:Inference; r:gives { - 2049 :numberToDigits (2 0 4 9). + 3049 :numberToDigits (3 0 4 9). }; r:evidence ( - [ a r:Fact; r:gives {(2049 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2049 1000) math:remainder 49}] + [ a r:Fact; r:gives {(3049 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3049 1000) math:remainder 49}] [ a r:Fact; r:gives {(49 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(49 100) math:remainder 49}] [ a r:Fact; r:gives {(49 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(49 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2049]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3049]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 49]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 49]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2129 a r:Inference; +skolem:lemma5544 a r:Inference; r:gives { - (0 2 4 9) :digitsToNumber 249 . + (0 3 4 9) :digitsToNumber 349 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(0 200 40 9) math:sum 249}] + [ a r:Fact; r:gives {(0 300 40 9) math:sum 349}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 349]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2130 a r:Inference; +skolem:lemma5545 a r:Inference; r:gives { - (9 4 2 0) :digitsToNumber 9420 . + (9 4 3 0) :digitsToNumber 9430 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(4 100) math:product 400}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 400 20 0) math:sum 9420}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(9000 400 30 0) math:sum 9430}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9430]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2131 a r:Inference; +skolem:lemma5546 a r:Inference; r:gives { - 2050 :numberToDigits (2 0 5 0). + 3050 :numberToDigits (3 0 5 0). }; r:evidence ( - [ a r:Fact; r:gives {(2050 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2050 1000) math:remainder 50}] + [ a r:Fact; r:gives {(3050 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3050 1000) math:remainder 50}] [ a r:Fact; r:gives {(50 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(50 100) math:remainder 50}] [ a r:Fact; r:gives {(50 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(50 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2050]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3050]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2132 a r:Inference; +skolem:lemma5547 a r:Inference; r:gives { - 2051 :numberToDigits (2 0 5 1). + 3051 :numberToDigits (3 0 5 1). }; r:evidence ( - [ a r:Fact; r:gives {(2051 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2051 1000) math:remainder 51}] + [ a r:Fact; r:gives {(3051 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3051 1000) math:remainder 51}] [ a r:Fact; r:gives {(51 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(51 100) math:remainder 51}] [ a r:Fact; r:gives {(51 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(51 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2051]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3051]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 51]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 51]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2133 a r:Inference; +skolem:lemma5548 a r:Inference; r:gives { - 2052 :numberToDigits (2 0 5 2). + 3052 :numberToDigits (3 0 5 2). }; r:evidence ( - [ a r:Fact; r:gives {(2052 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2052 1000) math:remainder 52}] + [ a r:Fact; r:gives {(3052 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3052 1000) math:remainder 52}] [ a r:Fact; r:gives {(52 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(52 100) math:remainder 52}] [ a r:Fact; r:gives {(52 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(52 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2052]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3052]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 52]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 52]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2134 a r:Inference; +skolem:lemma5549 a r:Inference; r:gives { - 2053 :numberToDigits (2 0 5 3). + 3053 :numberToDigits (3 0 5 3). }; r:evidence ( - [ a r:Fact; r:gives {(2053 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2053 1000) math:remainder 53}] + [ a r:Fact; r:gives {(3053 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3053 1000) math:remainder 53}] [ a r:Fact; r:gives {(53 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(53 100) math:remainder 53}] [ a r:Fact; r:gives {(53 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(53 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2053]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3053]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 53]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 53]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2135 a r:Inference; +skolem:lemma5550 a r:Inference; r:gives { - 2054 :numberToDigits (2 0 5 4). + 3054 :numberToDigits (3 0 5 4). }; r:evidence ( - [ a r:Fact; r:gives {(2054 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2054 1000) math:remainder 54}] + [ a r:Fact; r:gives {(3054 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3054 1000) math:remainder 54}] [ a r:Fact; r:gives {(54 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(54 100) math:remainder 54}] [ a r:Fact; r:gives {(54 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(54 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2054]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3054]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 54]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 54]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2136 a r:Inference; +skolem:lemma5551 a r:Inference; r:gives { - 2055 :numberToDigits (2 0 5 5). + 3055 :numberToDigits (3 0 5 5). }; r:evidence ( - [ a r:Fact; r:gives {(2055 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2055 1000) math:remainder 55}] + [ a r:Fact; r:gives {(3055 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3055 1000) math:remainder 55}] [ a r:Fact; r:gives {(55 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(55 100) math:remainder 55}] [ a r:Fact; r:gives {(55 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(55 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2055]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3055]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 55]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 55]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2137 a r:Inference; +skolem:lemma5552 a r:Inference; r:gives { - (0 2 5 5) :digitsToNumber 255 . + (0 3 5 5) :digitsToNumber 355 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(0 200 50 5) math:sum 255}] + [ a r:Fact; r:gives {(0 300 50 5) math:sum 355}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 355]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2138 a r:Inference; +skolem:lemma5553 a r:Inference; r:gives { - (5 5 2 0) :digitsToNumber 5520 . + (5 5 3 0) :digitsToNumber 5530 . }; r:evidence ( [ a r:Fact; r:gives {(5 1000) math:product 5000}] [ a r:Fact; r:gives {(5 100) math:product 500}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(5000 500 20 0) math:sum 5520}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(5000 500 30 0) math:sum 5530}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5530]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2139 a r:Inference; +skolem:lemma5554 a r:Inference; r:gives { - 2056 :numberToDigits (2 0 5 6). + 3056 :numberToDigits (3 0 5 6). }; r:evidence ( - [ a r:Fact; r:gives {(2056 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2056 1000) math:remainder 56}] + [ a r:Fact; r:gives {(3056 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3056 1000) math:remainder 56}] [ a r:Fact; r:gives {(56 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(56 100) math:remainder 56}] [ a r:Fact; r:gives {(56 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(56 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2056]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3056]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 56]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 56]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2140 a r:Inference; +skolem:lemma5555 a r:Inference; r:gives { - (0 2 5 6) :digitsToNumber 256 . + (0 3 5 6) :digitsToNumber 356 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(0 200 50 6) math:sum 256}] + [ a r:Fact; r:gives {(0 300 50 6) math:sum 356}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 356]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2141 a r:Inference; +skolem:lemma5556 a r:Inference; r:gives { - (6 5 2 0) :digitsToNumber 6520 . + (6 5 3 0) :digitsToNumber 6530 . }; r:evidence ( [ a r:Fact; r:gives {(6 1000) math:product 6000}] [ a r:Fact; r:gives {(5 100) math:product 500}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(6000 500 20 0) math:sum 6520}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(6000 500 30 0) math:sum 6530}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6530]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2142 a r:Inference; +skolem:lemma5557 a r:Inference; r:gives { - 2057 :numberToDigits (2 0 5 7). + 3057 :numberToDigits (3 0 5 7). }; r:evidence ( - [ a r:Fact; r:gives {(2057 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2057 1000) math:remainder 57}] + [ a r:Fact; r:gives {(3057 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3057 1000) math:remainder 57}] [ a r:Fact; r:gives {(57 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(57 100) math:remainder 57}] [ a r:Fact; r:gives {(57 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(57 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2057]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3057]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 57]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 57]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2143 a r:Inference; +skolem:lemma5558 a r:Inference; r:gives { - (0 2 5 7) :digitsToNumber 257 . + (0 3 5 7) :digitsToNumber 357 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(0 200 50 7) math:sum 257}] + [ a r:Fact; r:gives {(0 300 50 7) math:sum 357}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 357]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2144 a r:Inference; +skolem:lemma5559 a r:Inference; r:gives { - (7 5 2 0) :digitsToNumber 7520 . + (7 5 3 0) :digitsToNumber 7530 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(5 100) math:product 500}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(7000 500 20 0) math:sum 7520}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(7000 500 30 0) math:sum 7530}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7530]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2145 a r:Inference; +skolem:lemma5560 a r:Inference; r:gives { - 2058 :numberToDigits (2 0 5 8). + 3058 :numberToDigits (3 0 5 8). }; r:evidence ( - [ a r:Fact; r:gives {(2058 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2058 1000) math:remainder 58}] + [ a r:Fact; r:gives {(3058 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3058 1000) math:remainder 58}] [ a r:Fact; r:gives {(58 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(58 100) math:remainder 58}] [ a r:Fact; r:gives {(58 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(58 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2058]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3058]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 58]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 58]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2146 a r:Inference; +skolem:lemma5561 a r:Inference; r:gives { - (0 2 5 8) :digitsToNumber 258 . + (0 3 5 8) :digitsToNumber 358 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(0 200 50 8) math:sum 258}] + [ a r:Fact; r:gives {(0 300 50 8) math:sum 358}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 358]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2147 a r:Inference; +skolem:lemma5562 a r:Inference; r:gives { - (8 5 2 0) :digitsToNumber 8520 . + (8 5 3 0) :digitsToNumber 8530 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(5 100) math:product 500}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(8000 500 20 0) math:sum 8520}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(8000 500 30 0) math:sum 8530}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8530]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2148 a r:Inference; +skolem:lemma5563 a r:Inference; r:gives { - 2059 :numberToDigits (2 0 5 9). + 3059 :numberToDigits (3 0 5 9). }; r:evidence ( - [ a r:Fact; r:gives {(2059 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2059 1000) math:remainder 59}] + [ a r:Fact; r:gives {(3059 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3059 1000) math:remainder 59}] [ a r:Fact; r:gives {(59 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(59 100) math:remainder 59}] [ a r:Fact; r:gives {(59 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(59 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2059]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3059]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 59]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 59]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2149 a r:Inference; +skolem:lemma5564 a r:Inference; r:gives { - (0 2 5 9) :digitsToNumber 259 . + (0 3 5 9) :digitsToNumber 359 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(0 200 50 9) math:sum 259}] + [ a r:Fact; r:gives {(0 300 50 9) math:sum 359}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 359]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2150 a r:Inference; +skolem:lemma5565 a r:Inference; r:gives { - (9 5 2 0) :digitsToNumber 9520 . + (9 5 3 0) :digitsToNumber 9530 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(5 100) math:product 500}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 500 20 0) math:sum 9520}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(9000 500 30 0) math:sum 9530}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9530]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2151 a r:Inference; +skolem:lemma5566 a r:Inference; r:gives { - 2060 :numberToDigits (2 0 6 0). + 3060 :numberToDigits (3 0 6 0). }; r:evidence ( - [ a r:Fact; r:gives {(2060 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2060 1000) math:remainder 60}] + [ a r:Fact; r:gives {(3060 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3060 1000) math:remainder 60}] [ a r:Fact; r:gives {(60 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(60 100) math:remainder 60}] [ a r:Fact; r:gives {(60 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(60 10) math:remainder 0}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2060]; + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3060]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2152 a r:Inference; +skolem:lemma5567 a r:Inference; r:gives { - 2061 :numberToDigits (2 0 6 1). + 3061 :numberToDigits (3 0 6 1). }; r:evidence ( - [ a r:Fact; r:gives {(2061 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2061 1000) math:remainder 61}] + [ a r:Fact; r:gives {(3061 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3061 1000) math:remainder 61}] [ a r:Fact; r:gives {(61 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(61 100) math:remainder 61}] [ a r:Fact; r:gives {(61 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(61 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2061]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3061]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 61]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 61]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2153 a r:Inference; +skolem:lemma5568 a r:Inference; r:gives { - 2062 :numberToDigits (2 0 6 2). + 3062 :numberToDigits (3 0 6 2). }; r:evidence ( - [ a r:Fact; r:gives {(2062 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2062 1000) math:remainder 62}] + [ a r:Fact; r:gives {(3062 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3062 1000) math:remainder 62}] [ a r:Fact; r:gives {(62 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(62 100) math:remainder 62}] [ a r:Fact; r:gives {(62 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(62 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2062]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3062]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 62]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 62]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2154 a r:Inference; +skolem:lemma5569 a r:Inference; r:gives { - 2063 :numberToDigits (2 0 6 3). + 3063 :numberToDigits (3 0 6 3). }; r:evidence ( - [ a r:Fact; r:gives {(2063 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2063 1000) math:remainder 63}] + [ a r:Fact; r:gives {(3063 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3063 1000) math:remainder 63}] [ a r:Fact; r:gives {(63 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(63 100) math:remainder 63}] [ a r:Fact; r:gives {(63 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(63 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2063]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3063]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 63]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 63]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2155 a r:Inference; +skolem:lemma5570 a r:Inference; r:gives { - 2064 :numberToDigits (2 0 6 4). + 3064 :numberToDigits (3 0 6 4). }; r:evidence ( - [ a r:Fact; r:gives {(2064 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2064 1000) math:remainder 64}] + [ a r:Fact; r:gives {(3064 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3064 1000) math:remainder 64}] [ a r:Fact; r:gives {(64 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(64 100) math:remainder 64}] [ a r:Fact; r:gives {(64 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(64 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2064]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3064]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 64]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 64]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2156 a r:Inference; +skolem:lemma5571 a r:Inference; r:gives { - 2065 :numberToDigits (2 0 6 5). + 3065 :numberToDigits (3 0 6 5). }; r:evidence ( - [ a r:Fact; r:gives {(2065 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2065 1000) math:remainder 65}] + [ a r:Fact; r:gives {(3065 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3065 1000) math:remainder 65}] [ a r:Fact; r:gives {(65 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(65 100) math:remainder 65}] [ a r:Fact; r:gives {(65 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(65 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2065]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3065]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 65]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 65]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2157 a r:Inference; +skolem:lemma5572 a r:Inference; r:gives { - 2066 :numberToDigits (2 0 6 6). + 3066 :numberToDigits (3 0 6 6). }; r:evidence ( - [ a r:Fact; r:gives {(2066 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2066 1000) math:remainder 66}] + [ a r:Fact; r:gives {(3066 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3066 1000) math:remainder 66}] [ a r:Fact; r:gives {(66 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(66 100) math:remainder 66}] [ a r:Fact; r:gives {(66 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(66 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2066]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3066]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 66]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 66]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2158 a r:Inference; +skolem:lemma5573 a r:Inference; r:gives { - (0 2 6 6) :digitsToNumber 266 . + (0 3 6 6) :digitsToNumber 366 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(0 200 60 6) math:sum 266}] + [ a r:Fact; r:gives {(0 300 60 6) math:sum 366}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 366]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2159 a r:Inference; +skolem:lemma5574 a r:Inference; r:gives { - (6 6 2 0) :digitsToNumber 6620 . + (6 6 3 0) :digitsToNumber 6630 . }; r:evidence ( [ a r:Fact; r:gives {(6 1000) math:product 6000}] [ a r:Fact; r:gives {(6 100) math:product 600}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(6000 600 20 0) math:sum 6620}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(6000 600 30 0) math:sum 6630}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6630]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2160 a r:Inference; +skolem:lemma5575 a r:Inference; r:gives { - 2067 :numberToDigits (2 0 6 7). + 3067 :numberToDigits (3 0 6 7). }; r:evidence ( - [ a r:Fact; r:gives {(2067 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2067 1000) math:remainder 67}] + [ a r:Fact; r:gives {(3067 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3067 1000) math:remainder 67}] [ a r:Fact; r:gives {(67 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(67 100) math:remainder 67}] [ a r:Fact; r:gives {(67 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(67 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2067]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3067]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 67]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 67]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2161 a r:Inference; +skolem:lemma5576 a r:Inference; r:gives { - (0 2 6 7) :digitsToNumber 267 . + (0 3 6 7) :digitsToNumber 367 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(0 200 60 7) math:sum 267}] + [ a r:Fact; r:gives {(0 300 60 7) math:sum 367}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 367]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2162 a r:Inference; +skolem:lemma5577 a r:Inference; r:gives { - (7 6 2 0) :digitsToNumber 7620 . + (7 6 3 0) :digitsToNumber 7630 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(6 100) math:product 600}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(7000 600 20 0) math:sum 7620}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(7000 600 30 0) math:sum 7630}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7630]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2163 a r:Inference; +skolem:lemma5578 a r:Inference; r:gives { - 2068 :numberToDigits (2 0 6 8). + 3068 :numberToDigits (3 0 6 8). }; r:evidence ( - [ a r:Fact; r:gives {(2068 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2068 1000) math:remainder 68}] + [ a r:Fact; r:gives {(3068 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3068 1000) math:remainder 68}] [ a r:Fact; r:gives {(68 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(68 100) math:remainder 68}] [ a r:Fact; r:gives {(68 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(68 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2068]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3068]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 68]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 68]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2164 a r:Inference; +skolem:lemma5579 a r:Inference; r:gives { - (0 2 6 8) :digitsToNumber 268 . + (0 3 6 8) :digitsToNumber 368 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(0 200 60 8) math:sum 268}] + [ a r:Fact; r:gives {(0 300 60 8) math:sum 368}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 368]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2165 a r:Inference; +skolem:lemma5580 a r:Inference; r:gives { - (8 6 2 0) :digitsToNumber 8620 . + (8 6 3 0) :digitsToNumber 8630 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(6 100) math:product 600}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(8000 600 20 0) math:sum 8620}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(8000 600 30 0) math:sum 8630}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8630]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2166 a r:Inference; +skolem:lemma5581 a r:Inference; r:gives { - 2069 :numberToDigits (2 0 6 9). + 3069 :numberToDigits (3 0 6 9). }; r:evidence ( - [ a r:Fact; r:gives {(2069 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2069 1000) math:remainder 69}] + [ a r:Fact; r:gives {(3069 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3069 1000) math:remainder 69}] [ a r:Fact; r:gives {(69 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(69 100) math:remainder 69}] [ a r:Fact; r:gives {(69 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(69 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2069]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3069]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 69]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 69]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2167 a r:Inference; +skolem:lemma5582 a r:Inference; r:gives { - (0 2 6 9) :digitsToNumber 269 . + (0 3 6 9) :digitsToNumber 369 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(0 200 60 9) math:sum 269}] + [ a r:Fact; r:gives {(0 300 60 9) math:sum 369}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 369]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2168 a r:Inference; +skolem:lemma5583 a r:Inference; r:gives { - (9 6 2 0) :digitsToNumber 9620 . + (9 6 3 0) :digitsToNumber 9630 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(6 100) math:product 600}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 600 20 0) math:sum 9620}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(9000 600 30 0) math:sum 9630}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9630]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2169 a r:Inference; +skolem:lemma5584 a r:Inference; r:gives { - 2070 :numberToDigits (2 0 7 0). + 3070 :numberToDigits (3 0 7 0). }; r:evidence ( - [ a r:Fact; r:gives {(2070 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2070 1000) math:remainder 70}] + [ a r:Fact; r:gives {(3070 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3070 1000) math:remainder 70}] [ a r:Fact; r:gives {(70 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(70 100) math:remainder 70}] [ a r:Fact; r:gives {(70 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(70 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2070]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3070]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2170 a r:Inference; +skolem:lemma5585 a r:Inference; r:gives { - 2071 :numberToDigits (2 0 7 1). + 3071 :numberToDigits (3 0 7 1). }; r:evidence ( - [ a r:Fact; r:gives {(2071 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2071 1000) math:remainder 71}] + [ a r:Fact; r:gives {(3071 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3071 1000) math:remainder 71}] [ a r:Fact; r:gives {(71 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(71 100) math:remainder 71}] [ a r:Fact; r:gives {(71 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(71 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2071]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3071]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 71]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 71]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2171 a r:Inference; +skolem:lemma5586 a r:Inference; r:gives { - 2072 :numberToDigits (2 0 7 2). + 3072 :numberToDigits (3 0 7 2). }; r:evidence ( - [ a r:Fact; r:gives {(2072 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2072 1000) math:remainder 72}] + [ a r:Fact; r:gives {(3072 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3072 1000) math:remainder 72}] [ a r:Fact; r:gives {(72 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(72 100) math:remainder 72}] [ a r:Fact; r:gives {(72 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(72 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2072]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3072]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 72]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 72]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2172 a r:Inference; +skolem:lemma5587 a r:Inference; r:gives { - 2073 :numberToDigits (2 0 7 3). + 3073 :numberToDigits (3 0 7 3). }; r:evidence ( - [ a r:Fact; r:gives {(2073 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2073 1000) math:remainder 73}] + [ a r:Fact; r:gives {(3073 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3073 1000) math:remainder 73}] [ a r:Fact; r:gives {(73 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(73 100) math:remainder 73}] [ a r:Fact; r:gives {(73 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(73 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2073]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3073]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 73]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 73]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2173 a r:Inference; +skolem:lemma5588 a r:Inference; r:gives { - 2074 :numberToDigits (2 0 7 4). + 3074 :numberToDigits (3 0 7 4). }; r:evidence ( - [ a r:Fact; r:gives {(2074 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2074 1000) math:remainder 74}] + [ a r:Fact; r:gives {(3074 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3074 1000) math:remainder 74}] [ a r:Fact; r:gives {(74 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(74 100) math:remainder 74}] [ a r:Fact; r:gives {(74 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(74 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2074]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3074]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 74]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 74]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2174 a r:Inference; +skolem:lemma5589 a r:Inference; r:gives { - 2075 :numberToDigits (2 0 7 5). + 3075 :numberToDigits (3 0 7 5). }; r:evidence ( - [ a r:Fact; r:gives {(2075 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2075 1000) math:remainder 75}] + [ a r:Fact; r:gives {(3075 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3075 1000) math:remainder 75}] [ a r:Fact; r:gives {(75 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(75 100) math:remainder 75}] [ a r:Fact; r:gives {(75 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(75 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2075]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3075]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 75]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 75]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2175 a r:Inference; +skolem:lemma5590 a r:Inference; r:gives { - 2076 :numberToDigits (2 0 7 6). + 3076 :numberToDigits (3 0 7 6). }; r:evidence ( - [ a r:Fact; r:gives {(2076 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2076 1000) math:remainder 76}] + [ a r:Fact; r:gives {(3076 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3076 1000) math:remainder 76}] [ a r:Fact; r:gives {(76 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(76 100) math:remainder 76}] [ a r:Fact; r:gives {(76 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(76 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2076]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3076]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 76]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 76]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2176 a r:Inference; +skolem:lemma5591 a r:Inference; r:gives { - 2077 :numberToDigits (2 0 7 7). + 3077 :numberToDigits (3 0 7 7). }; r:evidence ( - [ a r:Fact; r:gives {(2077 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2077 1000) math:remainder 77}] + [ a r:Fact; r:gives {(3077 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3077 1000) math:remainder 77}] [ a r:Fact; r:gives {(77 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(77 100) math:remainder 77}] [ a r:Fact; r:gives {(77 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(77 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2077]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3077]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 77]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 77]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2177 a r:Inference; +skolem:lemma5592 a r:Inference; r:gives { - (0 2 7 7) :digitsToNumber 277 . + (0 3 7 7) :digitsToNumber 377 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(0 200 70 7) math:sum 277}] + [ a r:Fact; r:gives {(0 300 70 7) math:sum 377}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 277]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 377]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2178 a r:Inference; +skolem:lemma5593 a r:Inference; r:gives { - (7 7 2 0) :digitsToNumber 7720 . + (7 7 3 0) :digitsToNumber 7730 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(7 100) math:product 700}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(7000 700 20 0) math:sum 7720}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(7000 700 30 0) math:sum 7730}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7730]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2179 a r:Inference; +skolem:lemma5594 a r:Inference; r:gives { - 2078 :numberToDigits (2 0 7 8). + 3078 :numberToDigits (3 0 7 8). }; r:evidence ( - [ a r:Fact; r:gives {(2078 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2078 1000) math:remainder 78}] + [ a r:Fact; r:gives {(3078 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3078 1000) math:remainder 78}] [ a r:Fact; r:gives {(78 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(78 100) math:remainder 78}] [ a r:Fact; r:gives {(78 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(78 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2078]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3078]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 78]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 78]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2180 a r:Inference; +skolem:lemma5595 a r:Inference; r:gives { - (0 2 7 8) :digitsToNumber 278 . + (0 3 7 8) :digitsToNumber 378 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(0 200 70 8) math:sum 278}] + [ a r:Fact; r:gives {(0 300 70 8) math:sum 378}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 378]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2181 a r:Inference; +skolem:lemma5596 a r:Inference; r:gives { - (8 7 2 0) :digitsToNumber 8720 . + (8 7 3 0) :digitsToNumber 8730 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(7 100) math:product 700}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(8000 700 20 0) math:sum 8720}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(8000 700 30 0) math:sum 8730}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8730]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2182 a r:Inference; +skolem:lemma5597 a r:Inference; r:gives { - 2079 :numberToDigits (2 0 7 9). + 3079 :numberToDigits (3 0 7 9). }; r:evidence ( - [ a r:Fact; r:gives {(2079 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2079 1000) math:remainder 79}] + [ a r:Fact; r:gives {(3079 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3079 1000) math:remainder 79}] [ a r:Fact; r:gives {(79 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(79 100) math:remainder 79}] [ a r:Fact; r:gives {(79 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(79 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2079]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3079]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 79]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 79]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2183 a r:Inference; +skolem:lemma5598 a r:Inference; r:gives { - (0 2 7 9) :digitsToNumber 279 . + (0 3 7 9) :digitsToNumber 379 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(0 200 70 9) math:sum 279}] + [ a r:Fact; r:gives {(0 300 70 9) math:sum 379}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 379]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2184 a r:Inference; +skolem:lemma5599 a r:Inference; r:gives { - (9 7 2 0) :digitsToNumber 9720 . + (9 7 3 0) :digitsToNumber 9730 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(7 100) math:product 700}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 700 20 0) math:sum 9720}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(9000 700 30 0) math:sum 9730}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9730]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2185 a r:Inference; +skolem:lemma5600 a r:Inference; r:gives { - 2080 :numberToDigits (2 0 8 0). + 3080 :numberToDigits (3 0 8 0). }; r:evidence ( - [ a r:Fact; r:gives {(2080 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2080 1000) math:remainder 80}] + [ a r:Fact; r:gives {(3080 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3080 1000) math:remainder 80}] [ a r:Fact; r:gives {(80 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(80 100) math:remainder 80}] [ a r:Fact; r:gives {(80 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(80 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2080]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3080]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2186 a r:Inference; +skolem:lemma5601 a r:Inference; r:gives { - 2081 :numberToDigits (2 0 8 1). + 3081 :numberToDigits (3 0 8 1). }; r:evidence ( - [ a r:Fact; r:gives {(2081 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2081 1000) math:remainder 81}] + [ a r:Fact; r:gives {(3081 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3081 1000) math:remainder 81}] [ a r:Fact; r:gives {(81 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(81 100) math:remainder 81}] [ a r:Fact; r:gives {(81 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(81 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2081]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3081]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 81]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 81]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2187 a r:Inference; +skolem:lemma5602 a r:Inference; r:gives { - 2082 :numberToDigits (2 0 8 2). + 3082 :numberToDigits (3 0 8 2). }; r:evidence ( - [ a r:Fact; r:gives {(2082 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2082 1000) math:remainder 82}] + [ a r:Fact; r:gives {(3082 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3082 1000) math:remainder 82}] [ a r:Fact; r:gives {(82 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(82 100) math:remainder 82}] [ a r:Fact; r:gives {(82 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(82 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2082]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3082]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 82]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 82]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2188 a r:Inference; +skolem:lemma5603 a r:Inference; r:gives { - 2083 :numberToDigits (2 0 8 3). + 3083 :numberToDigits (3 0 8 3). }; r:evidence ( - [ a r:Fact; r:gives {(2083 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2083 1000) math:remainder 83}] + [ a r:Fact; r:gives {(3083 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3083 1000) math:remainder 83}] [ a r:Fact; r:gives {(83 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(83 100) math:remainder 83}] [ a r:Fact; r:gives {(83 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(83 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2083]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3083]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 83]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 83]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2189 a r:Inference; +skolem:lemma5604 a r:Inference; r:gives { - 2084 :numberToDigits (2 0 8 4). + 3084 :numberToDigits (3 0 8 4). }; r:evidence ( - [ a r:Fact; r:gives {(2084 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2084 1000) math:remainder 84}] + [ a r:Fact; r:gives {(3084 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3084 1000) math:remainder 84}] [ a r:Fact; r:gives {(84 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(84 100) math:remainder 84}] [ a r:Fact; r:gives {(84 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(84 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2084]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3084]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 84]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 84]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2190 a r:Inference; +skolem:lemma5605 a r:Inference; r:gives { - 2085 :numberToDigits (2 0 8 5). + 3085 :numberToDigits (3 0 8 5). }; r:evidence ( - [ a r:Fact; r:gives {(2085 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2085 1000) math:remainder 85}] + [ a r:Fact; r:gives {(3085 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3085 1000) math:remainder 85}] [ a r:Fact; r:gives {(85 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(85 100) math:remainder 85}] [ a r:Fact; r:gives {(85 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(85 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2085]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3085]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 85]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 85]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2191 a r:Inference; +skolem:lemma5606 a r:Inference; r:gives { - 2086 :numberToDigits (2 0 8 6). + 3086 :numberToDigits (3 0 8 6). }; r:evidence ( - [ a r:Fact; r:gives {(2086 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2086 1000) math:remainder 86}] + [ a r:Fact; r:gives {(3086 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3086 1000) math:remainder 86}] [ a r:Fact; r:gives {(86 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(86 100) math:remainder 86}] [ a r:Fact; r:gives {(86 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(86 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2086]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3086]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 86]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 86]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2192 a r:Inference; +skolem:lemma5607 a r:Inference; r:gives { - 2087 :numberToDigits (2 0 8 7). + 3087 :numberToDigits (3 0 8 7). }; r:evidence ( - [ a r:Fact; r:gives {(2087 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2087 1000) math:remainder 87}] + [ a r:Fact; r:gives {(3087 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3087 1000) math:remainder 87}] [ a r:Fact; r:gives {(87 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(87 100) math:remainder 87}] [ a r:Fact; r:gives {(87 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(87 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2087]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3087]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 87]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 87]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2193 a r:Inference; +skolem:lemma5608 a r:Inference; r:gives { - 2088 :numberToDigits (2 0 8 8). + 3088 :numberToDigits (3 0 8 8). }; r:evidence ( - [ a r:Fact; r:gives {(2088 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2088 1000) math:remainder 88}] + [ a r:Fact; r:gives {(3088 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3088 1000) math:remainder 88}] [ a r:Fact; r:gives {(88 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(88 100) math:remainder 88}] [ a r:Fact; r:gives {(88 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(88 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2088]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3088]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 88]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 88]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2194 a r:Inference; +skolem:lemma5609 a r:Inference; r:gives { - (0 2 8 8) :digitsToNumber 288 . + (0 3 8 8) :digitsToNumber 388 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(8 10) math:product 80}] - [ a r:Fact; r:gives {(0 200 80 8) math:sum 288}] + [ a r:Fact; r:gives {(0 300 80 8) math:sum 388}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 288]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 388]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2195 a r:Inference; +skolem:lemma5610 a r:Inference; r:gives { - (8 8 2 0) :digitsToNumber 8820 . + (8 8 3 0) :digitsToNumber 8830 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(8 100) math:product 800}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(8000 800 20 0) math:sum 8820}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(8000 800 30 0) math:sum 8830}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8820]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8830]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2196 a r:Inference; +skolem:lemma5611 a r:Inference; r:gives { - 2089 :numberToDigits (2 0 8 9). + 3089 :numberToDigits (3 0 8 9). }; r:evidence ( - [ a r:Fact; r:gives {(2089 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2089 1000) math:remainder 89}] + [ a r:Fact; r:gives {(3089 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3089 1000) math:remainder 89}] [ a r:Fact; r:gives {(89 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(89 100) math:remainder 89}] [ a r:Fact; r:gives {(89 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(89 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2089]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3089]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 89]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 89]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2197 a r:Inference; +skolem:lemma5612 a r:Inference; r:gives { - (0 2 8 9) :digitsToNumber 289 . + (0 3 8 9) :digitsToNumber 389 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(8 10) math:product 80}] - [ a r:Fact; r:gives {(0 200 80 9) math:sum 289}] + [ a r:Fact; r:gives {(0 300 80 9) math:sum 389}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 389]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2198 a r:Inference; +skolem:lemma5613 a r:Inference; r:gives { - (9 8 2 0) :digitsToNumber 9820 . + (9 8 3 0) :digitsToNumber 9830 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(8 100) math:product 800}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 800 20 0) math:sum 9820}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(9000 800 30 0) math:sum 9830}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9820]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9830]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2199 a r:Inference; +skolem:lemma5614 a r:Inference; r:gives { - 2090 :numberToDigits (2 0 9 0). + 3090 :numberToDigits (3 0 9 0). }; r:evidence ( - [ a r:Fact; r:gives {(2090 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2090 1000) math:remainder 90}] + [ a r:Fact; r:gives {(3090 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3090 1000) math:remainder 90}] [ a r:Fact; r:gives {(90 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(90 100) math:remainder 90}] [ a r:Fact; r:gives {(90 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(90 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2090]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3090]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 90]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 90]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2200 a r:Inference; +skolem:lemma5615 a r:Inference; r:gives { - 2091 :numberToDigits (2 0 9 1). + 3091 :numberToDigits (3 0 9 1). }; r:evidence ( - [ a r:Fact; r:gives {(2091 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2091 1000) math:remainder 91}] + [ a r:Fact; r:gives {(3091 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3091 1000) math:remainder 91}] [ a r:Fact; r:gives {(91 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(91 100) math:remainder 91}] [ a r:Fact; r:gives {(91 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(91 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2091]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3091]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 91]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 91]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2201 a r:Inference; +skolem:lemma5616 a r:Inference; r:gives { - 2092 :numberToDigits (2 0 9 2). + 3092 :numberToDigits (3 0 9 2). }; r:evidence ( - [ a r:Fact; r:gives {(2092 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2092 1000) math:remainder 92}] + [ a r:Fact; r:gives {(3092 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3092 1000) math:remainder 92}] [ a r:Fact; r:gives {(92 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(92 100) math:remainder 92}] [ a r:Fact; r:gives {(92 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(92 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2092]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3092]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 92]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 92]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2202 a r:Inference; +skolem:lemma5617 a r:Inference; r:gives { - 2093 :numberToDigits (2 0 9 3). + 3093 :numberToDigits (3 0 9 3). }; r:evidence ( - [ a r:Fact; r:gives {(2093 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2093 1000) math:remainder 93}] + [ a r:Fact; r:gives {(3093 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3093 1000) math:remainder 93}] [ a r:Fact; r:gives {(93 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(93 100) math:remainder 93}] [ a r:Fact; r:gives {(93 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(93 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2093]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3093]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 93]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 93]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2203 a r:Inference; +skolem:lemma5618 a r:Inference; r:gives { - 2094 :numberToDigits (2 0 9 4). + 3094 :numberToDigits (3 0 9 4). }; r:evidence ( - [ a r:Fact; r:gives {(2094 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2094 1000) math:remainder 94}] + [ a r:Fact; r:gives {(3094 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3094 1000) math:remainder 94}] [ a r:Fact; r:gives {(94 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(94 100) math:remainder 94}] [ a r:Fact; r:gives {(94 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(94 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2094]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3094]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 94]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 94]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2204 a r:Inference; +skolem:lemma5619 a r:Inference; r:gives { - 2095 :numberToDigits (2 0 9 5). + 3095 :numberToDigits (3 0 9 5). }; r:evidence ( - [ a r:Fact; r:gives {(2095 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2095 1000) math:remainder 95}] + [ a r:Fact; r:gives {(3095 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3095 1000) math:remainder 95}] [ a r:Fact; r:gives {(95 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(95 100) math:remainder 95}] [ a r:Fact; r:gives {(95 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(95 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2095]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3095]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 95]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 95]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2205 a r:Inference; +skolem:lemma5620 a r:Inference; r:gives { - 2096 :numberToDigits (2 0 9 6). + 3096 :numberToDigits (3 0 9 6). }; r:evidence ( - [ a r:Fact; r:gives {(2096 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2096 1000) math:remainder 96}] + [ a r:Fact; r:gives {(3096 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3096 1000) math:remainder 96}] [ a r:Fact; r:gives {(96 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(96 100) math:remainder 96}] [ a r:Fact; r:gives {(96 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(96 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2096]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3096]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 96]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 96]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2206 a r:Inference; +skolem:lemma5621 a r:Inference; r:gives { - 2097 :numberToDigits (2 0 9 7). + 3097 :numberToDigits (3 0 9 7). }; r:evidence ( - [ a r:Fact; r:gives {(2097 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2097 1000) math:remainder 97}] + [ a r:Fact; r:gives {(3097 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3097 1000) math:remainder 97}] [ a r:Fact; r:gives {(97 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(97 100) math:remainder 97}] [ a r:Fact; r:gives {(97 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(97 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2097]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3097]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 97]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 97]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2207 a r:Inference; +skolem:lemma5622 a r:Inference; r:gives { - 2098 :numberToDigits (2 0 9 8). + 3098 :numberToDigits (3 0 9 8). }; r:evidence ( - [ a r:Fact; r:gives {(2098 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2098 1000) math:remainder 98}] + [ a r:Fact; r:gives {(3098 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3098 1000) math:remainder 98}] [ a r:Fact; r:gives {(98 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(98 100) math:remainder 98}] [ a r:Fact; r:gives {(98 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(98 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2098]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3098]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 98]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 98]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2208 a r:Inference; +skolem:lemma5623 a r:Inference; r:gives { - 2099 :numberToDigits (2 0 9 9). + 3099 :numberToDigits (3 0 9 9). }; r:evidence ( - [ a r:Fact; r:gives {(2099 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2099 1000) math:remainder 99}] + [ a r:Fact; r:gives {(3099 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3099 1000) math:remainder 99}] [ a r:Fact; r:gives {(99 100) math:integerQuotient 0}] [ a r:Fact; r:gives {(99 100) math:remainder 99}] [ a r:Fact; r:gives {(99 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(99 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2099]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3099]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 99]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 99]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2209 a r:Inference; +skolem:lemma5624 a r:Inference; r:gives { - (0 2 9 9) :digitsToNumber 299 . + (0 3 9 9) :digitsToNumber 399 . }; r:evidence ( [ a r:Fact; r:gives {(0 1000) math:product 0}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(9 10) math:product 90}] - [ a r:Fact; r:gives {(0 200 90 9) math:sum 299}] + [ a r:Fact; r:gives {(0 300 90 9) math:sum 399}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 0]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 90]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 399]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2210 a r:Inference; +skolem:lemma5625 a r:Inference; r:gives { - (9 9 2 0) :digitsToNumber 9920 . + (9 9 3 0) :digitsToNumber 9930 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(9 100) math:product 900}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 900 20 0) math:sum 9920}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(9000 900 30 0) math:sum 9930}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 900]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9920]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9930]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2211 a r:Inference; +skolem:lemma5626 a r:Inference; r:gives { - 2100 :numberToDigits (2 1 0 0). + 3100 :numberToDigits (3 1 0 0). }; r:evidence ( - [ a r:Fact; r:gives {(2100 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2100 1000) math:remainder 100}] + [ a r:Fact; r:gives {(3100 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3100 1000) math:remainder 100}] [ a r:Fact; r:gives {(100 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(100 100) math:remainder 0}] [ a r:Fact; r:gives {(0 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(0 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2100]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3100]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 100]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2212 a r:Inference; +skolem:lemma5627 a r:Inference; r:gives { - 2101 :numberToDigits (2 1 0 1). + 3101 :numberToDigits (3 1 0 1). }; r:evidence ( - [ a r:Fact; r:gives {(2101 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2101 1000) math:remainder 101}] + [ a r:Fact; r:gives {(3101 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3101 1000) math:remainder 101}] [ a r:Fact; r:gives {(101 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(101 100) math:remainder 1}] [ a r:Fact; r:gives {(1 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(1 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2101]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3101]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 101]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2213 a r:Inference; +skolem:lemma5628 a r:Inference; r:gives { - 2102 :numberToDigits (2 1 0 2). + 3102 :numberToDigits (3 1 0 2). }; r:evidence ( - [ a r:Fact; r:gives {(2102 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2102 1000) math:remainder 102}] + [ a r:Fact; r:gives {(3102 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3102 1000) math:remainder 102}] [ a r:Fact; r:gives {(102 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(102 100) math:remainder 2}] [ a r:Fact; r:gives {(2 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(2 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2102]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3102]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 102]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2214 a r:Inference; +skolem:lemma5629 a r:Inference; r:gives { - 2103 :numberToDigits (2 1 0 3). + 3103 :numberToDigits (3 1 0 3). }; r:evidence ( - [ a r:Fact; r:gives {(2103 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2103 1000) math:remainder 103}] + [ a r:Fact; r:gives {(3103 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3103 1000) math:remainder 103}] [ a r:Fact; r:gives {(103 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(103 100) math:remainder 3}] [ a r:Fact; r:gives {(3 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(3 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2103]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3103]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 103]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2215 a r:Inference; +skolem:lemma5630 a r:Inference; r:gives { - 2104 :numberToDigits (2 1 0 4). + 3104 :numberToDigits (3 1 0 4). }; r:evidence ( - [ a r:Fact; r:gives {(2104 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2104 1000) math:remainder 104}] + [ a r:Fact; r:gives {(3104 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3104 1000) math:remainder 104}] [ a r:Fact; r:gives {(104 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(104 100) math:remainder 4}] [ a r:Fact; r:gives {(4 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(4 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2104]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3104]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 104]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2216 a r:Inference; +skolem:lemma5631 a r:Inference; r:gives { - 2105 :numberToDigits (2 1 0 5). + 3105 :numberToDigits (3 1 0 5). }; r:evidence ( - [ a r:Fact; r:gives {(2105 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2105 1000) math:remainder 105}] + [ a r:Fact; r:gives {(3105 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3105 1000) math:remainder 105}] [ a r:Fact; r:gives {(105 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(105 100) math:remainder 5}] [ a r:Fact; r:gives {(5 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(5 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2105]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3105]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 105]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2217 a r:Inference; +skolem:lemma5632 a r:Inference; r:gives { - 2106 :numberToDigits (2 1 0 6). + 3106 :numberToDigits (3 1 0 6). }; r:evidence ( - [ a r:Fact; r:gives {(2106 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2106 1000) math:remainder 106}] + [ a r:Fact; r:gives {(3106 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3106 1000) math:remainder 106}] [ a r:Fact; r:gives {(106 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(106 100) math:remainder 6}] [ a r:Fact; r:gives {(6 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(6 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2106]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3106]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 106]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2218 a r:Inference; +skolem:lemma5633 a r:Inference; r:gives { - 2107 :numberToDigits (2 1 0 7). + 3107 :numberToDigits (3 1 0 7). }; r:evidence ( - [ a r:Fact; r:gives {(2107 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2107 1000) math:remainder 107}] + [ a r:Fact; r:gives {(3107 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3107 1000) math:remainder 107}] [ a r:Fact; r:gives {(107 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(107 100) math:remainder 7}] [ a r:Fact; r:gives {(7 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(7 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2107]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3107]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 107]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2219 a r:Inference; +skolem:lemma5634 a r:Inference; r:gives { - 2108 :numberToDigits (2 1 0 8). + 3108 :numberToDigits (3 1 0 8). }; r:evidence ( - [ a r:Fact; r:gives {(2108 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2108 1000) math:remainder 108}] + [ a r:Fact; r:gives {(3108 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3108 1000) math:remainder 108}] [ a r:Fact; r:gives {(108 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(108 100) math:remainder 8}] [ a r:Fact; r:gives {(8 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(8 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2108]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3108]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 108]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2220 a r:Inference; +skolem:lemma5635 a r:Inference; r:gives { - 2109 :numberToDigits (2 1 0 9). + 3109 :numberToDigits (3 1 0 9). }; r:evidence ( - [ a r:Fact; r:gives {(2109 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2109 1000) math:remainder 109}] + [ a r:Fact; r:gives {(3109 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3109 1000) math:remainder 109}] [ a r:Fact; r:gives {(109 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(109 100) math:remainder 9}] [ a r:Fact; r:gives {(9 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(9 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2109]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3109]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 109]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2221 a r:Inference; +skolem:lemma5636 a r:Inference; r:gives { - 2110 :numberToDigits (2 1 1 0). + 3110 :numberToDigits (3 1 1 0). }; r:evidence ( - [ a r:Fact; r:gives {(2110 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2110 1000) math:remainder 110}] + [ a r:Fact; r:gives {(3110 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3110 1000) math:remainder 110}] [ a r:Fact; r:gives {(110 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(110 100) math:remainder 10}] [ a r:Fact; r:gives {(10 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(10 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2110]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3110]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 110]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2222 a r:Inference; +skolem:lemma5637 a r:Inference; r:gives { - 2111 :numberToDigits (2 1 1 1). + 3111 :numberToDigits (3 1 1 1). }; r:evidence ( - [ a r:Fact; r:gives {(2111 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2111 1000) math:remainder 111}] + [ a r:Fact; r:gives {(3111 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3111 1000) math:remainder 111}] [ a r:Fact; r:gives {(111 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(111 100) math:remainder 11}] [ a r:Fact; r:gives {(11 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(11 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2111]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3111]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 111]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 11]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2223 a r:Inference; +skolem:lemma5638 a r:Inference; r:gives { - (1 1 1 2) :digitsToNumber 1112 . + (1 1 1 3) :digitsToNumber 1113 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] [ a r:Fact; r:gives {(1 100) math:product 100}] [ a r:Fact; r:gives {(1 10) math:product 10}] - [ a r:Fact; r:gives {(1000 100 10 2) math:sum 1112}] + [ a r:Fact; r:gives {(1000 100 10 3) math:sum 1113}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; @@ -54565,7921 +133854,6121 @@ skolem:lemma2223 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1112]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1113]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2224 a r:Inference; +skolem:lemma5639 a r:Inference; r:gives { - (2 1 1 1) :digitsToNumber 2111 . + (3 1 1 1) :digitsToNumber 3111 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(1 100) math:product 100}] [ a r:Fact; r:gives {(1 10) math:product 10}] - [ a r:Fact; r:gives {(2000 100 10 1) math:sum 2111}] + [ a r:Fact; r:gives {(3000 100 10 1) math:sum 3111}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2111]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3111]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2225 a r:Inference; +skolem:lemma5640 a r:Inference; r:gives { - 2112 :numberToDigits (2 1 1 2). + 3112 :numberToDigits (3 1 1 2). }; r:evidence ( - [ a r:Fact; r:gives {(2112 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2112 1000) math:remainder 112}] + [ a r:Fact; r:gives {(3112 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3112 1000) math:remainder 112}] [ a r:Fact; r:gives {(112 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(112 100) math:remainder 12}] [ a r:Fact; r:gives {(12 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(12 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2112]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3112]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 112]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. - -skolem:lemma2226 a r:Inference; - r:gives { - (1 1 2 2) :digitsToNumber 1122 . - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(1 100) math:product 100}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(1000 100 20 2) math:sum 1122}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1122]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. - -skolem:lemma2227 a r:Inference; - r:gives { - (2 2 1 1) :digitsToNumber 2211 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(1 10) math:product 10}] - [ a r:Fact; r:gives {(2000 200 10 1) math:sum 2211}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2211]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2228 a r:Inference; +skolem:lemma5641 a r:Inference; r:gives { - 2113 :numberToDigits (2 1 1 3). + 3113 :numberToDigits (3 1 1 3). }; r:evidence ( - [ a r:Fact; r:gives {(2113 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2113 1000) math:remainder 113}] + [ a r:Fact; r:gives {(3113 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3113 1000) math:remainder 113}] [ a r:Fact; r:gives {(113 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(113 100) math:remainder 13}] [ a r:Fact; r:gives {(13 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(13 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2113]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3113]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 113]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 13]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2229 a r:Inference; +skolem:lemma5642 a r:Inference; r:gives { - (1 1 2 3) :digitsToNumber 1123 . + (1 1 3 3) :digitsToNumber 1133 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] [ a r:Fact; r:gives {(1 100) math:product 100}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(1000 100 20 3) math:sum 1123}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(1000 100 30 3) math:sum 1133}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1133]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2230 a r:Inference; +skolem:lemma5643 a r:Inference; r:gives { - (3 2 1 1) :digitsToNumber 3211 . + (3 3 1 1) :digitsToNumber 3311 . }; r:evidence ( [ a r:Fact; r:gives {(3 1000) math:product 3000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(1 10) math:product 10}] - [ a r:Fact; r:gives {(3000 200 10 1) math:sum 3211}] + [ a r:Fact; r:gives {(3000 300 10 1) math:sum 3311}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3311]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2231 a r:Inference; +skolem:lemma5644 a r:Inference; r:gives { - 2114 :numberToDigits (2 1 1 4). + 3114 :numberToDigits (3 1 1 4). }; r:evidence ( - [ a r:Fact; r:gives {(2114 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2114 1000) math:remainder 114}] + [ a r:Fact; r:gives {(3114 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3114 1000) math:remainder 114}] [ a r:Fact; r:gives {(114 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(114 100) math:remainder 14}] [ a r:Fact; r:gives {(14 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(14 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2114]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3114]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 114]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 14]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2232 a r:Inference; +skolem:lemma5645 a r:Inference; r:gives { - (1 1 2 4) :digitsToNumber 1124 . + (1 1 3 4) :digitsToNumber 1134 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] [ a r:Fact; r:gives {(1 100) math:product 100}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(1000 100 20 4) math:sum 1124}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(1000 100 30 4) math:sum 1134}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1134]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2233 a r:Inference; +skolem:lemma5646 a r:Inference; r:gives { - (4 2 1 1) :digitsToNumber 4211 . + (4 3 1 1) :digitsToNumber 4311 . }; r:evidence ( [ a r:Fact; r:gives {(4 1000) math:product 4000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(1 10) math:product 10}] - [ a r:Fact; r:gives {(4000 200 10 1) math:sum 4211}] + [ a r:Fact; r:gives {(4000 300 10 1) math:sum 4311}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4311]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2234 a r:Inference; +skolem:lemma5647 a r:Inference; r:gives { - 2115 :numberToDigits (2 1 1 5). + 3115 :numberToDigits (3 1 1 5). }; r:evidence ( - [ a r:Fact; r:gives {(2115 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2115 1000) math:remainder 115}] + [ a r:Fact; r:gives {(3115 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3115 1000) math:remainder 115}] [ a r:Fact; r:gives {(115 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(115 100) math:remainder 15}] [ a r:Fact; r:gives {(15 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(15 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2115]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3115]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 115]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 15]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2235 a r:Inference; +skolem:lemma5648 a r:Inference; r:gives { - (1 1 2 5) :digitsToNumber 1125 . + (1 1 3 5) :digitsToNumber 1135 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] [ a r:Fact; r:gives {(1 100) math:product 100}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(1000 100 20 5) math:sum 1125}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(1000 100 30 5) math:sum 1135}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1135]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2236 a r:Inference; +skolem:lemma5649 a r:Inference; r:gives { - (5 2 1 1) :digitsToNumber 5211 . + (5 3 1 1) :digitsToNumber 5311 . }; r:evidence ( [ a r:Fact; r:gives {(5 1000) math:product 5000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(1 10) math:product 10}] - [ a r:Fact; r:gives {(5000 200 10 1) math:sum 5211}] + [ a r:Fact; r:gives {(5000 300 10 1) math:sum 5311}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5311]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2237 a r:Inference; +skolem:lemma5650 a r:Inference; r:gives { - 2116 :numberToDigits (2 1 1 6). + 3116 :numberToDigits (3 1 1 6). }; r:evidence ( - [ a r:Fact; r:gives {(2116 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2116 1000) math:remainder 116}] + [ a r:Fact; r:gives {(3116 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3116 1000) math:remainder 116}] [ a r:Fact; r:gives {(116 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(116 100) math:remainder 16}] [ a r:Fact; r:gives {(16 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(16 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2116]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3116]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 116]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 16]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2238 a r:Inference; +skolem:lemma5651 a r:Inference; r:gives { - (1 1 2 6) :digitsToNumber 1126 . + (1 1 3 6) :digitsToNumber 1136 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] [ a r:Fact; r:gives {(1 100) math:product 100}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(1000 100 20 6) math:sum 1126}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(1000 100 30 6) math:sum 1136}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1136]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2239 a r:Inference; +skolem:lemma5652 a r:Inference; r:gives { - (6 2 1 1) :digitsToNumber 6211 . + (6 3 1 1) :digitsToNumber 6311 . }; r:evidence ( [ a r:Fact; r:gives {(6 1000) math:product 6000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(1 10) math:product 10}] - [ a r:Fact; r:gives {(6000 200 10 1) math:sum 6211}] + [ a r:Fact; r:gives {(6000 300 10 1) math:sum 6311}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6311]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2240 a r:Inference; +skolem:lemma5653 a r:Inference; r:gives { - 2117 :numberToDigits (2 1 1 7). + 3117 :numberToDigits (3 1 1 7). }; r:evidence ( - [ a r:Fact; r:gives {(2117 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2117 1000) math:remainder 117}] + [ a r:Fact; r:gives {(3117 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3117 1000) math:remainder 117}] [ a r:Fact; r:gives {(117 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(117 100) math:remainder 17}] [ a r:Fact; r:gives {(17 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(17 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2117]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3117]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 117]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 17]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2241 a r:Inference; +skolem:lemma5654 a r:Inference; r:gives { - (1 1 2 7) :digitsToNumber 1127 . + (1 1 3 7) :digitsToNumber 1137 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] [ a r:Fact; r:gives {(1 100) math:product 100}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(1000 100 20 7) math:sum 1127}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(1000 100 30 7) math:sum 1137}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1137]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2242 a r:Inference; +skolem:lemma5655 a r:Inference; r:gives { - (7 2 1 1) :digitsToNumber 7211 . + (7 3 1 1) :digitsToNumber 7311 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(1 10) math:product 10}] - [ a r:Fact; r:gives {(7000 200 10 1) math:sum 7211}] + [ a r:Fact; r:gives {(7000 300 10 1) math:sum 7311}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7311]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2243 a r:Inference; +skolem:lemma5656 a r:Inference; r:gives { - 2118 :numberToDigits (2 1 1 8). + 3118 :numberToDigits (3 1 1 8). }; r:evidence ( - [ a r:Fact; r:gives {(2118 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2118 1000) math:remainder 118}] + [ a r:Fact; r:gives {(3118 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3118 1000) math:remainder 118}] [ a r:Fact; r:gives {(118 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(118 100) math:remainder 18}] [ a r:Fact; r:gives {(18 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(18 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2118]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3118]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 118]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 18]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2244 a r:Inference; +skolem:lemma5657 a r:Inference; r:gives { - (1 1 2 8) :digitsToNumber 1128 . + (1 1 3 8) :digitsToNumber 1138 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] [ a r:Fact; r:gives {(1 100) math:product 100}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(1000 100 20 8) math:sum 1128}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(1000 100 30 8) math:sum 1138}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1138]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2245 a r:Inference; +skolem:lemma5658 a r:Inference; r:gives { - (8 2 1 1) :digitsToNumber 8211 . + (8 3 1 1) :digitsToNumber 8311 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(1 10) math:product 10}] - [ a r:Fact; r:gives {(8000 200 10 1) math:sum 8211}] + [ a r:Fact; r:gives {(8000 300 10 1) math:sum 8311}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8311]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2246 a r:Inference; +skolem:lemma5659 a r:Inference; r:gives { - 2119 :numberToDigits (2 1 1 9). + 3119 :numberToDigits (3 1 1 9). }; r:evidence ( - [ a r:Fact; r:gives {(2119 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2119 1000) math:remainder 119}] + [ a r:Fact; r:gives {(3119 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3119 1000) math:remainder 119}] [ a r:Fact; r:gives {(119 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(119 100) math:remainder 19}] [ a r:Fact; r:gives {(19 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(19 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2119]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3119]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 119]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 19]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2247 a r:Inference; +skolem:lemma5660 a r:Inference; r:gives { - (1 1 2 9) :digitsToNumber 1129 . + (1 1 3 9) :digitsToNumber 1139 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] [ a r:Fact; r:gives {(1 100) math:product 100}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(1000 100 20 9) math:sum 1129}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(1000 100 30 9) math:sum 1139}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 100]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1139]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2248 a r:Inference; +skolem:lemma5661 a r:Inference; r:gives { - (9 2 1 1) :digitsToNumber 9211 . + (9 3 1 1) :digitsToNumber 9311 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(1 10) math:product 10}] - [ a r:Fact; r:gives {(9000 200 10 1) math:sum 9211}] + [ a r:Fact; r:gives {(9000 300 10 1) math:sum 9311}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9311]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2249 a r:Inference; +skolem:lemma5662 a r:Inference; r:gives { - 2120 :numberToDigits (2 1 2 0). + 3120 :numberToDigits (3 1 2 0). }; r:evidence ( - [ a r:Fact; r:gives {(2120 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2120 1000) math:remainder 120}] + [ a r:Fact; r:gives {(3120 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3120 1000) math:remainder 120}] [ a r:Fact; r:gives {(120 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(120 100) math:remainder 20}] [ a r:Fact; r:gives {(20 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(20 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2120]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3120]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 120]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 20]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2250 a r:Inference; +skolem:lemma5663 a r:Inference; r:gives { - 2121 :numberToDigits (2 1 2 1). + 3121 :numberToDigits (3 1 2 1). }; r:evidence ( - [ a r:Fact; r:gives {(2121 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2121 1000) math:remainder 121}] + [ a r:Fact; r:gives {(3121 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3121 1000) math:remainder 121}] [ a r:Fact; r:gives {(121 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(121 100) math:remainder 21}] [ a r:Fact; r:gives {(21 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(21 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2121]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3121]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 121]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 21]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2251 a r:Inference; +skolem:lemma5664 a r:Inference; r:gives { - 2122 :numberToDigits (2 1 2 2). + 3122 :numberToDigits (3 1 2 2). }; r:evidence ( - [ a r:Fact; r:gives {(2122 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2122 1000) math:remainder 122}] + [ a r:Fact; r:gives {(3122 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3122 1000) math:remainder 122}] [ a r:Fact; r:gives {(122 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(122 100) math:remainder 22}] [ a r:Fact; r:gives {(22 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(22 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2122]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3122]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 122]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. - -skolem:lemma2252 a r:Inference; - r:gives { - (1 2 2 2) :digitsToNumber 1222 . - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(1000 200 20 2) math:sum 1222}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. - -skolem:lemma2253 a r:Inference; - r:gives { - (2 2 2 1) :digitsToNumber 2221 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(2000 200 20 1) math:sum 2221}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2254 a r:Inference; +skolem:lemma5665 a r:Inference; r:gives { - 2123 :numberToDigits (2 1 2 3). + 3123 :numberToDigits (3 1 2 3). }; r:evidence ( - [ a r:Fact; r:gives {(2123 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2123 1000) math:remainder 123}] + [ a r:Fact; r:gives {(3123 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3123 1000) math:remainder 123}] [ a r:Fact; r:gives {(123 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(123 100) math:remainder 23}] [ a r:Fact; r:gives {(23 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(23 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2123]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3123]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 123]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. - -skolem:lemma2255 a r:Inference; - r:gives { - (1 2 2 3) :digitsToNumber 1223 . - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(1000 200 20 3) math:sum 1223}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1223]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3439. - -skolem:lemma2256 a r:Inference; - r:gives { - (3 2 2 1) :digitsToNumber 3221 . - }; - r:evidence ( - [ a r:Fact; r:gives {(3 1000) math:product 3000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(3000 200 20 1) math:sum 3221}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2257 a r:Inference; +skolem:lemma5666 a r:Inference; r:gives { - 2124 :numberToDigits (2 1 2 4). + 3124 :numberToDigits (3 1 2 4). }; r:evidence ( - [ a r:Fact; r:gives {(2124 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2124 1000) math:remainder 124}] + [ a r:Fact; r:gives {(3124 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3124 1000) math:remainder 124}] [ a r:Fact; r:gives {(124 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(124 100) math:remainder 24}] [ a r:Fact; r:gives {(24 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(24 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2124]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3124]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 124]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. - -skolem:lemma2258 a r:Inference; - r:gives { - (1 2 2 4) :digitsToNumber 1224 . - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(1000 200 20 4) math:sum 1224}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1224]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3439. - -skolem:lemma2259 a r:Inference; - r:gives { - (4 2 2 1) :digitsToNumber 4221 . - }; - r:evidence ( - [ a r:Fact; r:gives {(4 1000) math:product 4000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(4000 200 20 1) math:sum 4221}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2260 a r:Inference; +skolem:lemma5667 a r:Inference; r:gives { - 2125 :numberToDigits (2 1 2 5). + 3125 :numberToDigits (3 1 2 5). }; r:evidence ( - [ a r:Fact; r:gives {(2125 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2125 1000) math:remainder 125}] + [ a r:Fact; r:gives {(3125 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3125 1000) math:remainder 125}] [ a r:Fact; r:gives {(125 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(125 100) math:remainder 25}] [ a r:Fact; r:gives {(25 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(25 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2125]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3125]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 125]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. - -skolem:lemma2261 a r:Inference; - r:gives { - (1 2 2 5) :digitsToNumber 1225 . - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(1000 200 20 5) math:sum 1225}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1225]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3439. - -skolem:lemma2262 a r:Inference; - r:gives { - (5 2 2 1) :digitsToNumber 5221 . - }; - r:evidence ( - [ a r:Fact; r:gives {(5 1000) math:product 5000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(5000 200 20 1) math:sum 5221}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2263 a r:Inference; +skolem:lemma5668 a r:Inference; r:gives { - 2126 :numberToDigits (2 1 2 6). + 3126 :numberToDigits (3 1 2 6). }; r:evidence ( - [ a r:Fact; r:gives {(2126 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2126 1000) math:remainder 126}] + [ a r:Fact; r:gives {(3126 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3126 1000) math:remainder 126}] [ a r:Fact; r:gives {(126 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(126 100) math:remainder 26}] [ a r:Fact; r:gives {(26 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(26 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2126]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3126]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 126]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. - -skolem:lemma2264 a r:Inference; - r:gives { - (1 2 2 6) :digitsToNumber 1226 . - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(1000 200 20 6) math:sum 1226}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1226]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. - -skolem:lemma2265 a r:Inference; - r:gives { - (6 2 2 1) :digitsToNumber 6221 . - }; - r:evidence ( - [ a r:Fact; r:gives {(6 1000) math:product 6000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(6000 200 20 1) math:sum 6221}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. - -skolem:lemma2266 a r:Inference; - r:gives { - 2127 :numberToDigits (2 1 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2127 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2127 1000) math:remainder 127}] - [ a r:Fact; r:gives {(127 100) math:integerQuotient 1}] - [ a r:Fact; r:gives {(127 100) math:remainder 27}] - [ a r:Fact; r:gives {(27 10) math:integerQuotient 2}] - [ a r:Fact; r:gives {(27 10) math:remainder 7}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2127]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 127]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. - -skolem:lemma2267 a r:Inference; - r:gives { - (1 2 2 7) :digitsToNumber 1227 . - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(1000 200 20 7) math:sum 1227}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1227]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. -skolem:lemma2268 a r:Inference; +skolem:lemma5669 a r:Inference; r:gives { - (7 2 2 1) :digitsToNumber 7221 . + 3127 :numberToDigits (3 1 2 7). }; r:evidence ( - [ a r:Fact; r:gives {(7 1000) math:product 7000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(7000 200 20 1) math:sum 7221}] + [ a r:Fact; r:gives {(3127 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3127 1000) math:remainder 127}] + [ a r:Fact; r:gives {(127 100) math:integerQuotient 1}] + [ a r:Fact; r:gives {(127 100) math:remainder 27}] + [ a r:Fact; r:gives {(27 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(27 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 127]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. -skolem:lemma2269 a r:Inference; +skolem:lemma5670 a r:Inference; r:gives { - 2128 :numberToDigits (2 1 2 8). + 3128 :numberToDigits (3 1 2 8). }; r:evidence ( - [ a r:Fact; r:gives {(2128 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2128 1000) math:remainder 128}] + [ a r:Fact; r:gives {(3128 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3128 1000) math:remainder 128}] [ a r:Fact; r:gives {(128 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(128 100) math:remainder 28}] [ a r:Fact; r:gives {(28 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(28 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2128]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3128]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 128]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. - -skolem:lemma2270 a r:Inference; - r:gives { - (1 2 2 8) :digitsToNumber 1228 . - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(1000 200 20 8) math:sum 1228}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1228]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. - -skolem:lemma2271 a r:Inference; - r:gives { - (8 2 2 1) :digitsToNumber 8221 . - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1000) math:product 8000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(8000 200 20 1) math:sum 8221}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2272 a r:Inference; +skolem:lemma5671 a r:Inference; r:gives { - 2129 :numberToDigits (2 1 2 9). + 3129 :numberToDigits (3 1 2 9). }; r:evidence ( - [ a r:Fact; r:gives {(2129 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2129 1000) math:remainder 129}] + [ a r:Fact; r:gives {(3129 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3129 1000) math:remainder 129}] [ a r:Fact; r:gives {(129 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(129 100) math:remainder 29}] [ a r:Fact; r:gives {(29 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(29 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2129]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3129]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 129]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. - -skolem:lemma2273 a r:Inference; - r:gives { - (1 2 2 9) :digitsToNumber 1229 . - }; - r:evidence ( - [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(1000 200 20 9) math:sum 1229}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1229]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2274 a r:Inference; - r:gives { - (9 2 2 1) :digitsToNumber 9221 . - }; - r:evidence ( - [ a r:Fact; r:gives {(9 1000) math:product 9000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 200 20 1) math:sum 9221}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9221]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. - -skolem:lemma2275 a r:Inference; +skolem:lemma5672 a r:Inference; r:gives { - 2130 :numberToDigits (2 1 3 0). + 3130 :numberToDigits (3 1 3 0). }; r:evidence ( - [ a r:Fact; r:gives {(2130 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2130 1000) math:remainder 130}] + [ a r:Fact; r:gives {(3130 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3130 1000) math:remainder 130}] [ a r:Fact; r:gives {(130 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(130 100) math:remainder 30}] [ a r:Fact; r:gives {(30 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(30 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2130]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3130]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 130]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2276 a r:Inference; +skolem:lemma5673 a r:Inference; r:gives { - 2131 :numberToDigits (2 1 3 1). + 3131 :numberToDigits (3 1 3 1). }; r:evidence ( - [ a r:Fact; r:gives {(2131 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2131 1000) math:remainder 131}] + [ a r:Fact; r:gives {(3131 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3131 1000) math:remainder 131}] [ a r:Fact; r:gives {(131 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(131 100) math:remainder 31}] [ a r:Fact; r:gives {(31 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(31 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2131]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3131]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 131]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 31]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2277 a r:Inference; +skolem:lemma5674 a r:Inference; r:gives { - 2132 :numberToDigits (2 1 3 2). + 3132 :numberToDigits (3 1 3 2). }; r:evidence ( - [ a r:Fact; r:gives {(2132 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2132 1000) math:remainder 132}] + [ a r:Fact; r:gives {(3132 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3132 1000) math:remainder 132}] [ a r:Fact; r:gives {(132 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(132 100) math:remainder 32}] [ a r:Fact; r:gives {(32 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(32 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2132]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3132]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 132]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 32]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2278 a r:Inference; +skolem:lemma5675 a r:Inference; r:gives { - 2133 :numberToDigits (2 1 3 3). + 3133 :numberToDigits (3 1 3 3). }; r:evidence ( - [ a r:Fact; r:gives {(2133 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2133 1000) math:remainder 133}] + [ a r:Fact; r:gives {(3133 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3133 1000) math:remainder 133}] [ a r:Fact; r:gives {(133 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(133 100) math:remainder 33}] [ a r:Fact; r:gives {(33 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(33 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2133]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3133]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 133]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 33]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2279 a r:Inference; +skolem:lemma5676 a r:Inference; r:gives { - (1 2 3 3) :digitsToNumber 1233 . + (1 3 3 3) :digitsToNumber 1333 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(1000 200 30 3) math:sum 1233}] + [ a r:Fact; r:gives {(1000 300 30 3) math:sum 1333}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1333]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2280 a r:Inference; +skolem:lemma5677 a r:Inference; r:gives { - (3 3 2 1) :digitsToNumber 3321 . + (3 3 3 1) :digitsToNumber 3331 . }; r:evidence ( [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(3000 300 20 1) math:sum 3321}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(3000 300 30 1) math:sum 3331}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3331]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2281 a r:Inference; +skolem:lemma5678 a r:Inference; r:gives { - 2134 :numberToDigits (2 1 3 4). + 3134 :numberToDigits (3 1 3 4). }; r:evidence ( - [ a r:Fact; r:gives {(2134 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2134 1000) math:remainder 134}] + [ a r:Fact; r:gives {(3134 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3134 1000) math:remainder 134}] [ a r:Fact; r:gives {(134 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(134 100) math:remainder 34}] [ a r:Fact; r:gives {(34 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(34 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2134]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3134]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 134]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 34]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2282 a r:Inference; +skolem:lemma5679 a r:Inference; r:gives { - (1 2 3 4) :digitsToNumber 1234 . + (1 3 3 4) :digitsToNumber 1334 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(1000 200 30 4) math:sum 1234}] + [ a r:Fact; r:gives {(1000 300 30 4) math:sum 1334}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1334]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2283 a r:Inference; +skolem:lemma5680 a r:Inference; r:gives { - (4 3 2 1) :digitsToNumber 4321 . + (4 3 3 1) :digitsToNumber 4331 . }; r:evidence ( [ a r:Fact; r:gives {(4 1000) math:product 4000}] [ a r:Fact; r:gives {(3 100) math:product 300}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(4000 300 20 1) math:sum 4321}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(4000 300 30 1) math:sum 4331}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4331]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2284 a r:Inference; +skolem:lemma5681 a r:Inference; r:gives { - 2135 :numberToDigits (2 1 3 5). + 3135 :numberToDigits (3 1 3 5). }; r:evidence ( - [ a r:Fact; r:gives {(2135 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2135 1000) math:remainder 135}] + [ a r:Fact; r:gives {(3135 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3135 1000) math:remainder 135}] [ a r:Fact; r:gives {(135 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(135 100) math:remainder 35}] [ a r:Fact; r:gives {(35 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(35 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2135]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3135]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 135]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 35]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2285 a r:Inference; +skolem:lemma5682 a r:Inference; r:gives { - (1 2 3 5) :digitsToNumber 1235 . + (1 3 3 5) :digitsToNumber 1335 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(1000 200 30 5) math:sum 1235}] + [ a r:Fact; r:gives {(1000 300 30 5) math:sum 1335}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1335]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2286 a r:Inference; +skolem:lemma5683 a r:Inference; r:gives { - (5 3 2 1) :digitsToNumber 5321 . + (5 3 3 1) :digitsToNumber 5331 . }; r:evidence ( [ a r:Fact; r:gives {(5 1000) math:product 5000}] [ a r:Fact; r:gives {(3 100) math:product 300}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(5000 300 20 1) math:sum 5321}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(5000 300 30 1) math:sum 5331}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5331]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2287 a r:Inference; +skolem:lemma5684 a r:Inference; r:gives { - 2136 :numberToDigits (2 1 3 6). + 3136 :numberToDigits (3 1 3 6). }; r:evidence ( - [ a r:Fact; r:gives {(2136 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2136 1000) math:remainder 136}] + [ a r:Fact; r:gives {(3136 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3136 1000) math:remainder 136}] [ a r:Fact; r:gives {(136 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(136 100) math:remainder 36}] [ a r:Fact; r:gives {(36 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(36 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2136]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3136]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 136]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 36]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2288 a r:Inference; +skolem:lemma5685 a r:Inference; r:gives { - (1 2 3 6) :digitsToNumber 1236 . + (1 3 3 6) :digitsToNumber 1336 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(1000 200 30 6) math:sum 1236}] + [ a r:Fact; r:gives {(1000 300 30 6) math:sum 1336}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1336]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2289 a r:Inference; +skolem:lemma5686 a r:Inference; r:gives { - (6 3 2 1) :digitsToNumber 6321 . + (6 3 3 1) :digitsToNumber 6331 . }; r:evidence ( [ a r:Fact; r:gives {(6 1000) math:product 6000}] [ a r:Fact; r:gives {(3 100) math:product 300}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(6000 300 20 1) math:sum 6321}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(6000 300 30 1) math:sum 6331}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6331]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2290 a r:Inference; +skolem:lemma5687 a r:Inference; r:gives { - 2137 :numberToDigits (2 1 3 7). + 3137 :numberToDigits (3 1 3 7). }; r:evidence ( - [ a r:Fact; r:gives {(2137 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2137 1000) math:remainder 137}] + [ a r:Fact; r:gives {(3137 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3137 1000) math:remainder 137}] [ a r:Fact; r:gives {(137 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(137 100) math:remainder 37}] [ a r:Fact; r:gives {(37 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(37 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2137]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3137]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 137]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 37]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2291 a r:Inference; +skolem:lemma5688 a r:Inference; r:gives { - (1 2 3 7) :digitsToNumber 1237 . + (1 3 3 7) :digitsToNumber 1337 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(1000 200 30 7) math:sum 1237}] + [ a r:Fact; r:gives {(1000 300 30 7) math:sum 1337}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1337]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2292 a r:Inference; +skolem:lemma5689 a r:Inference; r:gives { - (7 3 2 1) :digitsToNumber 7321 . + (7 3 3 1) :digitsToNumber 7331 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(3 100) math:product 300}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(7000 300 20 1) math:sum 7321}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(7000 300 30 1) math:sum 7331}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7331]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2293 a r:Inference; +skolem:lemma5690 a r:Inference; r:gives { - 2138 :numberToDigits (2 1 3 8). + 3138 :numberToDigits (3 1 3 8). }; r:evidence ( - [ a r:Fact; r:gives {(2138 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2138 1000) math:remainder 138}] + [ a r:Fact; r:gives {(3138 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3138 1000) math:remainder 138}] [ a r:Fact; r:gives {(138 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(138 100) math:remainder 38}] [ a r:Fact; r:gives {(38 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(38 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2138]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3138]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 138]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 38]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2294 a r:Inference; +skolem:lemma5691 a r:Inference; r:gives { - (1 2 3 8) :digitsToNumber 1238 . + (1 3 3 8) :digitsToNumber 1338 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(1000 200 30 8) math:sum 1238}] + [ a r:Fact; r:gives {(1000 300 30 8) math:sum 1338}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1338]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2295 a r:Inference; +skolem:lemma5692 a r:Inference; r:gives { - (8 3 2 1) :digitsToNumber 8321 . + (8 3 3 1) :digitsToNumber 8331 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(3 100) math:product 300}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(8000 300 20 1) math:sum 8321}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(8000 300 30 1) math:sum 8331}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8331]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2296 a r:Inference; +skolem:lemma5693 a r:Inference; r:gives { - 2139 :numberToDigits (2 1 3 9). + 3139 :numberToDigits (3 1 3 9). }; r:evidence ( - [ a r:Fact; r:gives {(2139 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2139 1000) math:remainder 139}] + [ a r:Fact; r:gives {(3139 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3139 1000) math:remainder 139}] [ a r:Fact; r:gives {(139 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(139 100) math:remainder 39}] [ a r:Fact; r:gives {(39 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(39 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2139]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3139]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 139]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 39]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2297 a r:Inference; +skolem:lemma5694 a r:Inference; r:gives { - (1 2 3 9) :digitsToNumber 1239 . + (1 3 3 9) :digitsToNumber 1339 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(1000 200 30 9) math:sum 1239}] + [ a r:Fact; r:gives {(1000 300 30 9) math:sum 1339}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1339]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2298 a r:Inference; +skolem:lemma5695 a r:Inference; r:gives { - (9 3 2 1) :digitsToNumber 9321 . + (9 3 3 1) :digitsToNumber 9331 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(3 100) math:product 300}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 300 20 1) math:sum 9321}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(9000 300 30 1) math:sum 9331}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9331]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2299 a r:Inference; +skolem:lemma5696 a r:Inference; r:gives { - 2140 :numberToDigits (2 1 4 0). + 3140 :numberToDigits (3 1 4 0). }; r:evidence ( - [ a r:Fact; r:gives {(2140 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2140 1000) math:remainder 140}] + [ a r:Fact; r:gives {(3140 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3140 1000) math:remainder 140}] [ a r:Fact; r:gives {(140 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(140 100) math:remainder 40}] [ a r:Fact; r:gives {(40 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(40 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2140]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3140]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 140]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2300 a r:Inference; +skolem:lemma5697 a r:Inference; r:gives { - 2141 :numberToDigits (2 1 4 1). + 3141 :numberToDigits (3 1 4 1). }; r:evidence ( - [ a r:Fact; r:gives {(2141 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2141 1000) math:remainder 141}] + [ a r:Fact; r:gives {(3141 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3141 1000) math:remainder 141}] [ a r:Fact; r:gives {(141 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(141 100) math:remainder 41}] [ a r:Fact; r:gives {(41 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(41 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2141]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3141]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 141]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 41]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2301 a r:Inference; +skolem:lemma5698 a r:Inference; r:gives { - 2142 :numberToDigits (2 1 4 2). + 3142 :numberToDigits (3 1 4 2). }; r:evidence ( - [ a r:Fact; r:gives {(2142 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2142 1000) math:remainder 142}] + [ a r:Fact; r:gives {(3142 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3142 1000) math:remainder 142}] [ a r:Fact; r:gives {(142 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(142 100) math:remainder 42}] [ a r:Fact; r:gives {(42 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(42 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2142]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3142]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 142]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 42]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2302 a r:Inference; +skolem:lemma5699 a r:Inference; r:gives { - 2143 :numberToDigits (2 1 4 3). + 3143 :numberToDigits (3 1 4 3). }; r:evidence ( - [ a r:Fact; r:gives {(2143 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2143 1000) math:remainder 143}] + [ a r:Fact; r:gives {(3143 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3143 1000) math:remainder 143}] [ a r:Fact; r:gives {(143 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(143 100) math:remainder 43}] [ a r:Fact; r:gives {(43 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(43 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2143]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3143]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 143]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 43]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2303 a r:Inference; +skolem:lemma5700 a r:Inference; r:gives { - 2144 :numberToDigits (2 1 4 4). + 3144 :numberToDigits (3 1 4 4). }; r:evidence ( - [ a r:Fact; r:gives {(2144 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2144 1000) math:remainder 144}] + [ a r:Fact; r:gives {(3144 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3144 1000) math:remainder 144}] [ a r:Fact; r:gives {(144 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(144 100) math:remainder 44}] [ a r:Fact; r:gives {(44 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(44 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2144]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3144]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 144]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 44]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2304 a r:Inference; +skolem:lemma5701 a r:Inference; r:gives { - (1 2 4 4) :digitsToNumber 1244 . + (1 3 4 4) :digitsToNumber 1344 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(1000 200 40 4) math:sum 1244}] + [ a r:Fact; r:gives {(1000 300 40 4) math:sum 1344}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1344]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2305 a r:Inference; +skolem:lemma5702 a r:Inference; r:gives { - (4 4 2 1) :digitsToNumber 4421 . + (4 4 3 1) :digitsToNumber 4431 . }; r:evidence ( [ a r:Fact; r:gives {(4 1000) math:product 4000}] [ a r:Fact; r:gives {(4 100) math:product 400}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(4000 400 20 1) math:sum 4421}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(4000 400 30 1) math:sum 4431}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4431]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2306 a r:Inference; +skolem:lemma5703 a r:Inference; r:gives { - 2145 :numberToDigits (2 1 4 5). + 3145 :numberToDigits (3 1 4 5). }; r:evidence ( - [ a r:Fact; r:gives {(2145 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2145 1000) math:remainder 145}] + [ a r:Fact; r:gives {(3145 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3145 1000) math:remainder 145}] [ a r:Fact; r:gives {(145 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(145 100) math:remainder 45}] [ a r:Fact; r:gives {(45 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(45 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2145]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3145]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 145]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 45]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2307 a r:Inference; +skolem:lemma5704 a r:Inference; r:gives { - (1 2 4 5) :digitsToNumber 1245 . + (1 3 4 5) :digitsToNumber 1345 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(1000 200 40 5) math:sum 1245}] + [ a r:Fact; r:gives {(1000 300 40 5) math:sum 1345}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1345]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2308 a r:Inference; +skolem:lemma5705 a r:Inference; r:gives { - (5 4 2 1) :digitsToNumber 5421 . + (5 4 3 1) :digitsToNumber 5431 . }; r:evidence ( [ a r:Fact; r:gives {(5 1000) math:product 5000}] [ a r:Fact; r:gives {(4 100) math:product 400}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(5000 400 20 1) math:sum 5421}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(5000 400 30 1) math:sum 5431}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5431]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2309 a r:Inference; +skolem:lemma5706 a r:Inference; r:gives { - 2146 :numberToDigits (2 1 4 6). + 3146 :numberToDigits (3 1 4 6). }; r:evidence ( - [ a r:Fact; r:gives {(2146 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2146 1000) math:remainder 146}] + [ a r:Fact; r:gives {(3146 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3146 1000) math:remainder 146}] [ a r:Fact; r:gives {(146 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(146 100) math:remainder 46}] [ a r:Fact; r:gives {(46 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(46 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2146]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3146]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 146]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 46]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2310 a r:Inference; +skolem:lemma5707 a r:Inference; r:gives { - (1 2 4 6) :digitsToNumber 1246 . + (1 3 4 6) :digitsToNumber 1346 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(1000 200 40 6) math:sum 1246}] + [ a r:Fact; r:gives {(1000 300 40 6) math:sum 1346}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1346]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2311 a r:Inference; +skolem:lemma5708 a r:Inference; r:gives { - (6 4 2 1) :digitsToNumber 6421 . + (6 4 3 1) :digitsToNumber 6431 . }; r:evidence ( [ a r:Fact; r:gives {(6 1000) math:product 6000}] [ a r:Fact; r:gives {(4 100) math:product 400}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(6000 400 20 1) math:sum 6421}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(6000 400 30 1) math:sum 6431}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6431]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2312 a r:Inference; +skolem:lemma5709 a r:Inference; r:gives { - 2147 :numberToDigits (2 1 4 7). + 3147 :numberToDigits (3 1 4 7). }; r:evidence ( - [ a r:Fact; r:gives {(2147 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2147 1000) math:remainder 147}] + [ a r:Fact; r:gives {(3147 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3147 1000) math:remainder 147}] [ a r:Fact; r:gives {(147 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(147 100) math:remainder 47}] [ a r:Fact; r:gives {(47 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(47 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2147]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3147]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 147]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 47]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2313 a r:Inference; +skolem:lemma5710 a r:Inference; r:gives { - (1 2 4 7) :digitsToNumber 1247 . + (1 3 4 7) :digitsToNumber 1347 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(1000 200 40 7) math:sum 1247}] + [ a r:Fact; r:gives {(1000 300 40 7) math:sum 1347}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1347]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2314 a r:Inference; +skolem:lemma5711 a r:Inference; r:gives { - (7 4 2 1) :digitsToNumber 7421 . + (7 4 3 1) :digitsToNumber 7431 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(4 100) math:product 400}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(7000 400 20 1) math:sum 7421}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(7000 400 30 1) math:sum 7431}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7431]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2315 a r:Inference; +skolem:lemma5712 a r:Inference; r:gives { - 2148 :numberToDigits (2 1 4 8). + 3148 :numberToDigits (3 1 4 8). }; r:evidence ( - [ a r:Fact; r:gives {(2148 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2148 1000) math:remainder 148}] + [ a r:Fact; r:gives {(3148 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3148 1000) math:remainder 148}] [ a r:Fact; r:gives {(148 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(148 100) math:remainder 48}] [ a r:Fact; r:gives {(48 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(48 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2148]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3148]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 148]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 48]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2316 a r:Inference; +skolem:lemma5713 a r:Inference; r:gives { - (1 2 4 8) :digitsToNumber 1248 . + (1 3 4 8) :digitsToNumber 1348 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(1000 200 40 8) math:sum 1248}] + [ a r:Fact; r:gives {(1000 300 40 8) math:sum 1348}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1348]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2317 a r:Inference; +skolem:lemma5714 a r:Inference; r:gives { - (8 4 2 1) :digitsToNumber 8421 . + (8 4 3 1) :digitsToNumber 8431 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(4 100) math:product 400}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(8000 400 20 1) math:sum 8421}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(8000 400 30 1) math:sum 8431}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8431]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2318 a r:Inference; +skolem:lemma5715 a r:Inference; r:gives { - 2149 :numberToDigits (2 1 4 9). + 3149 :numberToDigits (3 1 4 9). }; r:evidence ( - [ a r:Fact; r:gives {(2149 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2149 1000) math:remainder 149}] + [ a r:Fact; r:gives {(3149 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3149 1000) math:remainder 149}] [ a r:Fact; r:gives {(149 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(149 100) math:remainder 49}] [ a r:Fact; r:gives {(49 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(49 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2149]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3149]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 149]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 49]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2319 a r:Inference; +skolem:lemma5716 a r:Inference; r:gives { - (1 2 4 9) :digitsToNumber 1249 . + (1 3 4 9) :digitsToNumber 1349 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(1000 200 40 9) math:sum 1249}] + [ a r:Fact; r:gives {(1000 300 40 9) math:sum 1349}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1349]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2320 a r:Inference; +skolem:lemma5717 a r:Inference; r:gives { - (9 4 2 1) :digitsToNumber 9421 . + (9 4 3 1) :digitsToNumber 9431 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(4 100) math:product 400}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 400 20 1) math:sum 9421}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(9000 400 30 1) math:sum 9431}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9431]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2321 a r:Inference; +skolem:lemma5718 a r:Inference; r:gives { - 2150 :numberToDigits (2 1 5 0). + 3150 :numberToDigits (3 1 5 0). }; r:evidence ( - [ a r:Fact; r:gives {(2150 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2150 1000) math:remainder 150}] + [ a r:Fact; r:gives {(3150 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3150 1000) math:remainder 150}] [ a r:Fact; r:gives {(150 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(150 100) math:remainder 50}] [ a r:Fact; r:gives {(50 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(50 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2150]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3150]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 150]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2322 a r:Inference; +skolem:lemma5719 a r:Inference; r:gives { - 2151 :numberToDigits (2 1 5 1). + 3151 :numberToDigits (3 1 5 1). }; r:evidence ( - [ a r:Fact; r:gives {(2151 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2151 1000) math:remainder 151}] + [ a r:Fact; r:gives {(3151 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3151 1000) math:remainder 151}] [ a r:Fact; r:gives {(151 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(151 100) math:remainder 51}] [ a r:Fact; r:gives {(51 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(51 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2151]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3151]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 151]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 51]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2323 a r:Inference; +skolem:lemma5720 a r:Inference; r:gives { - 2152 :numberToDigits (2 1 5 2). + 3152 :numberToDigits (3 1 5 2). }; - r:evidence ( - [ a r:Fact; r:gives {(2152 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2152 1000) math:remainder 152}] + r:evidence ( + [ a r:Fact; r:gives {(3152 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3152 1000) math:remainder 152}] [ a r:Fact; r:gives {(152 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(152 100) math:remainder 52}] [ a r:Fact; r:gives {(52 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(52 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2152]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3152]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 152]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 52]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2324 a r:Inference; +skolem:lemma5721 a r:Inference; r:gives { - 2153 :numberToDigits (2 1 5 3). + 3153 :numberToDigits (3 1 5 3). }; r:evidence ( - [ a r:Fact; r:gives {(2153 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2153 1000) math:remainder 153}] + [ a r:Fact; r:gives {(3153 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3153 1000) math:remainder 153}] [ a r:Fact; r:gives {(153 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(153 100) math:remainder 53}] [ a r:Fact; r:gives {(53 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(53 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2153]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3153]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 153]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 53]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2325 a r:Inference; +skolem:lemma5722 a r:Inference; r:gives { - 2154 :numberToDigits (2 1 5 4). + 3154 :numberToDigits (3 1 5 4). }; r:evidence ( - [ a r:Fact; r:gives {(2154 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2154 1000) math:remainder 154}] + [ a r:Fact; r:gives {(3154 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3154 1000) math:remainder 154}] [ a r:Fact; r:gives {(154 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(154 100) math:remainder 54}] [ a r:Fact; r:gives {(54 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(54 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2154]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3154]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 154]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 54]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2326 a r:Inference; +skolem:lemma5723 a r:Inference; r:gives { - 2155 :numberToDigits (2 1 5 5). + 3155 :numberToDigits (3 1 5 5). }; r:evidence ( - [ a r:Fact; r:gives {(2155 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2155 1000) math:remainder 155}] + [ a r:Fact; r:gives {(3155 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3155 1000) math:remainder 155}] [ a r:Fact; r:gives {(155 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(155 100) math:remainder 55}] [ a r:Fact; r:gives {(55 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(55 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2155]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3155]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 155]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 55]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2327 a r:Inference; +skolem:lemma5724 a r:Inference; r:gives { - (1 2 5 5) :digitsToNumber 1255 . + (1 3 5 5) :digitsToNumber 1355 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(1000 200 50 5) math:sum 1255}] + [ a r:Fact; r:gives {(1000 300 50 5) math:sum 1355}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1355]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2328 a r:Inference; +skolem:lemma5725 a r:Inference; r:gives { - (5 5 2 1) :digitsToNumber 5521 . + (5 5 3 1) :digitsToNumber 5531 . }; r:evidence ( [ a r:Fact; r:gives {(5 1000) math:product 5000}] [ a r:Fact; r:gives {(5 100) math:product 500}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(5000 500 20 1) math:sum 5521}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(5000 500 30 1) math:sum 5531}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5531]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2329 a r:Inference; +skolem:lemma5726 a r:Inference; r:gives { - 2156 :numberToDigits (2 1 5 6). + 3156 :numberToDigits (3 1 5 6). }; r:evidence ( - [ a r:Fact; r:gives {(2156 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2156 1000) math:remainder 156}] + [ a r:Fact; r:gives {(3156 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3156 1000) math:remainder 156}] [ a r:Fact; r:gives {(156 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(156 100) math:remainder 56}] [ a r:Fact; r:gives {(56 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(56 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2156]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3156]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 156]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 56]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2330 a r:Inference; +skolem:lemma5727 a r:Inference; r:gives { - (1 2 5 6) :digitsToNumber 1256 . + (1 3 5 6) :digitsToNumber 1356 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(1000 200 50 6) math:sum 1256}] + [ a r:Fact; r:gives {(1000 300 50 6) math:sum 1356}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1356]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2331 a r:Inference; +skolem:lemma5728 a r:Inference; r:gives { - (6 5 2 1) :digitsToNumber 6521 . + (6 5 3 1) :digitsToNumber 6531 . }; r:evidence ( [ a r:Fact; r:gives {(6 1000) math:product 6000}] [ a r:Fact; r:gives {(5 100) math:product 500}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(6000 500 20 1) math:sum 6521}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(6000 500 30 1) math:sum 6531}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6531]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2332 a r:Inference; +skolem:lemma5729 a r:Inference; r:gives { - 2157 :numberToDigits (2 1 5 7). + 3157 :numberToDigits (3 1 5 7). }; r:evidence ( - [ a r:Fact; r:gives {(2157 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2157 1000) math:remainder 157}] + [ a r:Fact; r:gives {(3157 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3157 1000) math:remainder 157}] [ a r:Fact; r:gives {(157 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(157 100) math:remainder 57}] [ a r:Fact; r:gives {(57 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(57 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2157]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3157]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 157]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 57]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2333 a r:Inference; +skolem:lemma5730 a r:Inference; r:gives { - (1 2 5 7) :digitsToNumber 1257 . + (1 3 5 7) :digitsToNumber 1357 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(1000 200 50 7) math:sum 1257}] + [ a r:Fact; r:gives {(1000 300 50 7) math:sum 1357}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1357]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2334 a r:Inference; +skolem:lemma5731 a r:Inference; r:gives { - (7 5 2 1) :digitsToNumber 7521 . + (7 5 3 1) :digitsToNumber 7531 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(5 100) math:product 500}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(7000 500 20 1) math:sum 7521}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(7000 500 30 1) math:sum 7531}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7531]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2335 a r:Inference; +skolem:lemma5732 a r:Inference; r:gives { - 2158 :numberToDigits (2 1 5 8). + 3158 :numberToDigits (3 1 5 8). }; r:evidence ( - [ a r:Fact; r:gives {(2158 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2158 1000) math:remainder 158}] + [ a r:Fact; r:gives {(3158 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3158 1000) math:remainder 158}] [ a r:Fact; r:gives {(158 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(158 100) math:remainder 58}] [ a r:Fact; r:gives {(58 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(58 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2158]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3158]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 158]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 58]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2336 a r:Inference; +skolem:lemma5733 a r:Inference; r:gives { - (1 2 5 8) :digitsToNumber 1258 . + (1 3 5 8) :digitsToNumber 1358 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(1000 200 50 8) math:sum 1258}] + [ a r:Fact; r:gives {(1000 300 50 8) math:sum 1358}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1358]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2337 a r:Inference; +skolem:lemma5734 a r:Inference; r:gives { - (8 5 2 1) :digitsToNumber 8521 . + (8 5 3 1) :digitsToNumber 8531 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(5 100) math:product 500}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(8000 500 20 1) math:sum 8521}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(8000 500 30 1) math:sum 8531}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8531]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2338 a r:Inference; +skolem:lemma5735 a r:Inference; r:gives { - 2159 :numberToDigits (2 1 5 9). + 3159 :numberToDigits (3 1 5 9). }; r:evidence ( - [ a r:Fact; r:gives {(2159 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2159 1000) math:remainder 159}] + [ a r:Fact; r:gives {(3159 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3159 1000) math:remainder 159}] [ a r:Fact; r:gives {(159 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(159 100) math:remainder 59}] [ a r:Fact; r:gives {(59 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(59 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2159]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3159]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 159]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 59]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2339 a r:Inference; +skolem:lemma5736 a r:Inference; r:gives { - (1 2 5 9) :digitsToNumber 1259 . + (1 3 5 9) :digitsToNumber 1359 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(1000 200 50 9) math:sum 1259}] + [ a r:Fact; r:gives {(1000 300 50 9) math:sum 1359}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1359]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2340 a r:Inference; +skolem:lemma5737 a r:Inference; r:gives { - (9 5 2 1) :digitsToNumber 9521 . + (9 5 3 1) :digitsToNumber 9531 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(5 100) math:product 500}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 500 20 1) math:sum 9521}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(9000 500 30 1) math:sum 9531}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9531]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2341 a r:Inference; +skolem:lemma5738 a r:Inference; r:gives { - 2160 :numberToDigits (2 1 6 0). + 3160 :numberToDigits (3 1 6 0). }; r:evidence ( - [ a r:Fact; r:gives {(2160 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2160 1000) math:remainder 160}] + [ a r:Fact; r:gives {(3160 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3160 1000) math:remainder 160}] [ a r:Fact; r:gives {(160 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(160 100) math:remainder 60}] [ a r:Fact; r:gives {(60 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(60 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2160]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3160]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 160]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2342 a r:Inference; +skolem:lemma5739 a r:Inference; r:gives { - 2161 :numberToDigits (2 1 6 1). + 3161 :numberToDigits (3 1 6 1). }; r:evidence ( - [ a r:Fact; r:gives {(2161 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2161 1000) math:remainder 161}] + [ a r:Fact; r:gives {(3161 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3161 1000) math:remainder 161}] [ a r:Fact; r:gives {(161 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(161 100) math:remainder 61}] [ a r:Fact; r:gives {(61 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(61 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2161]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3161]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 161]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 61]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2343 a r:Inference; +skolem:lemma5740 a r:Inference; r:gives { - 2162 :numberToDigits (2 1 6 2). + 3162 :numberToDigits (3 1 6 2). }; r:evidence ( - [ a r:Fact; r:gives {(2162 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2162 1000) math:remainder 162}] + [ a r:Fact; r:gives {(3162 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3162 1000) math:remainder 162}] [ a r:Fact; r:gives {(162 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(162 100) math:remainder 62}] [ a r:Fact; r:gives {(62 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(62 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2162]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3162]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 162]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 62]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2344 a r:Inference; +skolem:lemma5741 a r:Inference; r:gives { - 2163 :numberToDigits (2 1 6 3). + 3163 :numberToDigits (3 1 6 3). }; r:evidence ( - [ a r:Fact; r:gives {(2163 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2163 1000) math:remainder 163}] + [ a r:Fact; r:gives {(3163 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3163 1000) math:remainder 163}] [ a r:Fact; r:gives {(163 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(163 100) math:remainder 63}] [ a r:Fact; r:gives {(63 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(63 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2163]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3163]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 163]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 63]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2345 a r:Inference; +skolem:lemma5742 a r:Inference; r:gives { - 2164 :numberToDigits (2 1 6 4). + 3164 :numberToDigits (3 1 6 4). }; r:evidence ( - [ a r:Fact; r:gives {(2164 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2164 1000) math:remainder 164}] + [ a r:Fact; r:gives {(3164 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3164 1000) math:remainder 164}] [ a r:Fact; r:gives {(164 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(164 100) math:remainder 64}] [ a r:Fact; r:gives {(64 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(64 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2164]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3164]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 164]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 64]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2346 a r:Inference; +skolem:lemma5743 a r:Inference; r:gives { - 2165 :numberToDigits (2 1 6 5). + 3165 :numberToDigits (3 1 6 5). }; r:evidence ( - [ a r:Fact; r:gives {(2165 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2165 1000) math:remainder 165}] + [ a r:Fact; r:gives {(3165 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3165 1000) math:remainder 165}] [ a r:Fact; r:gives {(165 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(165 100) math:remainder 65}] [ a r:Fact; r:gives {(65 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(65 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2165]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3165]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 165]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 65]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2347 a r:Inference; +skolem:lemma5744 a r:Inference; r:gives { - 2166 :numberToDigits (2 1 6 6). + 3166 :numberToDigits (3 1 6 6). }; r:evidence ( - [ a r:Fact; r:gives {(2166 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2166 1000) math:remainder 166}] + [ a r:Fact; r:gives {(3166 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3166 1000) math:remainder 166}] [ a r:Fact; r:gives {(166 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(166 100) math:remainder 66}] [ a r:Fact; r:gives {(66 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(66 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2166]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3166]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 166]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 66]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2348 a r:Inference; +skolem:lemma5745 a r:Inference; r:gives { - (1 2 6 6) :digitsToNumber 1266 . + (1 3 6 6) :digitsToNumber 1366 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(1000 200 60 6) math:sum 1266}] + [ a r:Fact; r:gives {(1000 300 60 6) math:sum 1366}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1366]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2349 a r:Inference; +skolem:lemma5746 a r:Inference; r:gives { - (6 6 2 1) :digitsToNumber 6621 . + (6 6 3 1) :digitsToNumber 6631 . }; r:evidence ( [ a r:Fact; r:gives {(6 1000) math:product 6000}] [ a r:Fact; r:gives {(6 100) math:product 600}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(6000 600 20 1) math:sum 6621}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(6000 600 30 1) math:sum 6631}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6631]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2350 a r:Inference; +skolem:lemma5747 a r:Inference; r:gives { - 2167 :numberToDigits (2 1 6 7). + 3167 :numberToDigits (3 1 6 7). }; r:evidence ( - [ a r:Fact; r:gives {(2167 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2167 1000) math:remainder 167}] + [ a r:Fact; r:gives {(3167 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3167 1000) math:remainder 167}] [ a r:Fact; r:gives {(167 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(167 100) math:remainder 67}] [ a r:Fact; r:gives {(67 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(67 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2167]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3167]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 167]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 67]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2351 a r:Inference; +skolem:lemma5748 a r:Inference; r:gives { - (1 2 6 7) :digitsToNumber 1267 . + (1 3 6 7) :digitsToNumber 1367 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(1000 200 60 7) math:sum 1267}] + [ a r:Fact; r:gives {(1000 300 60 7) math:sum 1367}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1367]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2352 a r:Inference; +skolem:lemma5749 a r:Inference; r:gives { - (7 6 2 1) :digitsToNumber 7621 . + (7 6 3 1) :digitsToNumber 7631 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(6 100) math:product 600}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(7000 600 20 1) math:sum 7621}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(7000 600 30 1) math:sum 7631}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7631]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2353 a r:Inference; +skolem:lemma5750 a r:Inference; r:gives { - 2168 :numberToDigits (2 1 6 8). + 3168 :numberToDigits (3 1 6 8). }; r:evidence ( - [ a r:Fact; r:gives {(2168 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2168 1000) math:remainder 168}] + [ a r:Fact; r:gives {(3168 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3168 1000) math:remainder 168}] [ a r:Fact; r:gives {(168 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(168 100) math:remainder 68}] [ a r:Fact; r:gives {(68 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(68 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2168]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3168]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 168]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 68]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2354 a r:Inference; +skolem:lemma5751 a r:Inference; r:gives { - (1 2 6 8) :digitsToNumber 1268 . + (1 3 6 8) :digitsToNumber 1368 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(1000 200 60 8) math:sum 1268}] + [ a r:Fact; r:gives {(1000 300 60 8) math:sum 1368}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1368]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2355 a r:Inference; +skolem:lemma5752 a r:Inference; r:gives { - (8 6 2 1) :digitsToNumber 8621 . + (8 6 3 1) :digitsToNumber 8631 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(6 100) math:product 600}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(8000 600 20 1) math:sum 8621}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(8000 600 30 1) math:sum 8631}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8631]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2356 a r:Inference; +skolem:lemma5753 a r:Inference; r:gives { - 2169 :numberToDigits (2 1 6 9). + 3169 :numberToDigits (3 1 6 9). }; r:evidence ( - [ a r:Fact; r:gives {(2169 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2169 1000) math:remainder 169}] + [ a r:Fact; r:gives {(3169 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3169 1000) math:remainder 169}] [ a r:Fact; r:gives {(169 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(169 100) math:remainder 69}] [ a r:Fact; r:gives {(69 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(69 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2169]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3169]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 169]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 69]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2357 a r:Inference; +skolem:lemma5754 a r:Inference; r:gives { - (1 2 6 9) :digitsToNumber 1269 . + (1 3 6 9) :digitsToNumber 1369 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(1000 200 60 9) math:sum 1269}] + [ a r:Fact; r:gives {(1000 300 60 9) math:sum 1369}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1369]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2358 a r:Inference; +skolem:lemma5755 a r:Inference; r:gives { - (9 6 2 1) :digitsToNumber 9621 . + (9 6 3 1) :digitsToNumber 9631 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(6 100) math:product 600}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 600 20 1) math:sum 9621}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(9000 600 30 1) math:sum 9631}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9631]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2359 a r:Inference; +skolem:lemma5756 a r:Inference; r:gives { - 2170 :numberToDigits (2 1 7 0). + 3170 :numberToDigits (3 1 7 0). }; r:evidence ( - [ a r:Fact; r:gives {(2170 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2170 1000) math:remainder 170}] + [ a r:Fact; r:gives {(3170 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3170 1000) math:remainder 170}] [ a r:Fact; r:gives {(170 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(170 100) math:remainder 70}] [ a r:Fact; r:gives {(70 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(70 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2170]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3170]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 170]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2360 a r:Inference; +skolem:lemma5757 a r:Inference; r:gives { - 2171 :numberToDigits (2 1 7 1). + 3171 :numberToDigits (3 1 7 1). }; r:evidence ( - [ a r:Fact; r:gives {(2171 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2171 1000) math:remainder 171}] + [ a r:Fact; r:gives {(3171 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3171 1000) math:remainder 171}] [ a r:Fact; r:gives {(171 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(171 100) math:remainder 71}] [ a r:Fact; r:gives {(71 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(71 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2171]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3171]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 171]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 71]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2361 a r:Inference; +skolem:lemma5758 a r:Inference; r:gives { - 2172 :numberToDigits (2 1 7 2). + 3172 :numberToDigits (3 1 7 2). }; r:evidence ( - [ a r:Fact; r:gives {(2172 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2172 1000) math:remainder 172}] + [ a r:Fact; r:gives {(3172 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3172 1000) math:remainder 172}] [ a r:Fact; r:gives {(172 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(172 100) math:remainder 72}] [ a r:Fact; r:gives {(72 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(72 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2172]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3172]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 172]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 72]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2362 a r:Inference; +skolem:lemma5759 a r:Inference; r:gives { - 2173 :numberToDigits (2 1 7 3). + 3173 :numberToDigits (3 1 7 3). }; r:evidence ( - [ a r:Fact; r:gives {(2173 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2173 1000) math:remainder 173}] + [ a r:Fact; r:gives {(3173 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3173 1000) math:remainder 173}] [ a r:Fact; r:gives {(173 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(173 100) math:remainder 73}] [ a r:Fact; r:gives {(73 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(73 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2173]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3173]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 173]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 73]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2363 a r:Inference; +skolem:lemma5760 a r:Inference; r:gives { - 2174 :numberToDigits (2 1 7 4). + 3174 :numberToDigits (3 1 7 4). }; r:evidence ( - [ a r:Fact; r:gives {(2174 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2174 1000) math:remainder 174}] + [ a r:Fact; r:gives {(3174 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3174 1000) math:remainder 174}] [ a r:Fact; r:gives {(174 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(174 100) math:remainder 74}] [ a r:Fact; r:gives {(74 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(74 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2174]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3174]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 174]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 74]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2364 a r:Inference; +skolem:lemma5761 a r:Inference; r:gives { - 2175 :numberToDigits (2 1 7 5). + 3175 :numberToDigits (3 1 7 5). }; r:evidence ( - [ a r:Fact; r:gives {(2175 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2175 1000) math:remainder 175}] + [ a r:Fact; r:gives {(3175 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3175 1000) math:remainder 175}] [ a r:Fact; r:gives {(175 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(175 100) math:remainder 75}] [ a r:Fact; r:gives {(75 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(75 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2175]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3175]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 175]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 75]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2365 a r:Inference; +skolem:lemma5762 a r:Inference; r:gives { - 2176 :numberToDigits (2 1 7 6). + 3176 :numberToDigits (3 1 7 6). }; r:evidence ( - [ a r:Fact; r:gives {(2176 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2176 1000) math:remainder 176}] + [ a r:Fact; r:gives {(3176 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3176 1000) math:remainder 176}] [ a r:Fact; r:gives {(176 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(176 100) math:remainder 76}] [ a r:Fact; r:gives {(76 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(76 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2176]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3176]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 176]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 76]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2366 a r:Inference; +skolem:lemma5763 a r:Inference; r:gives { - 2177 :numberToDigits (2 1 7 7). + 3177 :numberToDigits (3 1 7 7). }; r:evidence ( - [ a r:Fact; r:gives {(2177 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2177 1000) math:remainder 177}] + [ a r:Fact; r:gives {(3177 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3177 1000) math:remainder 177}] [ a r:Fact; r:gives {(177 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(177 100) math:remainder 77}] [ a r:Fact; r:gives {(77 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(77 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2177]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3177]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 177]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 77]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2367 a r:Inference; +skolem:lemma5764 a r:Inference; r:gives { - (1 2 7 7) :digitsToNumber 1277 . + (1 3 7 7) :digitsToNumber 1377 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(1000 200 70 7) math:sum 1277}] + [ a r:Fact; r:gives {(1000 300 70 7) math:sum 1377}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1277]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1377]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2368 a r:Inference; +skolem:lemma5765 a r:Inference; r:gives { - (7 7 2 1) :digitsToNumber 7721 . + (7 7 3 1) :digitsToNumber 7731 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(7 100) math:product 700}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(7000 700 20 1) math:sum 7721}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(7000 700 30 1) math:sum 7731}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7731]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2369 a r:Inference; +skolem:lemma5766 a r:Inference; r:gives { - 2178 :numberToDigits (2 1 7 8). + 3178 :numberToDigits (3 1 7 8). }; r:evidence ( - [ a r:Fact; r:gives {(2178 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2178 1000) math:remainder 178}] + [ a r:Fact; r:gives {(3178 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3178 1000) math:remainder 178}] [ a r:Fact; r:gives {(178 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(178 100) math:remainder 78}] [ a r:Fact; r:gives {(78 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(78 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2178]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3178]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 178]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 78]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2370 a r:Inference; +skolem:lemma5767 a r:Inference; r:gives { - (1 2 7 8) :digitsToNumber 1278 . + (1 3 7 8) :digitsToNumber 1378 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(1000 200 70 8) math:sum 1278}] + [ a r:Fact; r:gives {(1000 300 70 8) math:sum 1378}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1378]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2371 a r:Inference; +skolem:lemma5768 a r:Inference; r:gives { - (8 7 2 1) :digitsToNumber 8721 . + (8 7 3 1) :digitsToNumber 8731 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(7 100) math:product 700}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(8000 700 20 1) math:sum 8721}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(8000 700 30 1) math:sum 8731}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8731]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2372 a r:Inference; +skolem:lemma5769 a r:Inference; r:gives { - 2179 :numberToDigits (2 1 7 9). + 3179 :numberToDigits (3 1 7 9). }; r:evidence ( - [ a r:Fact; r:gives {(2179 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2179 1000) math:remainder 179}] + [ a r:Fact; r:gives {(3179 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3179 1000) math:remainder 179}] [ a r:Fact; r:gives {(179 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(179 100) math:remainder 79}] [ a r:Fact; r:gives {(79 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(79 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2179]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3179]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 179]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 79]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2373 a r:Inference; +skolem:lemma5770 a r:Inference; r:gives { - (1 2 7 9) :digitsToNumber 1279 . + (1 3 7 9) :digitsToNumber 1379 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(1000 200 70 9) math:sum 1279}] + [ a r:Fact; r:gives {(1000 300 70 9) math:sum 1379}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1379]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2374 a r:Inference; +skolem:lemma5771 a r:Inference; r:gives { - (9 7 2 1) :digitsToNumber 9721 . + (9 7 3 1) :digitsToNumber 9731 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(7 100) math:product 700}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 700 20 1) math:sum 9721}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(9000 700 30 1) math:sum 9731}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9731]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2375 a r:Inference; +skolem:lemma5772 a r:Inference; r:gives { - 2180 :numberToDigits (2 1 8 0). + 3180 :numberToDigits (3 1 8 0). }; r:evidence ( - [ a r:Fact; r:gives {(2180 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2180 1000) math:remainder 180}] + [ a r:Fact; r:gives {(3180 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3180 1000) math:remainder 180}] [ a r:Fact; r:gives {(180 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(180 100) math:remainder 80}] [ a r:Fact; r:gives {(80 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(80 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2180]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3180]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 180]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2376 a r:Inference; +skolem:lemma5773 a r:Inference; r:gives { - 2181 :numberToDigits (2 1 8 1). + 3181 :numberToDigits (3 1 8 1). }; r:evidence ( - [ a r:Fact; r:gives {(2181 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2181 1000) math:remainder 181}] + [ a r:Fact; r:gives {(3181 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3181 1000) math:remainder 181}] [ a r:Fact; r:gives {(181 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(181 100) math:remainder 81}] [ a r:Fact; r:gives {(81 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(81 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2181]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3181]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 181]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 81]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2377 a r:Inference; +skolem:lemma5774 a r:Inference; r:gives { - 2182 :numberToDigits (2 1 8 2). + 3182 :numberToDigits (3 1 8 2). }; r:evidence ( - [ a r:Fact; r:gives {(2182 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2182 1000) math:remainder 182}] + [ a r:Fact; r:gives {(3182 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3182 1000) math:remainder 182}] [ a r:Fact; r:gives {(182 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(182 100) math:remainder 82}] [ a r:Fact; r:gives {(82 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(82 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2182]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3182]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 182]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 82]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2378 a r:Inference; +skolem:lemma5775 a r:Inference; r:gives { - 2183 :numberToDigits (2 1 8 3). + 3183 :numberToDigits (3 1 8 3). }; r:evidence ( - [ a r:Fact; r:gives {(2183 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2183 1000) math:remainder 183}] + [ a r:Fact; r:gives {(3183 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3183 1000) math:remainder 183}] [ a r:Fact; r:gives {(183 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(183 100) math:remainder 83}] [ a r:Fact; r:gives {(83 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(83 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2183]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3183]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 183]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 83]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2379 a r:Inference; +skolem:lemma5776 a r:Inference; r:gives { - 2184 :numberToDigits (2 1 8 4). + 3184 :numberToDigits (3 1 8 4). }; r:evidence ( - [ a r:Fact; r:gives {(2184 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2184 1000) math:remainder 184}] + [ a r:Fact; r:gives {(3184 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3184 1000) math:remainder 184}] [ a r:Fact; r:gives {(184 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(184 100) math:remainder 84}] [ a r:Fact; r:gives {(84 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(84 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2184]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3184]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 184]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 84]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2380 a r:Inference; +skolem:lemma5777 a r:Inference; r:gives { - 2185 :numberToDigits (2 1 8 5). + 3185 :numberToDigits (3 1 8 5). }; r:evidence ( - [ a r:Fact; r:gives {(2185 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2185 1000) math:remainder 185}] + [ a r:Fact; r:gives {(3185 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3185 1000) math:remainder 185}] [ a r:Fact; r:gives {(185 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(185 100) math:remainder 85}] [ a r:Fact; r:gives {(85 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(85 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2185]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3185]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 185]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 85]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2381 a r:Inference; +skolem:lemma5778 a r:Inference; r:gives { - 2186 :numberToDigits (2 1 8 6). + 3186 :numberToDigits (3 1 8 6). }; r:evidence ( - [ a r:Fact; r:gives {(2186 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2186 1000) math:remainder 186}] + [ a r:Fact; r:gives {(3186 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3186 1000) math:remainder 186}] [ a r:Fact; r:gives {(186 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(186 100) math:remainder 86}] [ a r:Fact; r:gives {(86 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(86 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2186]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3186]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 186]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 86]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2382 a r:Inference; +skolem:lemma5779 a r:Inference; r:gives { - 2187 :numberToDigits (2 1 8 7). + 3187 :numberToDigits (3 1 8 7). }; r:evidence ( - [ a r:Fact; r:gives {(2187 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2187 1000) math:remainder 187}] + [ a r:Fact; r:gives {(3187 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3187 1000) math:remainder 187}] [ a r:Fact; r:gives {(187 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(187 100) math:remainder 87}] [ a r:Fact; r:gives {(87 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(87 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2187]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3187]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 187]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 87]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2383 a r:Inference; +skolem:lemma5780 a r:Inference; r:gives { - 2188 :numberToDigits (2 1 8 8). + 3188 :numberToDigits (3 1 8 8). }; r:evidence ( - [ a r:Fact; r:gives {(2188 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2188 1000) math:remainder 188}] + [ a r:Fact; r:gives {(3188 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3188 1000) math:remainder 188}] [ a r:Fact; r:gives {(188 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(188 100) math:remainder 88}] [ a r:Fact; r:gives {(88 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(88 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2188]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3188]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 188]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 88]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2384 a r:Inference; +skolem:lemma5781 a r:Inference; r:gives { - (1 2 8 8) :digitsToNumber 1288 . + (1 3 8 8) :digitsToNumber 1388 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(8 10) math:product 80}] - [ a r:Fact; r:gives {(1000 200 80 8) math:sum 1288}] + [ a r:Fact; r:gives {(1000 300 80 8) math:sum 1388}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1288]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1388]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2385 a r:Inference; +skolem:lemma5782 a r:Inference; r:gives { - (8 8 2 1) :digitsToNumber 8821 . + (8 8 3 1) :digitsToNumber 8831 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(8 100) math:product 800}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(8000 800 20 1) math:sum 8821}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(8000 800 30 1) math:sum 8831}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8821]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8831]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2386 a r:Inference; +skolem:lemma5783 a r:Inference; r:gives { - 2189 :numberToDigits (2 1 8 9). + 3189 :numberToDigits (3 1 8 9). }; r:evidence ( - [ a r:Fact; r:gives {(2189 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2189 1000) math:remainder 189}] + [ a r:Fact; r:gives {(3189 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3189 1000) math:remainder 189}] [ a r:Fact; r:gives {(189 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(189 100) math:remainder 89}] [ a r:Fact; r:gives {(89 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(89 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2189]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3189]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 189]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 89]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2387 a r:Inference; +skolem:lemma5784 a r:Inference; r:gives { - (1 2 8 9) :digitsToNumber 1289 . + (1 3 8 9) :digitsToNumber 1389 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(8 10) math:product 80}] - [ a r:Fact; r:gives {(1000 200 80 9) math:sum 1289}] + [ a r:Fact; r:gives {(1000 300 80 9) math:sum 1389}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1389]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2388 a r:Inference; +skolem:lemma5785 a r:Inference; r:gives { - (9 8 2 1) :digitsToNumber 9821 . + (9 8 3 1) :digitsToNumber 9831 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(8 100) math:product 800}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 800 20 1) math:sum 9821}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(9000 800 30 1) math:sum 9831}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9821]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9831]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2389 a r:Inference; +skolem:lemma5786 a r:Inference; r:gives { - 2190 :numberToDigits (2 1 9 0). + 3190 :numberToDigits (3 1 9 0). }; r:evidence ( - [ a r:Fact; r:gives {(2190 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2190 1000) math:remainder 190}] + [ a r:Fact; r:gives {(3190 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3190 1000) math:remainder 190}] [ a r:Fact; r:gives {(190 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(190 100) math:remainder 90}] [ a r:Fact; r:gives {(90 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(90 10) math:remainder 0}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2190]; + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3190]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 190]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 90]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2390 a r:Inference; +skolem:lemma5787 a r:Inference; r:gives { - 2191 :numberToDigits (2 1 9 1). + 3191 :numberToDigits (3 1 9 1). }; r:evidence ( - [ a r:Fact; r:gives {(2191 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2191 1000) math:remainder 191}] + [ a r:Fact; r:gives {(3191 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3191 1000) math:remainder 191}] [ a r:Fact; r:gives {(191 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(191 100) math:remainder 91}] [ a r:Fact; r:gives {(91 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(91 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2191]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3191]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 191]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 91]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2391 a r:Inference; +skolem:lemma5788 a r:Inference; r:gives { - 2192 :numberToDigits (2 1 9 2). + 3192 :numberToDigits (3 1 9 2). }; r:evidence ( - [ a r:Fact; r:gives {(2192 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2192 1000) math:remainder 192}] + [ a r:Fact; r:gives {(3192 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3192 1000) math:remainder 192}] [ a r:Fact; r:gives {(192 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(192 100) math:remainder 92}] [ a r:Fact; r:gives {(92 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(92 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2192]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3192]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 192]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 92]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2392 a r:Inference; +skolem:lemma5789 a r:Inference; r:gives { - 2193 :numberToDigits (2 1 9 3). + 3193 :numberToDigits (3 1 9 3). }; r:evidence ( - [ a r:Fact; r:gives {(2193 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2193 1000) math:remainder 193}] + [ a r:Fact; r:gives {(3193 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3193 1000) math:remainder 193}] [ a r:Fact; r:gives {(193 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(193 100) math:remainder 93}] [ a r:Fact; r:gives {(93 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(93 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2193]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3193]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 193]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 93]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2393 a r:Inference; +skolem:lemma5790 a r:Inference; r:gives { - 2194 :numberToDigits (2 1 9 4). + 3194 :numberToDigits (3 1 9 4). }; r:evidence ( - [ a r:Fact; r:gives {(2194 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2194 1000) math:remainder 194}] + [ a r:Fact; r:gives {(3194 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3194 1000) math:remainder 194}] [ a r:Fact; r:gives {(194 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(194 100) math:remainder 94}] [ a r:Fact; r:gives {(94 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(94 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2194]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3194]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 194]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 94]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2394 a r:Inference; +skolem:lemma5791 a r:Inference; r:gives { - 2195 :numberToDigits (2 1 9 5). + 3195 :numberToDigits (3 1 9 5). }; r:evidence ( - [ a r:Fact; r:gives {(2195 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2195 1000) math:remainder 195}] + [ a r:Fact; r:gives {(3195 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3195 1000) math:remainder 195}] [ a r:Fact; r:gives {(195 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(195 100) math:remainder 95}] [ a r:Fact; r:gives {(95 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(95 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2195]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3195]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 195]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 95]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2395 a r:Inference; +skolem:lemma5792 a r:Inference; r:gives { - 2196 :numberToDigits (2 1 9 6). + 3196 :numberToDigits (3 1 9 6). }; r:evidence ( - [ a r:Fact; r:gives {(2196 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2196 1000) math:remainder 196}] + [ a r:Fact; r:gives {(3196 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3196 1000) math:remainder 196}] [ a r:Fact; r:gives {(196 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(196 100) math:remainder 96}] [ a r:Fact; r:gives {(96 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(96 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2196]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3196]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 196]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 96]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2396 a r:Inference; +skolem:lemma5793 a r:Inference; r:gives { - 2197 :numberToDigits (2 1 9 7). + 3197 :numberToDigits (3 1 9 7). }; r:evidence ( - [ a r:Fact; r:gives {(2197 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2197 1000) math:remainder 197}] + [ a r:Fact; r:gives {(3197 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3197 1000) math:remainder 197}] [ a r:Fact; r:gives {(197 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(197 100) math:remainder 97}] [ a r:Fact; r:gives {(97 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(97 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2197]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3197]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 197]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 97]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2397 a r:Inference; +skolem:lemma5794 a r:Inference; r:gives { - 2198 :numberToDigits (2 1 9 8). + 3198 :numberToDigits (3 1 9 8). }; r:evidence ( - [ a r:Fact; r:gives {(2198 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2198 1000) math:remainder 198}] + [ a r:Fact; r:gives {(3198 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3198 1000) math:remainder 198}] [ a r:Fact; r:gives {(198 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(198 100) math:remainder 98}] [ a r:Fact; r:gives {(98 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(98 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2198]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3198]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 198]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 98]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2398 a r:Inference; +skolem:lemma5795 a r:Inference; r:gives { - 2199 :numberToDigits (2 1 9 9). + 3199 :numberToDigits (3 1 9 9). }; r:evidence ( - [ a r:Fact; r:gives {(2199 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2199 1000) math:remainder 199}] + [ a r:Fact; r:gives {(3199 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3199 1000) math:remainder 199}] [ a r:Fact; r:gives {(199 100) math:integerQuotient 1}] [ a r:Fact; r:gives {(199 100) math:remainder 99}] [ a r:Fact; r:gives {(99 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(99 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2199]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3199]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 199]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 99]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2399 a r:Inference; +skolem:lemma5796 a r:Inference; r:gives { - (1 2 9 9) :digitsToNumber 1299 . + (1 3 9 9) :digitsToNumber 1399 . }; r:evidence ( [ a r:Fact; r:gives {(1 1000) math:product 1000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] + [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(9 10) math:product 90}] - [ a r:Fact; r:gives {(1000 200 90 9) math:sum 1299}] + [ a r:Fact; r:gives {(1000 300 90 9) math:sum 1399}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 1000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 1]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 90]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 1399]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2400 a r:Inference; +skolem:lemma5797 a r:Inference; r:gives { - (9 9 2 1) :digitsToNumber 9921 . + (9 9 3 1) :digitsToNumber 9931 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(9 100) math:product 900}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 900 20 1) math:sum 9921}] + [ a r:Fact; r:gives {(3 10) math:product 30}] + [ a r:Fact; r:gives {(9000 900 30 1) math:sum 9931}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 900]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9921]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9931]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2401 a r:Inference; +skolem:lemma5798 a r:Inference; r:gives { - 2200 :numberToDigits (2 2 0 0). + 3200 :numberToDigits (3 2 0 0). }; r:evidence ( - [ a r:Fact; r:gives {(2200 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2200 1000) math:remainder 200}] + [ a r:Fact; r:gives {(3200 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3200 1000) math:remainder 200}] [ a r:Fact; r:gives {(200 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(200 100) math:remainder 0}] [ a r:Fact; r:gives {(0 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(0 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2200]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3200]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 200]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2402 a r:Inference; +skolem:lemma5799 a r:Inference; r:gives { - 2201 :numberToDigits (2 2 0 1). + 3201 :numberToDigits (3 2 0 1). }; r:evidence ( - [ a r:Fact; r:gives {(2201 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2201 1000) math:remainder 201}] + [ a r:Fact; r:gives {(3201 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3201 1000) math:remainder 201}] [ a r:Fact; r:gives {(201 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(201 100) math:remainder 1}] [ a r:Fact; r:gives {(1 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(1 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2201]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3201]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 201]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2403 a r:Inference; +skolem:lemma5800 a r:Inference; r:gives { - 2202 :numberToDigits (2 2 0 2). + 3202 :numberToDigits (3 2 0 2). }; r:evidence ( - [ a r:Fact; r:gives {(2202 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2202 1000) math:remainder 202}] + [ a r:Fact; r:gives {(3202 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3202 1000) math:remainder 202}] [ a r:Fact; r:gives {(202 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(202 100) math:remainder 2}] [ a r:Fact; r:gives {(2 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(2 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2202]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3202]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 202]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2404 a r:Inference; +skolem:lemma5801 a r:Inference; r:gives { - 2203 :numberToDigits (2 2 0 3). + 3203 :numberToDigits (3 2 0 3). }; r:evidence ( - [ a r:Fact; r:gives {(2203 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2203 1000) math:remainder 203}] + [ a r:Fact; r:gives {(3203 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3203 1000) math:remainder 203}] [ a r:Fact; r:gives {(203 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(203 100) math:remainder 3}] [ a r:Fact; r:gives {(3 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(3 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2203]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3203]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 203]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2405 a r:Inference; +skolem:lemma5802 a r:Inference; r:gives { - 2204 :numberToDigits (2 2 0 4). + 3204 :numberToDigits (3 2 0 4). }; r:evidence ( - [ a r:Fact; r:gives {(2204 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2204 1000) math:remainder 204}] + [ a r:Fact; r:gives {(3204 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3204 1000) math:remainder 204}] [ a r:Fact; r:gives {(204 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(204 100) math:remainder 4}] [ a r:Fact; r:gives {(4 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(4 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2204]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3204]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 204]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2406 a r:Inference; +skolem:lemma5803 a r:Inference; r:gives { - 2205 :numberToDigits (2 2 0 5). + 3205 :numberToDigits (3 2 0 5). }; r:evidence ( - [ a r:Fact; r:gives {(2205 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2205 1000) math:remainder 205}] + [ a r:Fact; r:gives {(3205 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3205 1000) math:remainder 205}] [ a r:Fact; r:gives {(205 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(205 100) math:remainder 5}] [ a r:Fact; r:gives {(5 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(5 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2205]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3205]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 205]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2407 a r:Inference; +skolem:lemma5804 a r:Inference; r:gives { - 2206 :numberToDigits (2 2 0 6). + 3206 :numberToDigits (3 2 0 6). }; r:evidence ( - [ a r:Fact; r:gives {(2206 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2206 1000) math:remainder 206}] + [ a r:Fact; r:gives {(3206 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3206 1000) math:remainder 206}] [ a r:Fact; r:gives {(206 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(206 100) math:remainder 6}] [ a r:Fact; r:gives {(6 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(6 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2206]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3206]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 206]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2408 a r:Inference; +skolem:lemma5805 a r:Inference; r:gives { - 2207 :numberToDigits (2 2 0 7). + 3207 :numberToDigits (3 2 0 7). }; r:evidence ( - [ a r:Fact; r:gives {(2207 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2207 1000) math:remainder 207}] + [ a r:Fact; r:gives {(3207 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3207 1000) math:remainder 207}] [ a r:Fact; r:gives {(207 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(207 100) math:remainder 7}] [ a r:Fact; r:gives {(7 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(7 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2207]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3207]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 207]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2409 a r:Inference; +skolem:lemma5806 a r:Inference; r:gives { - 2208 :numberToDigits (2 2 0 8). + 3208 :numberToDigits (3 2 0 8). }; r:evidence ( - [ a r:Fact; r:gives {(2208 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2208 1000) math:remainder 208}] + [ a r:Fact; r:gives {(3208 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3208 1000) math:remainder 208}] [ a r:Fact; r:gives {(208 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(208 100) math:remainder 8}] [ a r:Fact; r:gives {(8 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(8 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2208]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3208]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 208]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2410 a r:Inference; +skolem:lemma5807 a r:Inference; r:gives { - 2209 :numberToDigits (2 2 0 9). + 3209 :numberToDigits (3 2 0 9). }; r:evidence ( - [ a r:Fact; r:gives {(2209 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2209 1000) math:remainder 209}] + [ a r:Fact; r:gives {(3209 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3209 1000) math:remainder 209}] [ a r:Fact; r:gives {(209 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(209 100) math:remainder 9}] [ a r:Fact; r:gives {(9 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(9 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2209]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3209]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 209]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2411 a r:Inference; +skolem:lemma5808 a r:Inference; r:gives { - 2210 :numberToDigits (2 2 1 0). + 3210 :numberToDigits (3 2 1 0). }; r:evidence ( - [ a r:Fact; r:gives {(2210 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2210 1000) math:remainder 210}] + [ a r:Fact; r:gives {(3210 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3210 1000) math:remainder 210}] [ a r:Fact; r:gives {(210 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(210 100) math:remainder 10}] [ a r:Fact; r:gives {(10 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(10 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2210]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3210]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 210]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2412 a r:Inference; +skolem:lemma5809 a r:Inference; r:gives { - 2211 :numberToDigits (2 2 1 1). + 3211 :numberToDigits (3 2 1 1). }; r:evidence ( - [ a r:Fact; r:gives {(2211 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2211 1000) math:remainder 211}] + [ a r:Fact; r:gives {(3211 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3211 1000) math:remainder 211}] [ a r:Fact; r:gives {(211 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(211 100) math:remainder 11}] [ a r:Fact; r:gives {(11 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(11 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2211]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3211]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 211]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 11]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2413 a r:Inference; +skolem:lemma5810 a r:Inference; r:gives { - 2212 :numberToDigits (2 2 1 2). + 3212 :numberToDigits (3 2 1 2). }; r:evidence ( - [ a r:Fact; r:gives {(2212 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2212 1000) math:remainder 212}] + [ a r:Fact; r:gives {(3212 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3212 1000) math:remainder 212}] [ a r:Fact; r:gives {(212 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(212 100) math:remainder 12}] [ a r:Fact; r:gives {(12 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(12 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2212]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3212]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 212]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2414 a r:Inference; +skolem:lemma5811 a r:Inference; r:gives { - 2213 :numberToDigits (2 2 1 3). + 3213 :numberToDigits (3 2 1 3). }; r:evidence ( - [ a r:Fact; r:gives {(2213 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2213 1000) math:remainder 213}] + [ a r:Fact; r:gives {(3213 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3213 1000) math:remainder 213}] [ a r:Fact; r:gives {(213 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(213 100) math:remainder 13}] [ a r:Fact; r:gives {(13 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(13 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2213]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3213]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 213]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 13]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2415 a r:Inference; +skolem:lemma5812 a r:Inference; r:gives { - 2214 :numberToDigits (2 2 1 4). + 3214 :numberToDigits (3 2 1 4). }; r:evidence ( - [ a r:Fact; r:gives {(2214 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2214 1000) math:remainder 214}] + [ a r:Fact; r:gives {(3214 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3214 1000) math:remainder 214}] [ a r:Fact; r:gives {(214 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(214 100) math:remainder 14}] [ a r:Fact; r:gives {(14 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(14 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2214]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3214]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 214]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 14]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2416 a r:Inference; +skolem:lemma5813 a r:Inference; r:gives { - 2215 :numberToDigits (2 2 1 5). + 3215 :numberToDigits (3 2 1 5). }; r:evidence ( - [ a r:Fact; r:gives {(2215 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2215 1000) math:remainder 215}] + [ a r:Fact; r:gives {(3215 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3215 1000) math:remainder 215}] [ a r:Fact; r:gives {(215 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(215 100) math:remainder 15}] [ a r:Fact; r:gives {(15 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(15 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2215]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3215]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 215]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 15]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2417 a r:Inference; +skolem:lemma5814 a r:Inference; r:gives { - 2216 :numberToDigits (2 2 1 6). + 3216 :numberToDigits (3 2 1 6). }; r:evidence ( - [ a r:Fact; r:gives {(2216 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2216 1000) math:remainder 216}] + [ a r:Fact; r:gives {(3216 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3216 1000) math:remainder 216}] [ a r:Fact; r:gives {(216 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(216 100) math:remainder 16}] [ a r:Fact; r:gives {(16 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(16 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2216]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3216]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 216]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 16]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2418 a r:Inference; +skolem:lemma5815 a r:Inference; r:gives { - 2217 :numberToDigits (2 2 1 7). + 3217 :numberToDigits (3 2 1 7). }; r:evidence ( - [ a r:Fact; r:gives {(2217 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2217 1000) math:remainder 217}] + [ a r:Fact; r:gives {(3217 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3217 1000) math:remainder 217}] [ a r:Fact; r:gives {(217 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(217 100) math:remainder 17}] [ a r:Fact; r:gives {(17 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(17 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2217]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3217]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 217]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 17]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2419 a r:Inference; +skolem:lemma5816 a r:Inference; r:gives { - 2218 :numberToDigits (2 2 1 8). + 3218 :numberToDigits (3 2 1 8). }; r:evidence ( - [ a r:Fact; r:gives {(2218 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2218 1000) math:remainder 218}] + [ a r:Fact; r:gives {(3218 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3218 1000) math:remainder 218}] [ a r:Fact; r:gives {(218 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(218 100) math:remainder 18}] [ a r:Fact; r:gives {(18 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(18 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2218]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3218]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 218]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 18]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2420 a r:Inference; +skolem:lemma5817 a r:Inference; r:gives { - 2219 :numberToDigits (2 2 1 9). + 3219 :numberToDigits (3 2 1 9). }; r:evidence ( - [ a r:Fact; r:gives {(2219 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2219 1000) math:remainder 219}] + [ a r:Fact; r:gives {(3219 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3219 1000) math:remainder 219}] [ a r:Fact; r:gives {(219 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(219 100) math:remainder 19}] [ a r:Fact; r:gives {(19 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(19 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2219]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3219]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 219]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 19]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2421 a r:Inference; +skolem:lemma5818 a r:Inference; r:gives { - 2220 :numberToDigits (2 2 2 0). + 3220 :numberToDigits (3 2 2 0). }; r:evidence ( - [ a r:Fact; r:gives {(2220 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2220 1000) math:remainder 220}] + [ a r:Fact; r:gives {(3220 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3220 1000) math:remainder 220}] [ a r:Fact; r:gives {(220 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(220 100) math:remainder 20}] [ a r:Fact; r:gives {(20 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(20 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2220]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3220]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 220]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 20]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2422 a r:Inference; +skolem:lemma5819 a r:Inference; r:gives { - 2221 :numberToDigits (2 2 2 1). + 3221 :numberToDigits (3 2 2 1). }; r:evidence ( - [ a r:Fact; r:gives {(2221 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2221 1000) math:remainder 221}] + [ a r:Fact; r:gives {(3221 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3221 1000) math:remainder 221}] [ a r:Fact; r:gives {(221 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(221 100) math:remainder 21}] [ a r:Fact; r:gives {(21 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(21 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2221]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3221]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 221]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 21]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2423 a r:Inference; +skolem:lemma5820 a r:Inference; r:gives { - 2223 :numberToDigits (2 2 2 3). + 3222 :numberToDigits (3 2 2 2). }; r:evidence ( - [ a r:Fact; r:gives {(2223 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2223 1000) math:remainder 223}] + [ a r:Fact; r:gives {(3222 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3222 1000) math:remainder 222}] + [ a r:Fact; r:gives {(222 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(222 100) math:remainder 22}] + [ a r:Fact; r:gives {(22 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(22 10) math:remainder 2}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 222]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; + r:rule skolem:lemma6763. + +skolem:lemma5821 a r:Inference; + r:gives { + 3223 :numberToDigits (3 2 2 3). + }; + r:evidence ( + [ a r:Fact; r:gives {(3223 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3223 1000) math:remainder 223}] [ a r:Fact; r:gives {(223 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(223 100) math:remainder 23}] [ a r:Fact; r:gives {(23 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(23 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2223]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3223]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 223]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. - -skolem:lemma2424 a r:Inference; - r:gives { - (2 2 2 3) :digitsToNumber 2223 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(2000 200 20 3) math:sum 2223}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2223]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3439. - -skolem:lemma2425 a r:Inference; - r:gives { - (3 2 2 2) :digitsToNumber 3222 . - }; - r:evidence ( - [ a r:Fact; r:gives {(3 1000) math:product 3000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(3000 200 20 2) math:sum 3222}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2426 a r:Inference; +skolem:lemma5822 a r:Inference; r:gives { - 2224 :numberToDigits (2 2 2 4). + 3224 :numberToDigits (3 2 2 4). }; r:evidence ( - [ a r:Fact; r:gives {(2224 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2224 1000) math:remainder 224}] + [ a r:Fact; r:gives {(3224 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3224 1000) math:remainder 224}] [ a r:Fact; r:gives {(224 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(224 100) math:remainder 24}] [ a r:Fact; r:gives {(24 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(24 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2224]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3224]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 224]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. - -skolem:lemma2427 a r:Inference; - r:gives { - (2 2 2 4) :digitsToNumber 2224 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(2000 200 20 4) math:sum 2224}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2224]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3439. - -skolem:lemma2428 a r:Inference; - r:gives { - (4 2 2 2) :digitsToNumber 4222 . - }; - r:evidence ( - [ a r:Fact; r:gives {(4 1000) math:product 4000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(4000 200 20 2) math:sum 4222}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2429 a r:Inference; +skolem:lemma5823 a r:Inference; r:gives { - 2225 :numberToDigits (2 2 2 5). + 3225 :numberToDigits (3 2 2 5). }; r:evidence ( - [ a r:Fact; r:gives {(2225 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2225 1000) math:remainder 225}] + [ a r:Fact; r:gives {(3225 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3225 1000) math:remainder 225}] [ a r:Fact; r:gives {(225 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(225 100) math:remainder 25}] [ a r:Fact; r:gives {(25 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(25 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2225]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3225]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 225]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. - -skolem:lemma2430 a r:Inference; - r:gives { - (2 2 2 5) :digitsToNumber 2225 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(2000 200 20 5) math:sum 2225}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2225]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3439. - -skolem:lemma2431 a r:Inference; - r:gives { - (5 2 2 2) :digitsToNumber 5222 . - }; - r:evidence ( - [ a r:Fact; r:gives {(5 1000) math:product 5000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(5000 200 20 2) math:sum 5222}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2432 a r:Inference; +skolem:lemma5824 a r:Inference; r:gives { - 2226 :numberToDigits (2 2 2 6). + 3226 :numberToDigits (3 2 2 6). }; r:evidence ( - [ a r:Fact; r:gives {(2226 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2226 1000) math:remainder 226}] + [ a r:Fact; r:gives {(3226 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3226 1000) math:remainder 226}] [ a r:Fact; r:gives {(226 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(226 100) math:remainder 26}] [ a r:Fact; r:gives {(26 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(26 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2226]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3226]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 226]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. - -skolem:lemma2433 a r:Inference; - r:gives { - (2 2 2 6) :digitsToNumber 2226 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(2000 200 20 6) math:sum 2226}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2226]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. - -skolem:lemma2434 a r:Inference; - r:gives { - (6 2 2 2) :digitsToNumber 6222 . - }; - r:evidence ( - [ a r:Fact; r:gives {(6 1000) math:product 6000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(6000 200 20 2) math:sum 6222}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. - -skolem:lemma2435 a r:Inference; - r:gives { - 2227 :numberToDigits (2 2 2 7). - }; - r:evidence ( - [ a r:Fact; r:gives {(2227 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2227 1000) math:remainder 227}] - [ a r:Fact; r:gives {(227 100) math:integerQuotient 2}] - [ a r:Fact; r:gives {(227 100) math:remainder 27}] - [ a r:Fact; r:gives {(27 10) math:integerQuotient 2}] - [ a r:Fact; r:gives {(27 10) math:remainder 7}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2227]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 227]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. - -skolem:lemma2436 a r:Inference; - r:gives { - (2 2 2 7) :digitsToNumber 2227 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(2000 200 20 7) math:sum 2227}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2227]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. - -skolem:lemma2437 a r:Inference; - r:gives { - (7 2 2 2) :digitsToNumber 7222 . - }; - r:evidence ( - [ a r:Fact; r:gives {(7 1000) math:product 7000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(7000 200 20 2) math:sum 7222}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. - -skolem:lemma2438 a r:Inference; - r:gives { - 2228 :numberToDigits (2 2 2 8). - }; - r:evidence ( - [ a r:Fact; r:gives {(2228 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2228 1000) math:remainder 228}] - [ a r:Fact; r:gives {(228 100) math:integerQuotient 2}] - [ a r:Fact; r:gives {(228 100) math:remainder 28}] - [ a r:Fact; r:gives {(28 10) math:integerQuotient 2}] - [ a r:Fact; r:gives {(28 10) math:remainder 8}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2228]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 228]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. - -skolem:lemma2439 a r:Inference; - r:gives { - (2 2 2 8) :digitsToNumber 2228 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(2000 200 20 8) math:sum 2228}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2228]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. - -skolem:lemma2440 a r:Inference; - r:gives { - (8 2 2 2) :digitsToNumber 8222 . - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1000) math:product 8000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(8000 200 20 2) math:sum 8222}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2441 a r:Inference; +skolem:lemma5825 a r:Inference; r:gives { - 2229 :numberToDigits (2 2 2 9). + 3227 :numberToDigits (3 2 2 7). }; r:evidence ( - [ a r:Fact; r:gives {(2229 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2229 1000) math:remainder 229}] - [ a r:Fact; r:gives {(229 100) math:integerQuotient 2}] - [ a r:Fact; r:gives {(229 100) math:remainder 29}] - [ a r:Fact; r:gives {(29 10) math:integerQuotient 2}] - [ a r:Fact; r:gives {(29 10) math:remainder 9}] + [ a r:Fact; r:gives {(3227 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3227 1000) math:remainder 227}] + [ a r:Fact; r:gives {(227 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(227 100) math:remainder 27}] + [ a r:Fact; r:gives {(27 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(27 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2229]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3227]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 227]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; + r:rule skolem:lemma6763. -skolem:lemma2442 a r:Inference; +skolem:lemma5826 a r:Inference; r:gives { - (2 2 2 9) :digitsToNumber 2229 . + 3228 :numberToDigits (3 2 2 8). }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(2000 200 20 9) math:sum 2229}] + [ a r:Fact; r:gives {(3228 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3228 1000) math:remainder 228}] + [ a r:Fact; r:gives {(228 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(228 100) math:remainder 28}] + [ a r:Fact; r:gives {(28 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(28 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2229]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 228]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; + r:rule skolem:lemma6763. -skolem:lemma2443 a r:Inference; +skolem:lemma5827 a r:Inference; r:gives { - (9 2 2 2) :digitsToNumber 9222 . + 3229 :numberToDigits (3 2 2 9). }; r:evidence ( - [ a r:Fact; r:gives {(9 1000) math:product 9000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 200 20 2) math:sum 9222}] + [ a r:Fact; r:gives {(3229 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3229 1000) math:remainder 229}] + [ a r:Fact; r:gives {(229 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(229 100) math:remainder 29}] + [ a r:Fact; r:gives {(29 10) math:integerQuotient 2}] + [ a r:Fact; r:gives {(29 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9222]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 229]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; + r:rule skolem:lemma6763. -skolem:lemma2444 a r:Inference; +skolem:lemma5828 a r:Inference; r:gives { - 2230 :numberToDigits (2 2 3 0). + 3230 :numberToDigits (3 2 3 0). }; r:evidence ( - [ a r:Fact; r:gives {(2230 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2230 1000) math:remainder 230}] + [ a r:Fact; r:gives {(3230 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3230 1000) math:remainder 230}] [ a r:Fact; r:gives {(230 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(230 100) math:remainder 30}] [ a r:Fact; r:gives {(30 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(30 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2230]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3230]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 230]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2445 a r:Inference; +skolem:lemma5829 a r:Inference; r:gives { - 2231 :numberToDigits (2 2 3 1). + 3231 :numberToDigits (3 2 3 1). }; r:evidence ( - [ a r:Fact; r:gives {(2231 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2231 1000) math:remainder 231}] + [ a r:Fact; r:gives {(3231 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3231 1000) math:remainder 231}] [ a r:Fact; r:gives {(231 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(231 100) math:remainder 31}] [ a r:Fact; r:gives {(31 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(31 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2231]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3231]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 231]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 31]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2446 a r:Inference; +skolem:lemma5830 a r:Inference; r:gives { - 2232 :numberToDigits (2 2 3 2). + 3232 :numberToDigits (3 2 3 2). }; r:evidence ( - [ a r:Fact; r:gives {(2232 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2232 1000) math:remainder 232}] + [ a r:Fact; r:gives {(3232 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3232 1000) math:remainder 232}] [ a r:Fact; r:gives {(232 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(232 100) math:remainder 32}] [ a r:Fact; r:gives {(32 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(32 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2232]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3232]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 232]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 32]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2447 a r:Inference; +skolem:lemma5831 a r:Inference; r:gives { - 2233 :numberToDigits (2 2 3 3). + 3233 :numberToDigits (3 2 3 3). }; r:evidence ( - [ a r:Fact; r:gives {(2233 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2233 1000) math:remainder 233}] + [ a r:Fact; r:gives {(3233 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3233 1000) math:remainder 233}] [ a r:Fact; r:gives {(233 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(233 100) math:remainder 33}] [ a r:Fact; r:gives {(33 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(33 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2233]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3233]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 233]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 33]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. - -skolem:lemma2448 a r:Inference; - r:gives { - (2 2 3 3) :digitsToNumber 2233 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(2000 200 30 3) math:sum 2233}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2233]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3439. - -skolem:lemma2449 a r:Inference; - r:gives { - (3 3 2 2) :digitsToNumber 3322 . - }; - r:evidence ( - [ a r:Fact; r:gives {(3 1000) math:product 3000}] - [ a r:Fact; r:gives {(3 100) math:product 300}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(3000 300 20 2) math:sum 3322}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2450 a r:Inference; +skolem:lemma5832 a r:Inference; r:gives { - 2234 :numberToDigits (2 2 3 4). + 3234 :numberToDigits (3 2 3 4). }; r:evidence ( - [ a r:Fact; r:gives {(2234 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2234 1000) math:remainder 234}] + [ a r:Fact; r:gives {(3234 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3234 1000) math:remainder 234}] [ a r:Fact; r:gives {(234 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(234 100) math:remainder 34}] [ a r:Fact; r:gives {(34 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(34 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2234]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3234]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 234]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 34]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. - -skolem:lemma2451 a r:Inference; - r:gives { - (2 2 3 4) :digitsToNumber 2234 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(2000 200 30 4) math:sum 2234}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2234]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3439. - -skolem:lemma2452 a r:Inference; - r:gives { - (4 3 2 2) :digitsToNumber 4322 . - }; - r:evidence ( - [ a r:Fact; r:gives {(4 1000) math:product 4000}] - [ a r:Fact; r:gives {(3 100) math:product 300}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(4000 300 20 2) math:sum 4322}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2453 a r:Inference; +skolem:lemma5833 a r:Inference; r:gives { - 2235 :numberToDigits (2 2 3 5). + 3235 :numberToDigits (3 2 3 5). }; r:evidence ( - [ a r:Fact; r:gives {(2235 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2235 1000) math:remainder 235}] + [ a r:Fact; r:gives {(3235 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3235 1000) math:remainder 235}] [ a r:Fact; r:gives {(235 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(235 100) math:remainder 35}] [ a r:Fact; r:gives {(35 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(35 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2235]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3235]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 235]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 35]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. - -skolem:lemma2454 a r:Inference; - r:gives { - (2 2 3 5) :digitsToNumber 2235 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(2000 200 30 5) math:sum 2235}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2235]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3439. - -skolem:lemma2455 a r:Inference; - r:gives { - (5 3 2 2) :digitsToNumber 5322 . - }; - r:evidence ( - [ a r:Fact; r:gives {(5 1000) math:product 5000}] - [ a r:Fact; r:gives {(3 100) math:product 300}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(5000 300 20 2) math:sum 5322}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2456 a r:Inference; +skolem:lemma5834 a r:Inference; r:gives { - 2236 :numberToDigits (2 2 3 6). + 3236 :numberToDigits (3 2 3 6). }; r:evidence ( - [ a r:Fact; r:gives {(2236 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2236 1000) math:remainder 236}] + [ a r:Fact; r:gives {(3236 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3236 1000) math:remainder 236}] [ a r:Fact; r:gives {(236 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(236 100) math:remainder 36}] [ a r:Fact; r:gives {(36 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(36 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2236]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3236]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 236]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 36]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. - -skolem:lemma2457 a r:Inference; - r:gives { - (2 2 3 6) :digitsToNumber 2236 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(2000 200 30 6) math:sum 2236}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2236]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. - -skolem:lemma2458 a r:Inference; - r:gives { - (6 3 2 2) :digitsToNumber 6322 . - }; - r:evidence ( - [ a r:Fact; r:gives {(6 1000) math:product 6000}] - [ a r:Fact; r:gives {(3 100) math:product 300}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(6000 300 20 2) math:sum 6322}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2459 a r:Inference; +skolem:lemma5835 a r:Inference; r:gives { - 2237 :numberToDigits (2 2 3 7). + 3237 :numberToDigits (3 2 3 7). }; r:evidence ( - [ a r:Fact; r:gives {(2237 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2237 1000) math:remainder 237}] + [ a r:Fact; r:gives {(3237 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3237 1000) math:remainder 237}] [ a r:Fact; r:gives {(237 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(237 100) math:remainder 37}] [ a r:Fact; r:gives {(37 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(37 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2237]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3237]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 237]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 37]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. - -skolem:lemma2460 a r:Inference; - r:gives { - (2 2 3 7) :digitsToNumber 2237 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(2000 200 30 7) math:sum 2237}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2237]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. - -skolem:lemma2461 a r:Inference; - r:gives { - (7 3 2 2) :digitsToNumber 7322 . - }; - r:evidence ( - [ a r:Fact; r:gives {(7 1000) math:product 7000}] - [ a r:Fact; r:gives {(3 100) math:product 300}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(7000 300 20 2) math:sum 7322}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2462 a r:Inference; +skolem:lemma5836 a r:Inference; r:gives { - 2238 :numberToDigits (2 2 3 8). + 3238 :numberToDigits (3 2 3 8). }; r:evidence ( - [ a r:Fact; r:gives {(2238 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2238 1000) math:remainder 238}] + [ a r:Fact; r:gives {(3238 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3238 1000) math:remainder 238}] [ a r:Fact; r:gives {(238 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(238 100) math:remainder 38}] [ a r:Fact; r:gives {(38 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(38 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2238]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3238]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 238]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 38]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. - -skolem:lemma2463 a r:Inference; - r:gives { - (2 2 3 8) :digitsToNumber 2238 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(2000 200 30 8) math:sum 2238}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2238]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. - -skolem:lemma2464 a r:Inference; - r:gives { - (8 3 2 2) :digitsToNumber 8322 . - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1000) math:product 8000}] - [ a r:Fact; r:gives {(3 100) math:product 300}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(8000 300 20 2) math:sum 8322}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2465 a r:Inference; +skolem:lemma5837 a r:Inference; r:gives { - 2239 :numberToDigits (2 2 3 9). + 3239 :numberToDigits (3 2 3 9). }; r:evidence ( - [ a r:Fact; r:gives {(2239 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2239 1000) math:remainder 239}] + [ a r:Fact; r:gives {(3239 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3239 1000) math:remainder 239}] [ a r:Fact; r:gives {(239 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(239 100) math:remainder 39}] [ a r:Fact; r:gives {(39 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(39 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2239]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3239]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 239]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 39]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. - -skolem:lemma2466 a r:Inference; - r:gives { - (2 2 3 9) :digitsToNumber 2239 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(2000 200 30 9) math:sum 2239}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2239]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. - -skolem:lemma2467 a r:Inference; - r:gives { - (9 3 2 2) :digitsToNumber 9322 . - }; - r:evidence ( - [ a r:Fact; r:gives {(9 1000) math:product 9000}] - [ a r:Fact; r:gives {(3 100) math:product 300}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 300 20 2) math:sum 9322}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9322]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2468 a r:Inference; +skolem:lemma5838 a r:Inference; r:gives { - 2240 :numberToDigits (2 2 4 0). + 3240 :numberToDigits (3 2 4 0). }; r:evidence ( - [ a r:Fact; r:gives {(2240 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2240 1000) math:remainder 240}] + [ a r:Fact; r:gives {(3240 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3240 1000) math:remainder 240}] [ a r:Fact; r:gives {(240 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(240 100) math:remainder 40}] [ a r:Fact; r:gives {(40 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(40 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2240]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3240]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 240]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2469 a r:Inference; +skolem:lemma5839 a r:Inference; r:gives { - 2241 :numberToDigits (2 2 4 1). + 3241 :numberToDigits (3 2 4 1). }; r:evidence ( - [ a r:Fact; r:gives {(2241 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2241 1000) math:remainder 241}] + [ a r:Fact; r:gives {(3241 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3241 1000) math:remainder 241}] [ a r:Fact; r:gives {(241 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(241 100) math:remainder 41}] [ a r:Fact; r:gives {(41 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(41 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2241]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3241]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 241]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 41]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2470 a r:Inference; +skolem:lemma5840 a r:Inference; r:gives { - 2242 :numberToDigits (2 2 4 2). + 3242 :numberToDigits (3 2 4 2). }; r:evidence ( - [ a r:Fact; r:gives {(2242 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2242 1000) math:remainder 242}] + [ a r:Fact; r:gives {(3242 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3242 1000) math:remainder 242}] [ a r:Fact; r:gives {(242 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(242 100) math:remainder 42}] [ a r:Fact; r:gives {(42 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(42 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2242]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3242]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 242]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 42]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2471 a r:Inference; +skolem:lemma5841 a r:Inference; r:gives { - 2243 :numberToDigits (2 2 4 3). + 3243 :numberToDigits (3 2 4 3). }; r:evidence ( - [ a r:Fact; r:gives {(2243 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2243 1000) math:remainder 243}] + [ a r:Fact; r:gives {(3243 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3243 1000) math:remainder 243}] [ a r:Fact; r:gives {(243 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(243 100) math:remainder 43}] [ a r:Fact; r:gives {(43 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(43 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2243]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3243]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 243]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 43]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2472 a r:Inference; +skolem:lemma5842 a r:Inference; r:gives { - 2244 :numberToDigits (2 2 4 4). + 3244 :numberToDigits (3 2 4 4). }; r:evidence ( - [ a r:Fact; r:gives {(2244 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2244 1000) math:remainder 244}] + [ a r:Fact; r:gives {(3244 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3244 1000) math:remainder 244}] [ a r:Fact; r:gives {(244 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(244 100) math:remainder 44}] [ a r:Fact; r:gives {(44 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(44 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2244]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3244]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 244]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 44]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. - -skolem:lemma2473 a r:Inference; - r:gives { - (2 2 4 4) :digitsToNumber 2244 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(2000 200 40 4) math:sum 2244}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2244]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3439. - -skolem:lemma2474 a r:Inference; - r:gives { - (4 4 2 2) :digitsToNumber 4422 . - }; - r:evidence ( - [ a r:Fact; r:gives {(4 1000) math:product 4000}] - [ a r:Fact; r:gives {(4 100) math:product 400}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(4000 400 20 2) math:sum 4422}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. - -skolem:lemma2475 a r:Inference; - r:gives { - 2245 :numberToDigits (2 2 4 5). - }; - r:evidence ( - [ a r:Fact; r:gives {(2245 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2245 1000) math:remainder 245}] - [ a r:Fact; r:gives {(245 100) math:integerQuotient 2}] - [ a r:Fact; r:gives {(245 100) math:remainder 45}] - [ a r:Fact; r:gives {(45 10) math:integerQuotient 4}] - [ a r:Fact; r:gives {(45 10) math:remainder 5}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2245]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 245]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 45]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. - -skolem:lemma2476 a r:Inference; - r:gives { - (2 2 4 5) :digitsToNumber 2245 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(2000 200 40 5) math:sum 2245}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2245]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2477 a r:Inference; +skolem:lemma5843 a r:Inference; r:gives { - (5 4 2 2) :digitsToNumber 5422 . + 3245 :numberToDigits (3 2 4 5). }; r:evidence ( - [ a r:Fact; r:gives {(5 1000) math:product 5000}] - [ a r:Fact; r:gives {(4 100) math:product 400}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(5000 400 20 2) math:sum 5422}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + [ a r:Fact; r:gives {(3245 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3245 1000) math:remainder 245}] + [ a r:Fact; r:gives {(245 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(245 100) math:remainder 45}] + [ a r:Fact; r:gives {(45 10) math:integerQuotient 4}] + [ a r:Fact; r:gives {(45 10) math:remainder 5}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 245]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 45]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; + r:rule skolem:lemma6763. -skolem:lemma2478 a r:Inference; +skolem:lemma5844 a r:Inference; r:gives { - 2246 :numberToDigits (2 2 4 6). + 3246 :numberToDigits (3 2 4 6). }; r:evidence ( - [ a r:Fact; r:gives {(2246 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2246 1000) math:remainder 246}] + [ a r:Fact; r:gives {(3246 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3246 1000) math:remainder 246}] [ a r:Fact; r:gives {(246 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(246 100) math:remainder 46}] [ a r:Fact; r:gives {(46 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(46 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2246]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3246]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 246]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 46]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. - -skolem:lemma2479 a r:Inference; - r:gives { - (2 2 4 6) :digitsToNumber 2246 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(2000 200 40 6) math:sum 2246}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2246]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. - -skolem:lemma2480 a r:Inference; - r:gives { - (6 4 2 2) :digitsToNumber 6422 . - }; - r:evidence ( - [ a r:Fact; r:gives {(6 1000) math:product 6000}] - [ a r:Fact; r:gives {(4 100) math:product 400}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(6000 400 20 2) math:sum 6422}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2481 a r:Inference; +skolem:lemma5845 a r:Inference; r:gives { - 2247 :numberToDigits (2 2 4 7). + 3247 :numberToDigits (3 2 4 7). }; r:evidence ( - [ a r:Fact; r:gives {(2247 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2247 1000) math:remainder 247}] + [ a r:Fact; r:gives {(3247 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3247 1000) math:remainder 247}] [ a r:Fact; r:gives {(247 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(247 100) math:remainder 47}] [ a r:Fact; r:gives {(47 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(47 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2247]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3247]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 247]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 47]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. - -skolem:lemma2482 a r:Inference; - r:gives { - (2 2 4 7) :digitsToNumber 2247 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(2000 200 40 7) math:sum 2247}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2247]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. - -skolem:lemma2483 a r:Inference; - r:gives { - (7 4 2 2) :digitsToNumber 7422 . - }; - r:evidence ( - [ a r:Fact; r:gives {(7 1000) math:product 7000}] - [ a r:Fact; r:gives {(4 100) math:product 400}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(7000 400 20 2) math:sum 7422}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2484 a r:Inference; +skolem:lemma5846 a r:Inference; r:gives { - 2248 :numberToDigits (2 2 4 8). + 3248 :numberToDigits (3 2 4 8). }; r:evidence ( - [ a r:Fact; r:gives {(2248 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2248 1000) math:remainder 248}] + [ a r:Fact; r:gives {(3248 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3248 1000) math:remainder 248}] [ a r:Fact; r:gives {(248 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(248 100) math:remainder 48}] [ a r:Fact; r:gives {(48 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(48 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2248]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3248]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 248]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 48]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. - -skolem:lemma2485 a r:Inference; - r:gives { - (2 2 4 8) :digitsToNumber 2248 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(2000 200 40 8) math:sum 2248}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2248]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. - -skolem:lemma2486 a r:Inference; - r:gives { - (8 4 2 2) :digitsToNumber 8422 . - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1000) math:product 8000}] - [ a r:Fact; r:gives {(4 100) math:product 400}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(8000 400 20 2) math:sum 8422}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2487 a r:Inference; +skolem:lemma5847 a r:Inference; r:gives { - 2249 :numberToDigits (2 2 4 9). + 3249 :numberToDigits (3 2 4 9). }; r:evidence ( - [ a r:Fact; r:gives {(2249 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2249 1000) math:remainder 249}] + [ a r:Fact; r:gives {(3249 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3249 1000) math:remainder 249}] [ a r:Fact; r:gives {(249 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(249 100) math:remainder 49}] [ a r:Fact; r:gives {(49 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(49 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2249]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3249]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 249]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 49]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. - -skolem:lemma2488 a r:Inference; - r:gives { - (2 2 4 9) :digitsToNumber 2249 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(2000 200 40 9) math:sum 2249}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2249]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. - -skolem:lemma2489 a r:Inference; - r:gives { - (9 4 2 2) :digitsToNumber 9422 . - }; - r:evidence ( - [ a r:Fact; r:gives {(9 1000) math:product 9000}] - [ a r:Fact; r:gives {(4 100) math:product 400}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 400 20 2) math:sum 9422}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9422]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2490 a r:Inference; +skolem:lemma5848 a r:Inference; r:gives { - 2250 :numberToDigits (2 2 5 0). + 3250 :numberToDigits (3 2 5 0). }; r:evidence ( - [ a r:Fact; r:gives {(2250 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2250 1000) math:remainder 250}] + [ a r:Fact; r:gives {(3250 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3250 1000) math:remainder 250}] [ a r:Fact; r:gives {(250 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(250 100) math:remainder 50}] [ a r:Fact; r:gives {(50 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(50 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2250]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3250]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 250]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2491 a r:Inference; +skolem:lemma5849 a r:Inference; r:gives { - 2251 :numberToDigits (2 2 5 1). + 3251 :numberToDigits (3 2 5 1). }; r:evidence ( - [ a r:Fact; r:gives {(2251 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2251 1000) math:remainder 251}] + [ a r:Fact; r:gives {(3251 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3251 1000) math:remainder 251}] [ a r:Fact; r:gives {(251 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(251 100) math:remainder 51}] [ a r:Fact; r:gives {(51 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(51 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2251]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3251]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 251]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 51]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2492 a r:Inference; +skolem:lemma5850 a r:Inference; r:gives { - 2252 :numberToDigits (2 2 5 2). + 3252 :numberToDigits (3 2 5 2). }; r:evidence ( - [ a r:Fact; r:gives {(2252 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2252 1000) math:remainder 252}] + [ a r:Fact; r:gives {(3252 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3252 1000) math:remainder 252}] [ a r:Fact; r:gives {(252 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(252 100) math:remainder 52}] [ a r:Fact; r:gives {(52 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(52 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2252]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3252]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 252]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 52]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2493 a r:Inference; +skolem:lemma5851 a r:Inference; r:gives { - 2253 :numberToDigits (2 2 5 3). + 3253 :numberToDigits (3 2 5 3). }; r:evidence ( - [ a r:Fact; r:gives {(2253 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2253 1000) math:remainder 253}] + [ a r:Fact; r:gives {(3253 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3253 1000) math:remainder 253}] [ a r:Fact; r:gives {(253 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(253 100) math:remainder 53}] [ a r:Fact; r:gives {(53 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(53 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2253]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3253]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 253]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 53]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2494 a r:Inference; +skolem:lemma5852 a r:Inference; r:gives { - 2254 :numberToDigits (2 2 5 4). + 3254 :numberToDigits (3 2 5 4). }; r:evidence ( - [ a r:Fact; r:gives {(2254 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2254 1000) math:remainder 254}] + [ a r:Fact; r:gives {(3254 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3254 1000) math:remainder 254}] [ a r:Fact; r:gives {(254 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(254 100) math:remainder 54}] [ a r:Fact; r:gives {(54 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(54 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2254]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3254]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 254]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 54]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2495 a r:Inference; +skolem:lemma5853 a r:Inference; r:gives { - 2255 :numberToDigits (2 2 5 5). + 3255 :numberToDigits (3 2 5 5). }; r:evidence ( - [ a r:Fact; r:gives {(2255 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2255 1000) math:remainder 255}] + [ a r:Fact; r:gives {(3255 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3255 1000) math:remainder 255}] [ a r:Fact; r:gives {(255 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(255 100) math:remainder 55}] [ a r:Fact; r:gives {(55 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(55 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2255]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3255]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 255]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 55]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. - -skolem:lemma2496 a r:Inference; - r:gives { - (2 2 5 5) :digitsToNumber 2255 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(2000 200 50 5) math:sum 2255}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2255]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3439. - -skolem:lemma2497 a r:Inference; - r:gives { - (5 5 2 2) :digitsToNumber 5522 . - }; - r:evidence ( - [ a r:Fact; r:gives {(5 1000) math:product 5000}] - [ a r:Fact; r:gives {(5 100) math:product 500}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(5000 500 20 2) math:sum 5522}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2498 a r:Inference; +skolem:lemma5854 a r:Inference; r:gives { - 2256 :numberToDigits (2 2 5 6). + 3256 :numberToDigits (3 2 5 6). }; r:evidence ( - [ a r:Fact; r:gives {(2256 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2256 1000) math:remainder 256}] + [ a r:Fact; r:gives {(3256 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3256 1000) math:remainder 256}] [ a r:Fact; r:gives {(256 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(256 100) math:remainder 56}] [ a r:Fact; r:gives {(56 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(56 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2256]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3256]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 256]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 56]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. - -skolem:lemma2499 a r:Inference; - r:gives { - (2 2 5 6) :digitsToNumber 2256 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(2000 200 50 6) math:sum 2256}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2256]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. - -skolem:lemma2500 a r:Inference; - r:gives { - (6 5 2 2) :digitsToNumber 6522 . - }; - r:evidence ( - [ a r:Fact; r:gives {(6 1000) math:product 6000}] - [ a r:Fact; r:gives {(5 100) math:product 500}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(6000 500 20 2) math:sum 6522}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2501 a r:Inference; +skolem:lemma5855 a r:Inference; r:gives { - 2257 :numberToDigits (2 2 5 7). + 3257 :numberToDigits (3 2 5 7). }; r:evidence ( - [ a r:Fact; r:gives {(2257 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2257 1000) math:remainder 257}] + [ a r:Fact; r:gives {(3257 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3257 1000) math:remainder 257}] [ a r:Fact; r:gives {(257 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(257 100) math:remainder 57}] [ a r:Fact; r:gives {(57 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(57 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2257]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3257]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 257]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 57]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. - -skolem:lemma2502 a r:Inference; - r:gives { - (2 2 5 7) :digitsToNumber 2257 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(2000 200 50 7) math:sum 2257}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2257]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. - -skolem:lemma2503 a r:Inference; - r:gives { - (7 5 2 2) :digitsToNumber 7522 . - }; - r:evidence ( - [ a r:Fact; r:gives {(7 1000) math:product 7000}] - [ a r:Fact; r:gives {(5 100) math:product 500}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(7000 500 20 2) math:sum 7522}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2504 a r:Inference; +skolem:lemma5856 a r:Inference; r:gives { - 2258 :numberToDigits (2 2 5 8). + 3258 :numberToDigits (3 2 5 8). }; r:evidence ( - [ a r:Fact; r:gives {(2258 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2258 1000) math:remainder 258}] + [ a r:Fact; r:gives {(3258 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3258 1000) math:remainder 258}] [ a r:Fact; r:gives {(258 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(258 100) math:remainder 58}] [ a r:Fact; r:gives {(58 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(58 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2258]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3258]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 258]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 58]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. - -skolem:lemma2505 a r:Inference; - r:gives { - (2 2 5 8) :digitsToNumber 2258 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(2000 200 50 8) math:sum 2258}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2258]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. - -skolem:lemma2506 a r:Inference; - r:gives { - (8 5 2 2) :digitsToNumber 8522 . - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1000) math:product 8000}] - [ a r:Fact; r:gives {(5 100) math:product 500}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(8000 500 20 2) math:sum 8522}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2507 a r:Inference; +skolem:lemma5857 a r:Inference; r:gives { - 2259 :numberToDigits (2 2 5 9). + 3259 :numberToDigits (3 2 5 9). }; r:evidence ( - [ a r:Fact; r:gives {(2259 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2259 1000) math:remainder 259}] + [ a r:Fact; r:gives {(3259 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3259 1000) math:remainder 259}] [ a r:Fact; r:gives {(259 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(259 100) math:remainder 59}] [ a r:Fact; r:gives {(59 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(59 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2259]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3259]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 259]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 59]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. - -skolem:lemma2508 a r:Inference; - r:gives { - (2 2 5 9) :digitsToNumber 2259 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(2000 200 50 9) math:sum 2259}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2259]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. - -skolem:lemma2509 a r:Inference; - r:gives { - (9 5 2 2) :digitsToNumber 9522 . - }; - r:evidence ( - [ a r:Fact; r:gives {(9 1000) math:product 9000}] - [ a r:Fact; r:gives {(5 100) math:product 500}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 500 20 2) math:sum 9522}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9522]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2510 a r:Inference; +skolem:lemma5858 a r:Inference; r:gives { - 2260 :numberToDigits (2 2 6 0). + 3260 :numberToDigits (3 2 6 0). }; r:evidence ( - [ a r:Fact; r:gives {(2260 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2260 1000) math:remainder 260}] + [ a r:Fact; r:gives {(3260 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3260 1000) math:remainder 260}] [ a r:Fact; r:gives {(260 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(260 100) math:remainder 60}] [ a r:Fact; r:gives {(60 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(60 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2260]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3260]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 260]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2511 a r:Inference; +skolem:lemma5859 a r:Inference; r:gives { - 2261 :numberToDigits (2 2 6 1). + 3261 :numberToDigits (3 2 6 1). }; r:evidence ( - [ a r:Fact; r:gives {(2261 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2261 1000) math:remainder 261}] + [ a r:Fact; r:gives {(3261 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3261 1000) math:remainder 261}] [ a r:Fact; r:gives {(261 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(261 100) math:remainder 61}] [ a r:Fact; r:gives {(61 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(61 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2261]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3261]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 261]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 61]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2512 a r:Inference; +skolem:lemma5860 a r:Inference; r:gives { - 2262 :numberToDigits (2 2 6 2). + 3262 :numberToDigits (3 2 6 2). }; r:evidence ( - [ a r:Fact; r:gives {(2262 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2262 1000) math:remainder 262}] + [ a r:Fact; r:gives {(3262 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3262 1000) math:remainder 262}] [ a r:Fact; r:gives {(262 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(262 100) math:remainder 62}] [ a r:Fact; r:gives {(62 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(62 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2262]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3262]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 262]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 62]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2513 a r:Inference; +skolem:lemma5861 a r:Inference; r:gives { - 2263 :numberToDigits (2 2 6 3). + 3263 :numberToDigits (3 2 6 3). }; r:evidence ( - [ a r:Fact; r:gives {(2263 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2263 1000) math:remainder 263}] + [ a r:Fact; r:gives {(3263 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3263 1000) math:remainder 263}] [ a r:Fact; r:gives {(263 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(263 100) math:remainder 63}] [ a r:Fact; r:gives {(63 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(63 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2263]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3263]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 263]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 63]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2514 a r:Inference; +skolem:lemma5862 a r:Inference; r:gives { - 2264 :numberToDigits (2 2 6 4). + 3264 :numberToDigits (3 2 6 4). }; r:evidence ( - [ a r:Fact; r:gives {(2264 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2264 1000) math:remainder 264}] + [ a r:Fact; r:gives {(3264 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3264 1000) math:remainder 264}] [ a r:Fact; r:gives {(264 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(264 100) math:remainder 64}] [ a r:Fact; r:gives {(64 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(64 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2264]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3264]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 264]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 64]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2515 a r:Inference; +skolem:lemma5863 a r:Inference; r:gives { - 2265 :numberToDigits (2 2 6 5). + 3265 :numberToDigits (3 2 6 5). }; r:evidence ( - [ a r:Fact; r:gives {(2265 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2265 1000) math:remainder 265}] + [ a r:Fact; r:gives {(3265 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3265 1000) math:remainder 265}] [ a r:Fact; r:gives {(265 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(265 100) math:remainder 65}] [ a r:Fact; r:gives {(65 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(65 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2265]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3265]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 265]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 65]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. - -skolem:lemma2516 a r:Inference; - r:gives { - 2266 :numberToDigits (2 2 6 6). - }; - r:evidence ( - [ a r:Fact; r:gives {(2266 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2266 1000) math:remainder 266}] - [ a r:Fact; r:gives {(266 100) math:integerQuotient 2}] - [ a r:Fact; r:gives {(266 100) math:remainder 66}] - [ a r:Fact; r:gives {(66 10) math:integerQuotient 6}] - [ a r:Fact; r:gives {(66 10) math:remainder 6}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 66]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. - -skolem:lemma2517 a r:Inference; - r:gives { - (2 2 6 6) :digitsToNumber 2266 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(2000 200 60 6) math:sum 2266}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2266]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2518 a r:Inference; +skolem:lemma5864 a r:Inference; r:gives { - (6 6 2 2) :digitsToNumber 6622 . + 3266 :numberToDigits (3 2 6 6). }; r:evidence ( - [ a r:Fact; r:gives {(6 1000) math:product 6000}] - [ a r:Fact; r:gives {(6 100) math:product 600}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(6000 600 20 2) math:sum 6622}] + [ a r:Fact; r:gives {(3266 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3266 1000) math:remainder 266}] + [ a r:Fact; r:gives {(266 100) math:integerQuotient 2}] + [ a r:Fact; r:gives {(266 100) math:remainder 66}] + [ a r:Fact; r:gives {(66 10) math:integerQuotient 6}] + [ a r:Fact; r:gives {(66 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 266]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 66]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; + r:rule skolem:lemma6763. -skolem:lemma2519 a r:Inference; +skolem:lemma5865 a r:Inference; r:gives { - 2267 :numberToDigits (2 2 6 7). + 3267 :numberToDigits (3 2 6 7). }; r:evidence ( - [ a r:Fact; r:gives {(2267 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2267 1000) math:remainder 267}] + [ a r:Fact; r:gives {(3267 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3267 1000) math:remainder 267}] [ a r:Fact; r:gives {(267 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(267 100) math:remainder 67}] [ a r:Fact; r:gives {(67 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(67 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2267]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3267]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 267]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 67]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. - -skolem:lemma2520 a r:Inference; - r:gives { - (2 2 6 7) :digitsToNumber 2267 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(2000 200 60 7) math:sum 2267}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2267]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. - -skolem:lemma2521 a r:Inference; - r:gives { - (7 6 2 2) :digitsToNumber 7622 . - }; - r:evidence ( - [ a r:Fact; r:gives {(7 1000) math:product 7000}] - [ a r:Fact; r:gives {(6 100) math:product 600}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(7000 600 20 2) math:sum 7622}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2522 a r:Inference; +skolem:lemma5866 a r:Inference; r:gives { - 2268 :numberToDigits (2 2 6 8). + 3268 :numberToDigits (3 2 6 8). }; r:evidence ( - [ a r:Fact; r:gives {(2268 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2268 1000) math:remainder 268}] + [ a r:Fact; r:gives {(3268 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3268 1000) math:remainder 268}] [ a r:Fact; r:gives {(268 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(268 100) math:remainder 68}] [ a r:Fact; r:gives {(68 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(68 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2268]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3268]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 268]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 68]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. - -skolem:lemma2523 a r:Inference; - r:gives { - (2 2 6 8) :digitsToNumber 2268 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(2000 200 60 8) math:sum 2268}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2268]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. - -skolem:lemma2524 a r:Inference; - r:gives { - (8 6 2 2) :digitsToNumber 8622 . - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1000) math:product 8000}] - [ a r:Fact; r:gives {(6 100) math:product 600}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(8000 600 20 2) math:sum 8622}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2525 a r:Inference; +skolem:lemma5867 a r:Inference; r:gives { - 2269 :numberToDigits (2 2 6 9). + 3269 :numberToDigits (3 2 6 9). }; r:evidence ( - [ a r:Fact; r:gives {(2269 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2269 1000) math:remainder 269}] + [ a r:Fact; r:gives {(3269 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3269 1000) math:remainder 269}] [ a r:Fact; r:gives {(269 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(269 100) math:remainder 69}] [ a r:Fact; r:gives {(69 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(69 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2269]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3269]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 269]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 69]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. - -skolem:lemma2526 a r:Inference; - r:gives { - (2 2 6 9) :digitsToNumber 2269 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(2000 200 60 9) math:sum 2269}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2269]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. - -skolem:lemma2527 a r:Inference; - r:gives { - (9 6 2 2) :digitsToNumber 9622 . - }; - r:evidence ( - [ a r:Fact; r:gives {(9 1000) math:product 9000}] - [ a r:Fact; r:gives {(6 100) math:product 600}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 600 20 2) math:sum 9622}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9622]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2528 a r:Inference; +skolem:lemma5868 a r:Inference; r:gives { - 2270 :numberToDigits (2 2 7 0). + 3270 :numberToDigits (3 2 7 0). }; r:evidence ( - [ a r:Fact; r:gives {(2270 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2270 1000) math:remainder 270}] + [ a r:Fact; r:gives {(3270 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3270 1000) math:remainder 270}] [ a r:Fact; r:gives {(270 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(270 100) math:remainder 70}] [ a r:Fact; r:gives {(70 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(70 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2270]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3270]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 270]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2529 a r:Inference; +skolem:lemma5869 a r:Inference; r:gives { - 2271 :numberToDigits (2 2 7 1). + 3271 :numberToDigits (3 2 7 1). }; r:evidence ( - [ a r:Fact; r:gives {(2271 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2271 1000) math:remainder 271}] + [ a r:Fact; r:gives {(3271 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3271 1000) math:remainder 271}] [ a r:Fact; r:gives {(271 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(271 100) math:remainder 71}] [ a r:Fact; r:gives {(71 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(71 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2271]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3271]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 271]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 71]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2530 a r:Inference; +skolem:lemma5870 a r:Inference; r:gives { - 2272 :numberToDigits (2 2 7 2). + 3272 :numberToDigits (3 2 7 2). }; r:evidence ( - [ a r:Fact; r:gives {(2272 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2272 1000) math:remainder 272}] + [ a r:Fact; r:gives {(3272 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3272 1000) math:remainder 272}] [ a r:Fact; r:gives {(272 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(272 100) math:remainder 72}] [ a r:Fact; r:gives {(72 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(72 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2272]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3272]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 272]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 72]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2531 a r:Inference; +skolem:lemma5871 a r:Inference; r:gives { - 2273 :numberToDigits (2 2 7 3). + 3273 :numberToDigits (3 2 7 3). }; r:evidence ( - [ a r:Fact; r:gives {(2273 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2273 1000) math:remainder 273}] + [ a r:Fact; r:gives {(3273 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3273 1000) math:remainder 273}] [ a r:Fact; r:gives {(273 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(273 100) math:remainder 73}] [ a r:Fact; r:gives {(73 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(73 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2273]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3273]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 273]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 73]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2532 a r:Inference; +skolem:lemma5872 a r:Inference; r:gives { - 2274 :numberToDigits (2 2 7 4). + 3274 :numberToDigits (3 2 7 4). }; r:evidence ( - [ a r:Fact; r:gives {(2274 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2274 1000) math:remainder 274}] + [ a r:Fact; r:gives {(3274 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3274 1000) math:remainder 274}] [ a r:Fact; r:gives {(274 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(274 100) math:remainder 74}] [ a r:Fact; r:gives {(74 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(74 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2274]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3274]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 274]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 74]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2533 a r:Inference; +skolem:lemma5873 a r:Inference; r:gives { - 2275 :numberToDigits (2 2 7 5). + 3275 :numberToDigits (3 2 7 5). }; r:evidence ( - [ a r:Fact; r:gives {(2275 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2275 1000) math:remainder 275}] + [ a r:Fact; r:gives {(3275 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3275 1000) math:remainder 275}] [ a r:Fact; r:gives {(275 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(275 100) math:remainder 75}] [ a r:Fact; r:gives {(75 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(75 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2275]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3275]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 275]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 75]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2534 a r:Inference; +skolem:lemma5874 a r:Inference; r:gives { - 2276 :numberToDigits (2 2 7 6). + 3276 :numberToDigits (3 2 7 6). }; r:evidence ( - [ a r:Fact; r:gives {(2276 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2276 1000) math:remainder 276}] + [ a r:Fact; r:gives {(3276 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3276 1000) math:remainder 276}] [ a r:Fact; r:gives {(276 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(276 100) math:remainder 76}] [ a r:Fact; r:gives {(76 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(76 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2276]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3276]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 276]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 76]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2535 a r:Inference; +skolem:lemma5875 a r:Inference; r:gives { - 2277 :numberToDigits (2 2 7 7). + 3277 :numberToDigits (3 2 7 7). }; r:evidence ( - [ a r:Fact; r:gives {(2277 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2277 1000) math:remainder 277}] + [ a r:Fact; r:gives {(3277 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3277 1000) math:remainder 277}] [ a r:Fact; r:gives {(277 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(277 100) math:remainder 77}] [ a r:Fact; r:gives {(77 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(77 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2277]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3277]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 277]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 77]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. - -skolem:lemma2536 a r:Inference; - r:gives { - (2 2 7 7) :digitsToNumber 2277 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(2000 200 70 7) math:sum 2277}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2277]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. - -skolem:lemma2537 a r:Inference; - r:gives { - (7 7 2 2) :digitsToNumber 7722 . - }; - r:evidence ( - [ a r:Fact; r:gives {(7 1000) math:product 7000}] - [ a r:Fact; r:gives {(7 100) math:product 700}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(7000 700 20 2) math:sum 7722}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7722]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2538 a r:Inference; +skolem:lemma5876 a r:Inference; r:gives { - 2278 :numberToDigits (2 2 7 8). + 3278 :numberToDigits (3 2 7 8). }; r:evidence ( - [ a r:Fact; r:gives {(2278 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2278 1000) math:remainder 278}] + [ a r:Fact; r:gives {(3278 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3278 1000) math:remainder 278}] [ a r:Fact; r:gives {(278 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(278 100) math:remainder 78}] [ a r:Fact; r:gives {(78 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(78 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2278]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3278]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 278]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 78]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. - -skolem:lemma2539 a r:Inference; - r:gives { - (2 2 7 8) :digitsToNumber 2278 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(2000 200 70 8) math:sum 2278}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2278]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. - -skolem:lemma2540 a r:Inference; - r:gives { - (8 7 2 2) :digitsToNumber 8722 . - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1000) math:product 8000}] - [ a r:Fact; r:gives {(7 100) math:product 700}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(8000 700 20 2) math:sum 8722}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8722]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2541 a r:Inference; +skolem:lemma5877 a r:Inference; r:gives { - 2279 :numberToDigits (2 2 7 9). + 3279 :numberToDigits (3 2 7 9). }; r:evidence ( - [ a r:Fact; r:gives {(2279 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2279 1000) math:remainder 279}] + [ a r:Fact; r:gives {(3279 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3279 1000) math:remainder 279}] [ a r:Fact; r:gives {(279 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(279 100) math:remainder 79}] [ a r:Fact; r:gives {(79 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(79 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2279]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3279]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 279]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 79]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. - -skolem:lemma2542 a r:Inference; - r:gives { - (2 2 7 9) :digitsToNumber 2279 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(2000 200 70 9) math:sum 2279}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2279]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. - -skolem:lemma2543 a r:Inference; - r:gives { - (9 7 2 2) :digitsToNumber 9722 . - }; - r:evidence ( - [ a r:Fact; r:gives {(9 1000) math:product 9000}] - [ a r:Fact; r:gives {(7 100) math:product 700}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 700 20 2) math:sum 9722}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9722]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2544 a r:Inference; +skolem:lemma5878 a r:Inference; r:gives { - 2280 :numberToDigits (2 2 8 0). + 3280 :numberToDigits (3 2 8 0). }; r:evidence ( - [ a r:Fact; r:gives {(2280 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2280 1000) math:remainder 280}] + [ a r:Fact; r:gives {(3280 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3280 1000) math:remainder 280}] [ a r:Fact; r:gives {(280 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(280 100) math:remainder 80}] [ a r:Fact; r:gives {(80 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(80 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2280]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3280]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 280]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2545 a r:Inference; +skolem:lemma5879 a r:Inference; r:gives { - 2281 :numberToDigits (2 2 8 1). + 3281 :numberToDigits (3 2 8 1). }; r:evidence ( - [ a r:Fact; r:gives {(2281 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2281 1000) math:remainder 281}] + [ a r:Fact; r:gives {(3281 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3281 1000) math:remainder 281}] [ a r:Fact; r:gives {(281 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(281 100) math:remainder 81}] [ a r:Fact; r:gives {(81 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(81 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2281]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3281]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 281]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 81]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2546 a r:Inference; +skolem:lemma5880 a r:Inference; r:gives { - 2282 :numberToDigits (2 2 8 2). + 3282 :numberToDigits (3 2 8 2). }; r:evidence ( - [ a r:Fact; r:gives {(2282 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2282 1000) math:remainder 282}] + [ a r:Fact; r:gives {(3282 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3282 1000) math:remainder 282}] [ a r:Fact; r:gives {(282 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(282 100) math:remainder 82}] [ a r:Fact; r:gives {(82 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(82 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2282]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3282]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 282]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 82]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2547 a r:Inference; +skolem:lemma5881 a r:Inference; r:gives { - 2283 :numberToDigits (2 2 8 3). + 3283 :numberToDigits (3 2 8 3). }; r:evidence ( - [ a r:Fact; r:gives {(2283 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2283 1000) math:remainder 283}] + [ a r:Fact; r:gives {(3283 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3283 1000) math:remainder 283}] [ a r:Fact; r:gives {(283 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(283 100) math:remainder 83}] [ a r:Fact; r:gives {(83 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(83 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2283]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3283]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 283]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 83]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2548 a r:Inference; +skolem:lemma5882 a r:Inference; r:gives { - 2284 :numberToDigits (2 2 8 4). + 3284 :numberToDigits (3 2 8 4). }; r:evidence ( - [ a r:Fact; r:gives {(2284 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2284 1000) math:remainder 284}] + [ a r:Fact; r:gives {(3284 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3284 1000) math:remainder 284}] [ a r:Fact; r:gives {(284 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(284 100) math:remainder 84}] [ a r:Fact; r:gives {(84 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(84 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2284]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3284]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 284]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 84]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2549 a r:Inference; +skolem:lemma5883 a r:Inference; r:gives { - 2285 :numberToDigits (2 2 8 5). + 3285 :numberToDigits (3 2 8 5). }; r:evidence ( - [ a r:Fact; r:gives {(2285 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2285 1000) math:remainder 285}] + [ a r:Fact; r:gives {(3285 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3285 1000) math:remainder 285}] [ a r:Fact; r:gives {(285 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(285 100) math:remainder 85}] [ a r:Fact; r:gives {(85 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(85 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2285]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3285]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 285]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 85]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2550 a r:Inference; +skolem:lemma5884 a r:Inference; r:gives { - 2286 :numberToDigits (2 2 8 6). + 3286 :numberToDigits (3 2 8 6). }; r:evidence ( - [ a r:Fact; r:gives {(2286 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2286 1000) math:remainder 286}] + [ a r:Fact; r:gives {(3286 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3286 1000) math:remainder 286}] [ a r:Fact; r:gives {(286 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(286 100) math:remainder 86}] [ a r:Fact; r:gives {(86 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(86 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2286]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3286]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 286]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 86]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2551 a r:Inference; +skolem:lemma5885 a r:Inference; r:gives { - 2287 :numberToDigits (2 2 8 7). + 3287 :numberToDigits (3 2 8 7). }; r:evidence ( - [ a r:Fact; r:gives {(2287 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2287 1000) math:remainder 287}] + [ a r:Fact; r:gives {(3287 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3287 1000) math:remainder 287}] [ a r:Fact; r:gives {(287 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(287 100) math:remainder 87}] [ a r:Fact; r:gives {(87 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(87 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2287]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3287]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 287]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 87]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2552 a r:Inference; +skolem:lemma5886 a r:Inference; r:gives { - 2288 :numberToDigits (2 2 8 8). + 3288 :numberToDigits (3 2 8 8). }; r:evidence ( - [ a r:Fact; r:gives {(2288 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2288 1000) math:remainder 288}] + [ a r:Fact; r:gives {(3288 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3288 1000) math:remainder 288}] [ a r:Fact; r:gives {(288 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(288 100) math:remainder 88}] [ a r:Fact; r:gives {(88 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(88 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2288]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3288]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 288]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 88]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. - -skolem:lemma2553 a r:Inference; - r:gives { - (2 2 8 8) :digitsToNumber 2288 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(8 10) math:product 80}] - [ a r:Fact; r:gives {(2000 200 80 8) math:sum 2288}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2288]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. - -skolem:lemma2554 a r:Inference; - r:gives { - (8 8 2 2) :digitsToNumber 8822 . - }; - r:evidence ( - [ a r:Fact; r:gives {(8 1000) math:product 8000}] - [ a r:Fact; r:gives {(8 100) math:product 800}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(8000 800 20 2) math:sum 8822}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8822]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2555 a r:Inference; +skolem:lemma5887 a r:Inference; r:gives { - 2289 :numberToDigits (2 2 8 9). + 3289 :numberToDigits (3 2 8 9). }; r:evidence ( - [ a r:Fact; r:gives {(2289 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2289 1000) math:remainder 289}] + [ a r:Fact; r:gives {(3289 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3289 1000) math:remainder 289}] [ a r:Fact; r:gives {(289 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(289 100) math:remainder 89}] [ a r:Fact; r:gives {(89 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(89 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2289]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3289]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 289]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 89]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. - -skolem:lemma2556 a r:Inference; - r:gives { - (2 2 8 9) :digitsToNumber 2289 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(8 10) math:product 80}] - [ a r:Fact; r:gives {(2000 200 80 9) math:sum 2289}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2289]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. - -skolem:lemma2557 a r:Inference; - r:gives { - (9 8 2 2) :digitsToNumber 9822 . - }; - r:evidence ( - [ a r:Fact; r:gives {(9 1000) math:product 9000}] - [ a r:Fact; r:gives {(8 100) math:product 800}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 800 20 2) math:sum 9822}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9822]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2558 a r:Inference; +skolem:lemma5888 a r:Inference; r:gives { - 2290 :numberToDigits (2 2 9 0). + 3290 :numberToDigits (3 2 9 0). }; r:evidence ( - [ a r:Fact; r:gives {(2290 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2290 1000) math:remainder 290}] + [ a r:Fact; r:gives {(3290 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3290 1000) math:remainder 290}] [ a r:Fact; r:gives {(290 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(290 100) math:remainder 90}] [ a r:Fact; r:gives {(90 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(90 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2290]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3290]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 290]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 90]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2559 a r:Inference; +skolem:lemma5889 a r:Inference; r:gives { - 2291 :numberToDigits (2 2 9 1). + 3291 :numberToDigits (3 2 9 1). }; r:evidence ( - [ a r:Fact; r:gives {(2291 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2291 1000) math:remainder 291}] + [ a r:Fact; r:gives {(3291 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3291 1000) math:remainder 291}] [ a r:Fact; r:gives {(291 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(291 100) math:remainder 91}] [ a r:Fact; r:gives {(91 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(91 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2291]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3291]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 291]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 91]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2560 a r:Inference; +skolem:lemma5890 a r:Inference; r:gives { - 2292 :numberToDigits (2 2 9 2). + 3292 :numberToDigits (3 2 9 2). }; r:evidence ( - [ a r:Fact; r:gives {(2292 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2292 1000) math:remainder 292}] + [ a r:Fact; r:gives {(3292 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3292 1000) math:remainder 292}] [ a r:Fact; r:gives {(292 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(292 100) math:remainder 92}] [ a r:Fact; r:gives {(92 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(92 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2292]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3292]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 292]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 92]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2561 a r:Inference; +skolem:lemma5891 a r:Inference; r:gives { - 2293 :numberToDigits (2 2 9 3). + 3293 :numberToDigits (3 2 9 3). }; r:evidence ( - [ a r:Fact; r:gives {(2293 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2293 1000) math:remainder 293}] + [ a r:Fact; r:gives {(3293 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3293 1000) math:remainder 293}] [ a r:Fact; r:gives {(293 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(293 100) math:remainder 93}] [ a r:Fact; r:gives {(93 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(93 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2293]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3293]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 293]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 93]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2562 a r:Inference; +skolem:lemma5892 a r:Inference; r:gives { - 2294 :numberToDigits (2 2 9 4). + 3294 :numberToDigits (3 2 9 4). }; r:evidence ( - [ a r:Fact; r:gives {(2294 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2294 1000) math:remainder 294}] + [ a r:Fact; r:gives {(3294 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3294 1000) math:remainder 294}] [ a r:Fact; r:gives {(294 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(294 100) math:remainder 94}] [ a r:Fact; r:gives {(94 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(94 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2294]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3294]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 294]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 94]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2563 a r:Inference; +skolem:lemma5893 a r:Inference; r:gives { - 2295 :numberToDigits (2 2 9 5). + 3295 :numberToDigits (3 2 9 5). }; r:evidence ( - [ a r:Fact; r:gives {(2295 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2295 1000) math:remainder 295}] + [ a r:Fact; r:gives {(3295 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3295 1000) math:remainder 295}] [ a r:Fact; r:gives {(295 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(295 100) math:remainder 95}] [ a r:Fact; r:gives {(95 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(95 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2295]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3295]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 295]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 95]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2564 a r:Inference; +skolem:lemma5894 a r:Inference; r:gives { - 2296 :numberToDigits (2 2 9 6). + 3296 :numberToDigits (3 2 9 6). }; r:evidence ( - [ a r:Fact; r:gives {(2296 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2296 1000) math:remainder 296}] + [ a r:Fact; r:gives {(3296 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3296 1000) math:remainder 296}] [ a r:Fact; r:gives {(296 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(296 100) math:remainder 96}] [ a r:Fact; r:gives {(96 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(96 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2296]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3296]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 296]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 96]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2565 a r:Inference; +skolem:lemma5895 a r:Inference; r:gives { - 2297 :numberToDigits (2 2 9 7). + 3297 :numberToDigits (3 2 9 7). }; r:evidence ( - [ a r:Fact; r:gives {(2297 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2297 1000) math:remainder 297}] + [ a r:Fact; r:gives {(3297 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3297 1000) math:remainder 297}] [ a r:Fact; r:gives {(297 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(297 100) math:remainder 97}] [ a r:Fact; r:gives {(97 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(97 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2297]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3297]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 297]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 97]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2566 a r:Inference; +skolem:lemma5896 a r:Inference; r:gives { - 2298 :numberToDigits (2 2 9 8). + 3298 :numberToDigits (3 2 9 8). }; r:evidence ( - [ a r:Fact; r:gives {(2298 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2298 1000) math:remainder 298}] + [ a r:Fact; r:gives {(3298 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3298 1000) math:remainder 298}] [ a r:Fact; r:gives {(298 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(298 100) math:remainder 98}] [ a r:Fact; r:gives {(98 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(98 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2298]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3298]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 298]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 98]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2567 a r:Inference; +skolem:lemma5897 a r:Inference; r:gives { - 2299 :numberToDigits (2 2 9 9). + 3299 :numberToDigits (3 2 9 9). }; r:evidence ( - [ a r:Fact; r:gives {(2299 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2299 1000) math:remainder 299}] + [ a r:Fact; r:gives {(3299 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3299 1000) math:remainder 299}] [ a r:Fact; r:gives {(299 100) math:integerQuotient 2}] [ a r:Fact; r:gives {(299 100) math:remainder 99}] [ a r:Fact; r:gives {(99 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(99 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2299]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3299]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 299]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 99]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. - -skolem:lemma2568 a r:Inference; - r:gives { - (2 2 9 9) :digitsToNumber 2299 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(2 100) math:product 200}] - [ a r:Fact; r:gives {(9 10) math:product 90}] - [ a r:Fact; r:gives {(2000 200 90 9) math:sum 2299}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 200]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 90]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2299]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. - -skolem:lemma2569 a r:Inference; - r:gives { - (9 9 2 2) :digitsToNumber 9922 . - }; - r:evidence ( - [ a r:Fact; r:gives {(9 1000) math:product 9000}] - [ a r:Fact; r:gives {(9 100) math:product 900}] - [ a r:Fact; r:gives {(2 10) math:product 20}] - [ a r:Fact; r:gives {(9000 900 20 2) math:sum 9922}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 900]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 20]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9922]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2570 a r:Inference; +skolem:lemma5898 a r:Inference; r:gives { - 2300 :numberToDigits (2 3 0 0). + 3300 :numberToDigits (3 3 0 0). }; r:evidence ( - [ a r:Fact; r:gives {(2300 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2300 1000) math:remainder 300}] + [ a r:Fact; r:gives {(3300 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3300 1000) math:remainder 300}] [ a r:Fact; r:gives {(300 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(300 100) math:remainder 0}] [ a r:Fact; r:gives {(0 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(0 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2300]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2571 a r:Inference; +skolem:lemma5899 a r:Inference; r:gives { - 2301 :numberToDigits (2 3 0 1). + 3301 :numberToDigits (3 3 0 1). }; r:evidence ( - [ a r:Fact; r:gives {(2301 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2301 1000) math:remainder 301}] + [ a r:Fact; r:gives {(3301 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3301 1000) math:remainder 301}] [ a r:Fact; r:gives {(301 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(301 100) math:remainder 1}] [ a r:Fact; r:gives {(1 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(1 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2301]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3301]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 301]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2572 a r:Inference; +skolem:lemma5900 a r:Inference; r:gives { - 2302 :numberToDigits (2 3 0 2). + 3302 :numberToDigits (3 3 0 2). }; r:evidence ( - [ a r:Fact; r:gives {(2302 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2302 1000) math:remainder 302}] + [ a r:Fact; r:gives {(3302 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3302 1000) math:remainder 302}] [ a r:Fact; r:gives {(302 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(302 100) math:remainder 2}] [ a r:Fact; r:gives {(2 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(2 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2302]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3302]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 302]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2573 a r:Inference; +skolem:lemma5901 a r:Inference; r:gives { - 2303 :numberToDigits (2 3 0 3). + 3303 :numberToDigits (3 3 0 3). }; r:evidence ( - [ a r:Fact; r:gives {(2303 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2303 1000) math:remainder 303}] + [ a r:Fact; r:gives {(3303 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3303 1000) math:remainder 303}] [ a r:Fact; r:gives {(303 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(303 100) math:remainder 3}] [ a r:Fact; r:gives {(3 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(3 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2303]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3303]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 303]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2574 a r:Inference; +skolem:lemma5902 a r:Inference; r:gives { - 2304 :numberToDigits (2 3 0 4). + 3304 :numberToDigits (3 3 0 4). }; r:evidence ( - [ a r:Fact; r:gives {(2304 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2304 1000) math:remainder 304}] + [ a r:Fact; r:gives {(3304 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3304 1000) math:remainder 304}] [ a r:Fact; r:gives {(304 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(304 100) math:remainder 4}] [ a r:Fact; r:gives {(4 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(4 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2304]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3304]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 304]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2575 a r:Inference; +skolem:lemma5903 a r:Inference; r:gives { - 2305 :numberToDigits (2 3 0 5). + 3305 :numberToDigits (3 3 0 5). }; r:evidence ( - [ a r:Fact; r:gives {(2305 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2305 1000) math:remainder 305}] + [ a r:Fact; r:gives {(3305 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3305 1000) math:remainder 305}] [ a r:Fact; r:gives {(305 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(305 100) math:remainder 5}] [ a r:Fact; r:gives {(5 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(5 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2305]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3305]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 305]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2576 a r:Inference; +skolem:lemma5904 a r:Inference; r:gives { - 2306 :numberToDigits (2 3 0 6). + 3306 :numberToDigits (3 3 0 6). }; r:evidence ( - [ a r:Fact; r:gives {(2306 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2306 1000) math:remainder 306}] + [ a r:Fact; r:gives {(3306 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3306 1000) math:remainder 306}] [ a r:Fact; r:gives {(306 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(306 100) math:remainder 6}] [ a r:Fact; r:gives {(6 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(6 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2306]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3306]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 306]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2577 a r:Inference; +skolem:lemma5905 a r:Inference; r:gives { - 2307 :numberToDigits (2 3 0 7). + 3307 :numberToDigits (3 3 0 7). }; r:evidence ( - [ a r:Fact; r:gives {(2307 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2307 1000) math:remainder 307}] + [ a r:Fact; r:gives {(3307 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3307 1000) math:remainder 307}] [ a r:Fact; r:gives {(307 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(307 100) math:remainder 7}] [ a r:Fact; r:gives {(7 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(7 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2307]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3307]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 307]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2578 a r:Inference; +skolem:lemma5906 a r:Inference; r:gives { - 2308 :numberToDigits (2 3 0 8). + 3308 :numberToDigits (3 3 0 8). }; r:evidence ( - [ a r:Fact; r:gives {(2308 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2308 1000) math:remainder 308}] + [ a r:Fact; r:gives {(3308 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3308 1000) math:remainder 308}] [ a r:Fact; r:gives {(308 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(308 100) math:remainder 8}] [ a r:Fact; r:gives {(8 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(8 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2308]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3308]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 308]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2579 a r:Inference; +skolem:lemma5907 a r:Inference; r:gives { - 2309 :numberToDigits (2 3 0 9). + 3309 :numberToDigits (3 3 0 9). }; r:evidence ( - [ a r:Fact; r:gives {(2309 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2309 1000) math:remainder 309}] + [ a r:Fact; r:gives {(3309 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3309 1000) math:remainder 309}] [ a r:Fact; r:gives {(309 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(309 100) math:remainder 9}] [ a r:Fact; r:gives {(9 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(9 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2309]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3309]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 309]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2580 a r:Inference; +skolem:lemma5908 a r:Inference; r:gives { - 2310 :numberToDigits (2 3 1 0). + 3310 :numberToDigits (3 3 1 0). }; r:evidence ( - [ a r:Fact; r:gives {(2310 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2310 1000) math:remainder 310}] + [ a r:Fact; r:gives {(3310 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3310 1000) math:remainder 310}] [ a r:Fact; r:gives {(310 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(310 100) math:remainder 10}] [ a r:Fact; r:gives {(10 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(10 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2310]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3310]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 310]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2581 a r:Inference; +skolem:lemma5909 a r:Inference; r:gives { - 2311 :numberToDigits (2 3 1 1). + 3311 :numberToDigits (3 3 1 1). }; r:evidence ( - [ a r:Fact; r:gives {(2311 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2311 1000) math:remainder 311}] + [ a r:Fact; r:gives {(3311 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3311 1000) math:remainder 311}] [ a r:Fact; r:gives {(311 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(311 100) math:remainder 11}] [ a r:Fact; r:gives {(11 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(11 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2311]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3311]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 311]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 11]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2582 a r:Inference; +skolem:lemma5910 a r:Inference; r:gives { - 2312 :numberToDigits (2 3 1 2). + 3312 :numberToDigits (3 3 1 2). }; r:evidence ( - [ a r:Fact; r:gives {(2312 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2312 1000) math:remainder 312}] + [ a r:Fact; r:gives {(3312 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3312 1000) math:remainder 312}] [ a r:Fact; r:gives {(312 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(312 100) math:remainder 12}] [ a r:Fact; r:gives {(12 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(12 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2312]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3312]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 312]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2583 a r:Inference; +skolem:lemma5911 a r:Inference; r:gives { - 2313 :numberToDigits (2 3 1 3). + 3313 :numberToDigits (3 3 1 3). }; r:evidence ( - [ a r:Fact; r:gives {(2313 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2313 1000) math:remainder 313}] + [ a r:Fact; r:gives {(3313 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3313 1000) math:remainder 313}] [ a r:Fact; r:gives {(313 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(313 100) math:remainder 13}] [ a r:Fact; r:gives {(13 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(13 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2313]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3313]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 313]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 13]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2584 a r:Inference; +skolem:lemma5912 a r:Inference; r:gives { - 2314 :numberToDigits (2 3 1 4). + 3314 :numberToDigits (3 3 1 4). }; r:evidence ( - [ a r:Fact; r:gives {(2314 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2314 1000) math:remainder 314}] + [ a r:Fact; r:gives {(3314 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3314 1000) math:remainder 314}] [ a r:Fact; r:gives {(314 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(314 100) math:remainder 14}] [ a r:Fact; r:gives {(14 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(14 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2314]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3314]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 314]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 14]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2585 a r:Inference; +skolem:lemma5913 a r:Inference; r:gives { - 2315 :numberToDigits (2 3 1 5). + 3315 :numberToDigits (3 3 1 5). }; r:evidence ( - [ a r:Fact; r:gives {(2315 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2315 1000) math:remainder 315}] + [ a r:Fact; r:gives {(3315 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3315 1000) math:remainder 315}] [ a r:Fact; r:gives {(315 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(315 100) math:remainder 15}] [ a r:Fact; r:gives {(15 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(15 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2315]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3315]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 315]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 15]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2586 a r:Inference; +skolem:lemma5914 a r:Inference; r:gives { - 2316 :numberToDigits (2 3 1 6). + 3316 :numberToDigits (3 3 1 6). }; r:evidence ( - [ a r:Fact; r:gives {(2316 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2316 1000) math:remainder 316}] + [ a r:Fact; r:gives {(3316 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3316 1000) math:remainder 316}] [ a r:Fact; r:gives {(316 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(316 100) math:remainder 16}] [ a r:Fact; r:gives {(16 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(16 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2316]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3316]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 316]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 16]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2587 a r:Inference; +skolem:lemma5915 a r:Inference; r:gives { - 2317 :numberToDigits (2 3 1 7). + 3317 :numberToDigits (3 3 1 7). }; r:evidence ( - [ a r:Fact; r:gives {(2317 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2317 1000) math:remainder 317}] + [ a r:Fact; r:gives {(3317 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3317 1000) math:remainder 317}] [ a r:Fact; r:gives {(317 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(317 100) math:remainder 17}] [ a r:Fact; r:gives {(17 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(17 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2317]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3317]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 317]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 17]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2588 a r:Inference; +skolem:lemma5916 a r:Inference; r:gives { - 2318 :numberToDigits (2 3 1 8). + 3318 :numberToDigits (3 3 1 8). }; r:evidence ( - [ a r:Fact; r:gives {(2318 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2318 1000) math:remainder 318}] + [ a r:Fact; r:gives {(3318 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3318 1000) math:remainder 318}] [ a r:Fact; r:gives {(318 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(318 100) math:remainder 18}] [ a r:Fact; r:gives {(18 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(18 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2318]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3318]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 318]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 18]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2589 a r:Inference; +skolem:lemma5917 a r:Inference; r:gives { - 2319 :numberToDigits (2 3 1 9). + 3319 :numberToDigits (3 3 1 9). }; r:evidence ( - [ a r:Fact; r:gives {(2319 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2319 1000) math:remainder 319}] + [ a r:Fact; r:gives {(3319 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3319 1000) math:remainder 319}] [ a r:Fact; r:gives {(319 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(319 100) math:remainder 19}] [ a r:Fact; r:gives {(19 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(19 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2319]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3319]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 319]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 19]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2590 a r:Inference; +skolem:lemma5918 a r:Inference; r:gives { - 2320 :numberToDigits (2 3 2 0). + 3320 :numberToDigits (3 3 2 0). }; r:evidence ( - [ a r:Fact; r:gives {(2320 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2320 1000) math:remainder 320}] + [ a r:Fact; r:gives {(3320 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3320 1000) math:remainder 320}] [ a r:Fact; r:gives {(320 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(320 100) math:remainder 20}] [ a r:Fact; r:gives {(20 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(20 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2320]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3320]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 320]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 20]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2591 a r:Inference; +skolem:lemma5919 a r:Inference; r:gives { - 2321 :numberToDigits (2 3 2 1). + 3321 :numberToDigits (3 3 2 1). }; r:evidence ( - [ a r:Fact; r:gives {(2321 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2321 1000) math:remainder 321}] + [ a r:Fact; r:gives {(3321 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3321 1000) math:remainder 321}] [ a r:Fact; r:gives {(321 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(321 100) math:remainder 21}] [ a r:Fact; r:gives {(21 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(21 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2321]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3321]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 321]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 21]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2592 a r:Inference; +skolem:lemma5920 a r:Inference; r:gives { - 2322 :numberToDigits (2 3 2 2). + 3322 :numberToDigits (3 3 2 2). }; r:evidence ( - [ a r:Fact; r:gives {(2322 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2322 1000) math:remainder 322}] + [ a r:Fact; r:gives {(3322 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3322 1000) math:remainder 322}] [ a r:Fact; r:gives {(322 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(322 100) math:remainder 22}] [ a r:Fact; r:gives {(22 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(22 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2322]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3322]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 322]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2593 a r:Inference; +skolem:lemma5921 a r:Inference; r:gives { - 2323 :numberToDigits (2 3 2 3). + 3323 :numberToDigits (3 3 2 3). }; r:evidence ( - [ a r:Fact; r:gives {(2323 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2323 1000) math:remainder 323}] + [ a r:Fact; r:gives {(3323 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3323 1000) math:remainder 323}] [ a r:Fact; r:gives {(323 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(323 100) math:remainder 23}] [ a r:Fact; r:gives {(23 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(23 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2323]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3323]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 323]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2594 a r:Inference; +skolem:lemma5922 a r:Inference; r:gives { - 2324 :numberToDigits (2 3 2 4). + 3324 :numberToDigits (3 3 2 4). }; r:evidence ( - [ a r:Fact; r:gives {(2324 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2324 1000) math:remainder 324}] + [ a r:Fact; r:gives {(3324 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3324 1000) math:remainder 324}] [ a r:Fact; r:gives {(324 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(324 100) math:remainder 24}] [ a r:Fact; r:gives {(24 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(24 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2324]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3324]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 324]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2595 a r:Inference; +skolem:lemma5923 a r:Inference; r:gives { - 2325 :numberToDigits (2 3 2 5). + 3325 :numberToDigits (3 3 2 5). }; r:evidence ( - [ a r:Fact; r:gives {(2325 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2325 1000) math:remainder 325}] + [ a r:Fact; r:gives {(3325 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3325 1000) math:remainder 325}] [ a r:Fact; r:gives {(325 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(325 100) math:remainder 25}] [ a r:Fact; r:gives {(25 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(25 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2325]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3325]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 325]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2596 a r:Inference; +skolem:lemma5924 a r:Inference; r:gives { - 2326 :numberToDigits (2 3 2 6). + 3326 :numberToDigits (3 3 2 6). }; r:evidence ( - [ a r:Fact; r:gives {(2326 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2326 1000) math:remainder 326}] + [ a r:Fact; r:gives {(3326 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3326 1000) math:remainder 326}] [ a r:Fact; r:gives {(326 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(326 100) math:remainder 26}] [ a r:Fact; r:gives {(26 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(26 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2326]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3326]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 326]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2597 a r:Inference; +skolem:lemma5925 a r:Inference; r:gives { - 2327 :numberToDigits (2 3 2 7). + 3327 :numberToDigits (3 3 2 7). }; r:evidence ( - [ a r:Fact; r:gives {(2327 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2327 1000) math:remainder 327}] + [ a r:Fact; r:gives {(3327 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3327 1000) math:remainder 327}] [ a r:Fact; r:gives {(327 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(327 100) math:remainder 27}] [ a r:Fact; r:gives {(27 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(27 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2327]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3327]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 327]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2598 a r:Inference; +skolem:lemma5926 a r:Inference; r:gives { - 2328 :numberToDigits (2 3 2 8). + 3328 :numberToDigits (3 3 2 8). }; r:evidence ( - [ a r:Fact; r:gives {(2328 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2328 1000) math:remainder 328}] + [ a r:Fact; r:gives {(3328 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3328 1000) math:remainder 328}] [ a r:Fact; r:gives {(328 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(328 100) math:remainder 28}] [ a r:Fact; r:gives {(28 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(28 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2328]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3328]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 328]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2599 a r:Inference; +skolem:lemma5927 a r:Inference; r:gives { - 2329 :numberToDigits (2 3 2 9). + 3329 :numberToDigits (3 3 2 9). }; r:evidence ( - [ a r:Fact; r:gives {(2329 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2329 1000) math:remainder 329}] + [ a r:Fact; r:gives {(3329 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3329 1000) math:remainder 329}] [ a r:Fact; r:gives {(329 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(329 100) math:remainder 29}] [ a r:Fact; r:gives {(29 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(29 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2329]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3329]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 329]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2600 a r:Inference; +skolem:lemma5928 a r:Inference; r:gives { - 2330 :numberToDigits (2 3 3 0). + 3330 :numberToDigits (3 3 3 0). }; r:evidence ( - [ a r:Fact; r:gives {(2330 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2330 1000) math:remainder 330}] + [ a r:Fact; r:gives {(3330 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3330 1000) math:remainder 330}] [ a r:Fact; r:gives {(330 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(330 100) math:remainder 30}] [ a r:Fact; r:gives {(30 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(30 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2330]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3330]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 330]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2601 a r:Inference; +skolem:lemma5929 a r:Inference; r:gives { - 2331 :numberToDigits (2 3 3 1). + 3331 :numberToDigits (3 3 3 1). }; r:evidence ( - [ a r:Fact; r:gives {(2331 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2331 1000) math:remainder 331}] + [ a r:Fact; r:gives {(3331 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3331 1000) math:remainder 331}] [ a r:Fact; r:gives {(331 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(331 100) math:remainder 31}] [ a r:Fact; r:gives {(31 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(31 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2331]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3331]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 331]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 31]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2602 a r:Inference; +skolem:lemma5930 a r:Inference; r:gives { - 2332 :numberToDigits (2 3 3 2). + 3332 :numberToDigits (3 3 3 2). }; r:evidence ( - [ a r:Fact; r:gives {(2332 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2332 1000) math:remainder 332}] + [ a r:Fact; r:gives {(3332 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3332 1000) math:remainder 332}] [ a r:Fact; r:gives {(332 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(332 100) math:remainder 32}] [ a r:Fact; r:gives {(32 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(32 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2332]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3332]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 332]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 32]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. - -skolem:lemma2603 a r:Inference; - r:gives { - 2333 :numberToDigits (2 3 3 3). - }; - r:evidence ( - [ a r:Fact; r:gives {(2333 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2333 1000) math:remainder 333}] - [ a r:Fact; r:gives {(333 100) math:integerQuotient 3}] - [ a r:Fact; r:gives {(333 100) math:remainder 33}] - [ a r:Fact; r:gives {(33 10) math:integerQuotient 3}] - [ a r:Fact; r:gives {(33 10) math:remainder 3}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2333]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 333]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 33]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. - -skolem:lemma2604 a r:Inference; - r:gives { - (2 3 3 3) :digitsToNumber 2333 . - }; - r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] - [ a r:Fact; r:gives {(3 100) math:product 300}] - [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(2000 300 30 3) math:sum 2333}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2333]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3439. - -skolem:lemma2605 a r:Inference; - r:gives { - (3 3 3 2) :digitsToNumber 3332 . - }; - r:evidence ( - [ a r:Fact; r:gives {(3 1000) math:product 3000}] - [ a r:Fact; r:gives {(3 100) math:product 300}] - [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(3000 300 30 2) math:sum 3332}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6763. -skolem:lemma2606 a r:Inference; +skolem:lemma5931 a r:Inference; r:gives { - 2334 :numberToDigits (2 3 3 4). + 3334 :numberToDigits (3 3 3 4). }; r:evidence ( - [ a r:Fact; r:gives {(2334 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2334 1000) math:remainder 334}] + [ a r:Fact; r:gives {(3334 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3334 1000) math:remainder 334}] [ a r:Fact; r:gives {(334 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(334 100) math:remainder 34}] [ a r:Fact; r:gives {(34 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(34 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3334]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 334]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 34]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2607 a r:Inference; +skolem:lemma5932 a r:Inference; r:gives { - (2 3 3 4) :digitsToNumber 2334 . + (3 3 3 4) :digitsToNumber 3334 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(2000 300 30 4) math:sum 2334}] + [ a r:Fact; r:gives {(3000 300 30 4) math:sum 3334}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2334]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3334]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2608 a r:Inference; +skolem:lemma5933 a r:Inference; r:gives { - (4 3 3 2) :digitsToNumber 4332 . + (4 3 3 3) :digitsToNumber 4333 . }; r:evidence ( [ a r:Fact; r:gives {(4 1000) math:product 4000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(4000 300 30 2) math:sum 4332}] + [ a r:Fact; r:gives {(4000 300 30 3) math:sum 4333}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; @@ -62487,60 +139976,60 @@ skolem:lemma2608 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2609 a r:Inference; +skolem:lemma5934 a r:Inference; r:gives { - 2335 :numberToDigits (2 3 3 5). + 3335 :numberToDigits (3 3 3 5). }; r:evidence ( - [ a r:Fact; r:gives {(2335 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2335 1000) math:remainder 335}] + [ a r:Fact; r:gives {(3335 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3335 1000) math:remainder 335}] [ a r:Fact; r:gives {(335 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(335 100) math:remainder 35}] [ a r:Fact; r:gives {(35 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(35 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3335]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 335]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 35]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2610 a r:Inference; +skolem:lemma5935 a r:Inference; r:gives { - (2 3 3 5) :digitsToNumber 2335 . + (3 3 3 5) :digitsToNumber 3335 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(2000 300 30 5) math:sum 2335}] + [ a r:Fact; r:gives {(3000 300 30 5) math:sum 3335}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2335]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3335]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2611 a r:Inference; +skolem:lemma5936 a r:Inference; r:gives { - (5 3 3 2) :digitsToNumber 5332 . + (5 3 3 3) :digitsToNumber 5333 . }; r:evidence ( [ a r:Fact; r:gives {(5 1000) math:product 5000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(5000 300 30 2) math:sum 5332}] + [ a r:Fact; r:gives {(5000 300 30 3) math:sum 5333}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; @@ -62548,60 +140037,60 @@ skolem:lemma2611 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2612 a r:Inference; +skolem:lemma5937 a r:Inference; r:gives { - 2336 :numberToDigits (2 3 3 6). + 3336 :numberToDigits (3 3 3 6). }; r:evidence ( - [ a r:Fact; r:gives {(2336 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2336 1000) math:remainder 336}] + [ a r:Fact; r:gives {(3336 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3336 1000) math:remainder 336}] [ a r:Fact; r:gives {(336 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(336 100) math:remainder 36}] [ a r:Fact; r:gives {(36 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(36 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3336]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 336]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 36]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2613 a r:Inference; +skolem:lemma5938 a r:Inference; r:gives { - (2 3 3 6) :digitsToNumber 2336 . + (3 3 3 6) :digitsToNumber 3336 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(2000 300 30 6) math:sum 2336}] + [ a r:Fact; r:gives {(3000 300 30 6) math:sum 3336}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2336]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3336]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2614 a r:Inference; +skolem:lemma5939 a r:Inference; r:gives { - (6 3 3 2) :digitsToNumber 6332 . + (6 3 3 3) :digitsToNumber 6333 . }; r:evidence ( [ a r:Fact; r:gives {(6 1000) math:product 6000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(6000 300 30 2) math:sum 6332}] + [ a r:Fact; r:gives {(6000 300 30 3) math:sum 6333}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; @@ -62609,60 +140098,60 @@ skolem:lemma2614 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2615 a r:Inference; +skolem:lemma5940 a r:Inference; r:gives { - 2337 :numberToDigits (2 3 3 7). + 3337 :numberToDigits (3 3 3 7). }; r:evidence ( - [ a r:Fact; r:gives {(2337 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2337 1000) math:remainder 337}] + [ a r:Fact; r:gives {(3337 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3337 1000) math:remainder 337}] [ a r:Fact; r:gives {(337 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(337 100) math:remainder 37}] [ a r:Fact; r:gives {(37 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(37 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3337]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 337]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 37]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2616 a r:Inference; +skolem:lemma5941 a r:Inference; r:gives { - (2 3 3 7) :digitsToNumber 2337 . + (3 3 3 7) :digitsToNumber 3337 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(2000 300 30 7) math:sum 2337}] + [ a r:Fact; r:gives {(3000 300 30 7) math:sum 3337}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2337]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3337]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2617 a r:Inference; +skolem:lemma5942 a r:Inference; r:gives { - (7 3 3 2) :digitsToNumber 7332 . + (7 3 3 3) :digitsToNumber 7333 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(7000 300 30 2) math:sum 7332}] + [ a r:Fact; r:gives {(7000 300 30 3) math:sum 7333}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; @@ -62670,60 +140159,60 @@ skolem:lemma2617 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2618 a r:Inference; +skolem:lemma5943 a r:Inference; r:gives { - 2338 :numberToDigits (2 3 3 8). + 3338 :numberToDigits (3 3 3 8). }; r:evidence ( - [ a r:Fact; r:gives {(2338 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2338 1000) math:remainder 338}] + [ a r:Fact; r:gives {(3338 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3338 1000) math:remainder 338}] [ a r:Fact; r:gives {(338 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(338 100) math:remainder 38}] [ a r:Fact; r:gives {(38 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(38 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3338]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 338]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 38]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2619 a r:Inference; +skolem:lemma5944 a r:Inference; r:gives { - (2 3 3 8) :digitsToNumber 2338 . + (3 3 3 8) :digitsToNumber 3338 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(2000 300 30 8) math:sum 2338}] + [ a r:Fact; r:gives {(3000 300 30 8) math:sum 3338}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2338]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3338]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2620 a r:Inference; +skolem:lemma5945 a r:Inference; r:gives { - (8 3 3 2) :digitsToNumber 8332 . + (8 3 3 3) :digitsToNumber 8333 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(8000 300 30 2) math:sum 8332}] + [ a r:Fact; r:gives {(8000 300 30 3) math:sum 8333}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; @@ -62731,60 +140220,60 @@ skolem:lemma2620 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2621 a r:Inference; +skolem:lemma5946 a r:Inference; r:gives { - 2339 :numberToDigits (2 3 3 9). + 3339 :numberToDigits (3 3 3 9). }; r:evidence ( - [ a r:Fact; r:gives {(2339 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2339 1000) math:remainder 339}] + [ a r:Fact; r:gives {(3339 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3339 1000) math:remainder 339}] [ a r:Fact; r:gives {(339 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(339 100) math:remainder 39}] [ a r:Fact; r:gives {(39 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(39 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3339]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 339]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 39]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2622 a r:Inference; +skolem:lemma5947 a r:Inference; r:gives { - (2 3 3 9) :digitsToNumber 2339 . + (3 3 3 9) :digitsToNumber 3339 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(2000 300 30 9) math:sum 2339}] + [ a r:Fact; r:gives {(3000 300 30 9) math:sum 3339}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2339]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3339]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2623 a r:Inference; +skolem:lemma5948 a r:Inference; r:gives { - (9 3 3 2) :digitsToNumber 9332 . + (9 3 3 3) :digitsToNumber 9333 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(9000 300 30 2) math:sum 9332}] + [ a r:Fact; r:gives {(9000 300 30 3) math:sum 9333}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -62792,144 +140281,144 @@ skolem:lemma2623 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9332]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9333]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2624 a r:Inference; +skolem:lemma5949 a r:Inference; r:gives { - 2340 :numberToDigits (2 3 4 0). + 3340 :numberToDigits (3 3 4 0). }; r:evidence ( - [ a r:Fact; r:gives {(2340 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2340 1000) math:remainder 340}] + [ a r:Fact; r:gives {(3340 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3340 1000) math:remainder 340}] [ a r:Fact; r:gives {(340 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(340 100) math:remainder 40}] [ a r:Fact; r:gives {(40 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(40 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2340]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3340]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 340]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2625 a r:Inference; +skolem:lemma5950 a r:Inference; r:gives { - 2341 :numberToDigits (2 3 4 1). + 3341 :numberToDigits (3 3 4 1). }; r:evidence ( - [ a r:Fact; r:gives {(2341 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2341 1000) math:remainder 341}] + [ a r:Fact; r:gives {(3341 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3341 1000) math:remainder 341}] [ a r:Fact; r:gives {(341 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(341 100) math:remainder 41}] [ a r:Fact; r:gives {(41 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(41 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2341]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3341]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 341]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 41]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2626 a r:Inference; +skolem:lemma5951 a r:Inference; r:gives { - 2342 :numberToDigits (2 3 4 2). + 3342 :numberToDigits (3 3 4 2). }; r:evidence ( - [ a r:Fact; r:gives {(2342 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2342 1000) math:remainder 342}] + [ a r:Fact; r:gives {(3342 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3342 1000) math:remainder 342}] [ a r:Fact; r:gives {(342 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(342 100) math:remainder 42}] [ a r:Fact; r:gives {(42 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(42 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2342]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3342]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 342]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 42]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2627 a r:Inference; +skolem:lemma5952 a r:Inference; r:gives { - 2343 :numberToDigits (2 3 4 3). + 3343 :numberToDigits (3 3 4 3). }; r:evidence ( - [ a r:Fact; r:gives {(2343 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2343 1000) math:remainder 343}] + [ a r:Fact; r:gives {(3343 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3343 1000) math:remainder 343}] [ a r:Fact; r:gives {(343 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(343 100) math:remainder 43}] [ a r:Fact; r:gives {(43 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(43 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2343]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3343]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 343]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 43]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2628 a r:Inference; +skolem:lemma5953 a r:Inference; r:gives { - 2344 :numberToDigits (2 3 4 4). + 3344 :numberToDigits (3 3 4 4). }; r:evidence ( - [ a r:Fact; r:gives {(2344 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2344 1000) math:remainder 344}] + [ a r:Fact; r:gives {(3344 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3344 1000) math:remainder 344}] [ a r:Fact; r:gives {(344 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(344 100) math:remainder 44}] [ a r:Fact; r:gives {(44 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(44 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3344]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 344]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 44]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2629 a r:Inference; +skolem:lemma5954 a r:Inference; r:gives { - (2 3 4 4) :digitsToNumber 2344 . + (3 3 4 4) :digitsToNumber 3344 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(2000 300 40 4) math:sum 2344}] + [ a r:Fact; r:gives {(3000 300 40 4) math:sum 3344}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2344]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3344]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2630 a r:Inference; +skolem:lemma5955 a r:Inference; r:gives { - (4 4 3 2) :digitsToNumber 4432 . + (4 4 3 3) :digitsToNumber 4433 . }; r:evidence ( [ a r:Fact; r:gives {(4 1000) math:product 4000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(4000 400 30 2) math:sum 4432}] + [ a r:Fact; r:gives {(4000 400 30 3) math:sum 4433}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; @@ -62937,60 +140426,60 @@ skolem:lemma2630 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2631 a r:Inference; +skolem:lemma5956 a r:Inference; r:gives { - 2345 :numberToDigits (2 3 4 5). + 3345 :numberToDigits (3 3 4 5). }; r:evidence ( - [ a r:Fact; r:gives {(2345 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2345 1000) math:remainder 345}] + [ a r:Fact; r:gives {(3345 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3345 1000) math:remainder 345}] [ a r:Fact; r:gives {(345 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(345 100) math:remainder 45}] [ a r:Fact; r:gives {(45 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(45 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3345]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 345]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 45]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2632 a r:Inference; +skolem:lemma5957 a r:Inference; r:gives { - (2 3 4 5) :digitsToNumber 2345 . + (3 3 4 5) :digitsToNumber 3345 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(2000 300 40 5) math:sum 2345}] + [ a r:Fact; r:gives {(3000 300 40 5) math:sum 3345}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2345]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3345]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2633 a r:Inference; +skolem:lemma5958 a r:Inference; r:gives { - (5 4 3 2) :digitsToNumber 5432 . + (5 4 3 3) :digitsToNumber 5433 . }; r:evidence ( [ a r:Fact; r:gives {(5 1000) math:product 5000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(5000 400 30 2) math:sum 5432}] + [ a r:Fact; r:gives {(5000 400 30 3) math:sum 5433}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; @@ -62998,60 +140487,60 @@ skolem:lemma2633 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2634 a r:Inference; +skolem:lemma5959 a r:Inference; r:gives { - 2346 :numberToDigits (2 3 4 6). + 3346 :numberToDigits (3 3 4 6). }; r:evidence ( - [ a r:Fact; r:gives {(2346 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2346 1000) math:remainder 346}] + [ a r:Fact; r:gives {(3346 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3346 1000) math:remainder 346}] [ a r:Fact; r:gives {(346 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(346 100) math:remainder 46}] [ a r:Fact; r:gives {(46 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(46 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3346]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 346]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 46]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2635 a r:Inference; +skolem:lemma5960 a r:Inference; r:gives { - (2 3 4 6) :digitsToNumber 2346 . + (3 3 4 6) :digitsToNumber 3346 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(2000 300 40 6) math:sum 2346}] + [ a r:Fact; r:gives {(3000 300 40 6) math:sum 3346}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2346]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3346]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2636 a r:Inference; +skolem:lemma5961 a r:Inference; r:gives { - (6 4 3 2) :digitsToNumber 6432 . + (6 4 3 3) :digitsToNumber 6433 . }; r:evidence ( [ a r:Fact; r:gives {(6 1000) math:product 6000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(6000 400 30 2) math:sum 6432}] + [ a r:Fact; r:gives {(6000 400 30 3) math:sum 6433}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; @@ -63059,60 +140548,60 @@ skolem:lemma2636 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2637 a r:Inference; +skolem:lemma5962 a r:Inference; r:gives { - 2347 :numberToDigits (2 3 4 7). + 3347 :numberToDigits (3 3 4 7). }; r:evidence ( - [ a r:Fact; r:gives {(2347 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2347 1000) math:remainder 347}] + [ a r:Fact; r:gives {(3347 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3347 1000) math:remainder 347}] [ a r:Fact; r:gives {(347 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(347 100) math:remainder 47}] [ a r:Fact; r:gives {(47 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(47 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3347]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 347]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 47]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2638 a r:Inference; +skolem:lemma5963 a r:Inference; r:gives { - (2 3 4 7) :digitsToNumber 2347 . + (3 3 4 7) :digitsToNumber 3347 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(2000 300 40 7) math:sum 2347}] + [ a r:Fact; r:gives {(3000 300 40 7) math:sum 3347}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2347]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3347]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2639 a r:Inference; +skolem:lemma5964 a r:Inference; r:gives { - (7 4 3 2) :digitsToNumber 7432 . + (7 4 3 3) :digitsToNumber 7433 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(7000 400 30 2) math:sum 7432}] + [ a r:Fact; r:gives {(7000 400 30 3) math:sum 7433}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; @@ -63120,60 +140609,60 @@ skolem:lemma2639 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2640 a r:Inference; +skolem:lemma5965 a r:Inference; r:gives { - 2348 :numberToDigits (2 3 4 8). + 3348 :numberToDigits (3 3 4 8). }; r:evidence ( - [ a r:Fact; r:gives {(2348 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2348 1000) math:remainder 348}] + [ a r:Fact; r:gives {(3348 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3348 1000) math:remainder 348}] [ a r:Fact; r:gives {(348 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(348 100) math:remainder 48}] [ a r:Fact; r:gives {(48 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(48 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3348]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 348]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 48]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2641 a r:Inference; +skolem:lemma5966 a r:Inference; r:gives { - (2 3 4 8) :digitsToNumber 2348 . + (3 3 4 8) :digitsToNumber 3348 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(2000 300 40 8) math:sum 2348}] + [ a r:Fact; r:gives {(3000 300 40 8) math:sum 3348}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2348]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3348]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2642 a r:Inference; +skolem:lemma5967 a r:Inference; r:gives { - (8 4 3 2) :digitsToNumber 8432 . + (8 4 3 3) :digitsToNumber 8433 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(8000 400 30 2) math:sum 8432}] + [ a r:Fact; r:gives {(8000 400 30 3) math:sum 8433}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; @@ -63181,60 +140670,60 @@ skolem:lemma2642 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2643 a r:Inference; +skolem:lemma5968 a r:Inference; r:gives { - 2349 :numberToDigits (2 3 4 9). + 3349 :numberToDigits (3 3 4 9). }; r:evidence ( - [ a r:Fact; r:gives {(2349 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2349 1000) math:remainder 349}] + [ a r:Fact; r:gives {(3349 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3349 1000) math:remainder 349}] [ a r:Fact; r:gives {(349 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(349 100) math:remainder 49}] [ a r:Fact; r:gives {(49 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(49 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3349]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 349]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 49]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2644 a r:Inference; +skolem:lemma5969 a r:Inference; r:gives { - (2 3 4 9) :digitsToNumber 2349 . + (3 3 4 9) :digitsToNumber 3349 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(2000 300 40 9) math:sum 2349}] + [ a r:Fact; r:gives {(3000 300 40 9) math:sum 3349}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2349]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3349]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2645 a r:Inference; +skolem:lemma5970 a r:Inference; r:gives { - (9 4 3 2) :digitsToNumber 9432 . + (9 4 3 3) :digitsToNumber 9433 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(9000 400 30 2) math:sum 9432}] + [ a r:Fact; r:gives {(9000 400 30 3) math:sum 9433}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -63242,165 +140731,165 @@ skolem:lemma2645 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9432]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2646 a r:Inference; +skolem:lemma5971 a r:Inference; r:gives { - 2350 :numberToDigits (2 3 5 0). + 3350 :numberToDigits (3 3 5 0). }; r:evidence ( - [ a r:Fact; r:gives {(2350 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2350 1000) math:remainder 350}] + [ a r:Fact; r:gives {(3350 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3350 1000) math:remainder 350}] [ a r:Fact; r:gives {(350 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(350 100) math:remainder 50}] [ a r:Fact; r:gives {(50 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(50 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2350]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3350]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 350]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2647 a r:Inference; +skolem:lemma5972 a r:Inference; r:gives { - 2351 :numberToDigits (2 3 5 1). + 3351 :numberToDigits (3 3 5 1). }; r:evidence ( - [ a r:Fact; r:gives {(2351 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2351 1000) math:remainder 351}] + [ a r:Fact; r:gives {(3351 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3351 1000) math:remainder 351}] [ a r:Fact; r:gives {(351 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(351 100) math:remainder 51}] [ a r:Fact; r:gives {(51 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(51 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2351]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3351]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 351]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 51]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2648 a r:Inference; +skolem:lemma5973 a r:Inference; r:gives { - 2352 :numberToDigits (2 3 5 2). + 3352 :numberToDigits (3 3 5 2). }; r:evidence ( - [ a r:Fact; r:gives {(2352 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2352 1000) math:remainder 352}] + [ a r:Fact; r:gives {(3352 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3352 1000) math:remainder 352}] [ a r:Fact; r:gives {(352 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(352 100) math:remainder 52}] [ a r:Fact; r:gives {(52 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(52 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2352]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3352]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 352]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 52]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2649 a r:Inference; +skolem:lemma5974 a r:Inference; r:gives { - 2353 :numberToDigits (2 3 5 3). + 3353 :numberToDigits (3 3 5 3). }; r:evidence ( - [ a r:Fact; r:gives {(2353 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2353 1000) math:remainder 353}] + [ a r:Fact; r:gives {(3353 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3353 1000) math:remainder 353}] [ a r:Fact; r:gives {(353 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(353 100) math:remainder 53}] [ a r:Fact; r:gives {(53 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(53 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2353]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3353]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 353]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 53]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2650 a r:Inference; +skolem:lemma5975 a r:Inference; r:gives { - 2354 :numberToDigits (2 3 5 4). + 3354 :numberToDigits (3 3 5 4). }; r:evidence ( - [ a r:Fact; r:gives {(2354 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2354 1000) math:remainder 354}] + [ a r:Fact; r:gives {(3354 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3354 1000) math:remainder 354}] [ a r:Fact; r:gives {(354 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(354 100) math:remainder 54}] [ a r:Fact; r:gives {(54 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(54 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2354]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3354]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 354]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 54]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2651 a r:Inference; +skolem:lemma5976 a r:Inference; r:gives { - 2355 :numberToDigits (2 3 5 5). + 3355 :numberToDigits (3 3 5 5). }; r:evidence ( - [ a r:Fact; r:gives {(2355 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2355 1000) math:remainder 355}] + [ a r:Fact; r:gives {(3355 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3355 1000) math:remainder 355}] [ a r:Fact; r:gives {(355 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(355 100) math:remainder 55}] [ a r:Fact; r:gives {(55 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(55 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3355]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 355]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 55]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2652 a r:Inference; +skolem:lemma5977 a r:Inference; r:gives { - (2 3 5 5) :digitsToNumber 2355 . + (3 3 5 5) :digitsToNumber 3355 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(2000 300 50 5) math:sum 2355}] + [ a r:Fact; r:gives {(3000 300 50 5) math:sum 3355}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2355]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3355]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2653 a r:Inference; +skolem:lemma5978 a r:Inference; r:gives { - (5 5 3 2) :digitsToNumber 5532 . + (5 5 3 3) :digitsToNumber 5533 . }; r:evidence ( [ a r:Fact; r:gives {(5 1000) math:product 5000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(5000 500 30 2) math:sum 5532}] + [ a r:Fact; r:gives {(5000 500 30 3) math:sum 5533}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; @@ -63408,60 +140897,60 @@ skolem:lemma2653 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2654 a r:Inference; +skolem:lemma5979 a r:Inference; r:gives { - 2356 :numberToDigits (2 3 5 6). + 3356 :numberToDigits (3 3 5 6). }; r:evidence ( - [ a r:Fact; r:gives {(2356 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2356 1000) math:remainder 356}] + [ a r:Fact; r:gives {(3356 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3356 1000) math:remainder 356}] [ a r:Fact; r:gives {(356 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(356 100) math:remainder 56}] [ a r:Fact; r:gives {(56 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(56 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3356]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 356]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 56]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2655 a r:Inference; +skolem:lemma5980 a r:Inference; r:gives { - (2 3 5 6) :digitsToNumber 2356 . + (3 3 5 6) :digitsToNumber 3356 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(2000 300 50 6) math:sum 2356}] + [ a r:Fact; r:gives {(3000 300 50 6) math:sum 3356}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2356]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3356]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2656 a r:Inference; +skolem:lemma5981 a r:Inference; r:gives { - (6 5 3 2) :digitsToNumber 6532 . + (6 5 3 3) :digitsToNumber 6533 . }; r:evidence ( [ a r:Fact; r:gives {(6 1000) math:product 6000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(6000 500 30 2) math:sum 6532}] + [ a r:Fact; r:gives {(6000 500 30 3) math:sum 6533}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; @@ -63469,60 +140958,60 @@ skolem:lemma2656 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2657 a r:Inference; +skolem:lemma5982 a r:Inference; r:gives { - 2357 :numberToDigits (2 3 5 7). + 3357 :numberToDigits (3 3 5 7). }; r:evidence ( - [ a r:Fact; r:gives {(2357 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2357 1000) math:remainder 357}] + [ a r:Fact; r:gives {(3357 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3357 1000) math:remainder 357}] [ a r:Fact; r:gives {(357 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(357 100) math:remainder 57}] [ a r:Fact; r:gives {(57 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(57 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3357]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 357]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 57]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2658 a r:Inference; +skolem:lemma5983 a r:Inference; r:gives { - (2 3 5 7) :digitsToNumber 2357 . + (3 3 5 7) :digitsToNumber 3357 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(2000 300 50 7) math:sum 2357}] + [ a r:Fact; r:gives {(3000 300 50 7) math:sum 3357}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2357]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3357]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2659 a r:Inference; +skolem:lemma5984 a r:Inference; r:gives { - (7 5 3 2) :digitsToNumber 7532 . + (7 5 3 3) :digitsToNumber 7533 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(7000 500 30 2) math:sum 7532}] + [ a r:Fact; r:gives {(7000 500 30 3) math:sum 7533}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; @@ -63530,60 +141019,60 @@ skolem:lemma2659 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2660 a r:Inference; +skolem:lemma5985 a r:Inference; r:gives { - 2358 :numberToDigits (2 3 5 8). + 3358 :numberToDigits (3 3 5 8). }; r:evidence ( - [ a r:Fact; r:gives {(2358 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2358 1000) math:remainder 358}] + [ a r:Fact; r:gives {(3358 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3358 1000) math:remainder 358}] [ a r:Fact; r:gives {(358 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(358 100) math:remainder 58}] [ a r:Fact; r:gives {(58 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(58 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3358]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 358]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 58]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2661 a r:Inference; +skolem:lemma5986 a r:Inference; r:gives { - (2 3 5 8) :digitsToNumber 2358 . + (3 3 5 8) :digitsToNumber 3358 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(2000 300 50 8) math:sum 2358}] + [ a r:Fact; r:gives {(3000 300 50 8) math:sum 3358}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2358]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3358]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2662 a r:Inference; +skolem:lemma5987 a r:Inference; r:gives { - (8 5 3 2) :digitsToNumber 8532 . + (8 5 3 3) :digitsToNumber 8533 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(8000 500 30 2) math:sum 8532}] + [ a r:Fact; r:gives {(8000 500 30 3) math:sum 8533}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; @@ -63591,60 +141080,60 @@ skolem:lemma2662 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2663 a r:Inference; +skolem:lemma5988 a r:Inference; r:gives { - 2359 :numberToDigits (2 3 5 9). + 3359 :numberToDigits (3 3 5 9). }; r:evidence ( - [ a r:Fact; r:gives {(2359 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2359 1000) math:remainder 359}] + [ a r:Fact; r:gives {(3359 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3359 1000) math:remainder 359}] [ a r:Fact; r:gives {(359 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(359 100) math:remainder 59}] [ a r:Fact; r:gives {(59 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(59 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3359]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 359]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 59]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2664 a r:Inference; +skolem:lemma5989 a r:Inference; r:gives { - (2 3 5 9) :digitsToNumber 2359 . + (3 3 5 9) :digitsToNumber 3359 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(2000 300 50 9) math:sum 2359}] + [ a r:Fact; r:gives {(3000 300 50 9) math:sum 3359}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2359]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3359]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2665 a r:Inference; +skolem:lemma5990 a r:Inference; r:gives { - (9 5 3 2) :digitsToNumber 9532 . + (9 5 3 3) :digitsToNumber 9533 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(9000 500 30 2) math:sum 9532}] + [ a r:Fact; r:gives {(9000 500 30 3) math:sum 9533}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -63652,186 +141141,186 @@ skolem:lemma2665 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9532]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2666 a r:Inference; +skolem:lemma5991 a r:Inference; r:gives { - 2360 :numberToDigits (2 3 6 0). + 3360 :numberToDigits (3 3 6 0). }; r:evidence ( - [ a r:Fact; r:gives {(2360 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2360 1000) math:remainder 360}] + [ a r:Fact; r:gives {(3360 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3360 1000) math:remainder 360}] [ a r:Fact; r:gives {(360 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(360 100) math:remainder 60}] [ a r:Fact; r:gives {(60 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(60 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2360]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3360]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 360]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2667 a r:Inference; +skolem:lemma5992 a r:Inference; r:gives { - 2361 :numberToDigits (2 3 6 1). + 3361 :numberToDigits (3 3 6 1). }; r:evidence ( - [ a r:Fact; r:gives {(2361 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2361 1000) math:remainder 361}] + [ a r:Fact; r:gives {(3361 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3361 1000) math:remainder 361}] [ a r:Fact; r:gives {(361 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(361 100) math:remainder 61}] [ a r:Fact; r:gives {(61 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(61 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2361]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3361]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 361]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 61]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2668 a r:Inference; +skolem:lemma5993 a r:Inference; r:gives { - 2362 :numberToDigits (2 3 6 2). + 3362 :numberToDigits (3 3 6 2). }; r:evidence ( - [ a r:Fact; r:gives {(2362 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2362 1000) math:remainder 362}] + [ a r:Fact; r:gives {(3362 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3362 1000) math:remainder 362}] [ a r:Fact; r:gives {(362 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(362 100) math:remainder 62}] [ a r:Fact; r:gives {(62 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(62 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2362]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3362]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 362]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 62]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2669 a r:Inference; +skolem:lemma5994 a r:Inference; r:gives { - 2363 :numberToDigits (2 3 6 3). + 3363 :numberToDigits (3 3 6 3). }; r:evidence ( - [ a r:Fact; r:gives {(2363 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2363 1000) math:remainder 363}] + [ a r:Fact; r:gives {(3363 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3363 1000) math:remainder 363}] [ a r:Fact; r:gives {(363 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(363 100) math:remainder 63}] [ a r:Fact; r:gives {(63 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(63 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2363]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3363]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 363]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 63]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2670 a r:Inference; +skolem:lemma5995 a r:Inference; r:gives { - 2364 :numberToDigits (2 3 6 4). + 3364 :numberToDigits (3 3 6 4). }; r:evidence ( - [ a r:Fact; r:gives {(2364 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2364 1000) math:remainder 364}] + [ a r:Fact; r:gives {(3364 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3364 1000) math:remainder 364}] [ a r:Fact; r:gives {(364 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(364 100) math:remainder 64}] [ a r:Fact; r:gives {(64 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(64 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2364]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3364]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 364]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 64]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2671 a r:Inference; +skolem:lemma5996 a r:Inference; r:gives { - 2365 :numberToDigits (2 3 6 5). + 3365 :numberToDigits (3 3 6 5). }; r:evidence ( - [ a r:Fact; r:gives {(2365 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2365 1000) math:remainder 365}] + [ a r:Fact; r:gives {(3365 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3365 1000) math:remainder 365}] [ a r:Fact; r:gives {(365 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(365 100) math:remainder 65}] [ a r:Fact; r:gives {(65 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(65 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2365]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3365]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 365]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 65]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2672 a r:Inference; +skolem:lemma5997 a r:Inference; r:gives { - 2366 :numberToDigits (2 3 6 6). + 3366 :numberToDigits (3 3 6 6). }; r:evidence ( - [ a r:Fact; r:gives {(2366 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2366 1000) math:remainder 366}] + [ a r:Fact; r:gives {(3366 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3366 1000) math:remainder 366}] [ a r:Fact; r:gives {(366 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(366 100) math:remainder 66}] [ a r:Fact; r:gives {(66 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(66 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3366]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 366]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 66]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2673 a r:Inference; +skolem:lemma5998 a r:Inference; r:gives { - (2 3 6 6) :digitsToNumber 2366 . + (3 3 6 6) :digitsToNumber 3366 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(2000 300 60 6) math:sum 2366}] + [ a r:Fact; r:gives {(3000 300 60 6) math:sum 3366}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2366]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3366]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2674 a r:Inference; +skolem:lemma5999 a r:Inference; r:gives { - (6 6 3 2) :digitsToNumber 6632 . + (6 6 3 3) :digitsToNumber 6633 . }; r:evidence ( [ a r:Fact; r:gives {(6 1000) math:product 6000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(6000 600 30 2) math:sum 6632}] + [ a r:Fact; r:gives {(6000 600 30 3) math:sum 6633}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; @@ -63839,60 +141328,60 @@ skolem:lemma2674 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2675 a r:Inference; +skolem:lemma6000 a r:Inference; r:gives { - 2367 :numberToDigits (2 3 6 7). + 3367 :numberToDigits (3 3 6 7). }; r:evidence ( - [ a r:Fact; r:gives {(2367 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2367 1000) math:remainder 367}] + [ a r:Fact; r:gives {(3367 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3367 1000) math:remainder 367}] [ a r:Fact; r:gives {(367 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(367 100) math:remainder 67}] [ a r:Fact; r:gives {(67 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(67 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3367]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 367]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 67]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2676 a r:Inference; +skolem:lemma6001 a r:Inference; r:gives { - (2 3 6 7) :digitsToNumber 2367 . + (3 3 6 7) :digitsToNumber 3367 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(2000 300 60 7) math:sum 2367}] + [ a r:Fact; r:gives {(3000 300 60 7) math:sum 3367}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2367]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3367]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2677 a r:Inference; +skolem:lemma6002 a r:Inference; r:gives { - (7 6 3 2) :digitsToNumber 7632 . + (7 6 3 3) :digitsToNumber 7633 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(7000 600 30 2) math:sum 7632}] + [ a r:Fact; r:gives {(7000 600 30 3) math:sum 7633}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; @@ -63900,60 +141389,60 @@ skolem:lemma2677 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2678 a r:Inference; +skolem:lemma6003 a r:Inference; r:gives { - 2368 :numberToDigits (2 3 6 8). + 3368 :numberToDigits (3 3 6 8). }; r:evidence ( - [ a r:Fact; r:gives {(2368 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2368 1000) math:remainder 368}] + [ a r:Fact; r:gives {(3368 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3368 1000) math:remainder 368}] [ a r:Fact; r:gives {(368 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(368 100) math:remainder 68}] [ a r:Fact; r:gives {(68 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(68 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3368]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 368]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 68]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2679 a r:Inference; +skolem:lemma6004 a r:Inference; r:gives { - (2 3 6 8) :digitsToNumber 2368 . + (3 3 6 8) :digitsToNumber 3368 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(2000 300 60 8) math:sum 2368}] + [ a r:Fact; r:gives {(3000 300 60 8) math:sum 3368}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2368]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3368]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2680 a r:Inference; +skolem:lemma6005 a r:Inference; r:gives { - (8 6 3 2) :digitsToNumber 8632 . + (8 6 3 3) :digitsToNumber 8633 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(8000 600 30 2) math:sum 8632}] + [ a r:Fact; r:gives {(8000 600 30 3) math:sum 8633}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; @@ -63961,60 +141450,60 @@ skolem:lemma2680 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2681 a r:Inference; +skolem:lemma6006 a r:Inference; r:gives { - 2369 :numberToDigits (2 3 6 9). + 3369 :numberToDigits (3 3 6 9). }; r:evidence ( - [ a r:Fact; r:gives {(2369 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2369 1000) math:remainder 369}] + [ a r:Fact; r:gives {(3369 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3369 1000) math:remainder 369}] [ a r:Fact; r:gives {(369 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(369 100) math:remainder 69}] [ a r:Fact; r:gives {(69 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(69 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3369]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 369]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 69]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2682 a r:Inference; +skolem:lemma6007 a r:Inference; r:gives { - (2 3 6 9) :digitsToNumber 2369 . + (3 3 6 9) :digitsToNumber 3369 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(2000 300 60 9) math:sum 2369}] + [ a r:Fact; r:gives {(3000 300 60 9) math:sum 3369}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2369]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3369]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2683 a r:Inference; +skolem:lemma6008 a r:Inference; r:gives { - (9 6 3 2) :digitsToNumber 9632 . + (9 6 3 3) :digitsToNumber 9633 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(9000 600 30 2) math:sum 9632}] + [ a r:Fact; r:gives {(9000 600 30 3) math:sum 9633}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -64022,207 +141511,207 @@ skolem:lemma2683 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9632]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2684 a r:Inference; +skolem:lemma6009 a r:Inference; r:gives { - 2370 :numberToDigits (2 3 7 0). + 3370 :numberToDigits (3 3 7 0). }; r:evidence ( - [ a r:Fact; r:gives {(2370 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2370 1000) math:remainder 370}] + [ a r:Fact; r:gives {(3370 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3370 1000) math:remainder 370}] [ a r:Fact; r:gives {(370 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(370 100) math:remainder 70}] [ a r:Fact; r:gives {(70 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(70 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2370]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3370]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 370]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2685 a r:Inference; +skolem:lemma6010 a r:Inference; r:gives { - 2371 :numberToDigits (2 3 7 1). + 3371 :numberToDigits (3 3 7 1). }; r:evidence ( - [ a r:Fact; r:gives {(2371 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2371 1000) math:remainder 371}] + [ a r:Fact; r:gives {(3371 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3371 1000) math:remainder 371}] [ a r:Fact; r:gives {(371 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(371 100) math:remainder 71}] [ a r:Fact; r:gives {(71 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(71 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2371]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3371]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 371]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 71]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2686 a r:Inference; +skolem:lemma6011 a r:Inference; r:gives { - 2372 :numberToDigits (2 3 7 2). + 3372 :numberToDigits (3 3 7 2). }; r:evidence ( - [ a r:Fact; r:gives {(2372 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2372 1000) math:remainder 372}] + [ a r:Fact; r:gives {(3372 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3372 1000) math:remainder 372}] [ a r:Fact; r:gives {(372 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(372 100) math:remainder 72}] [ a r:Fact; r:gives {(72 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(72 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2372]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3372]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 372]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 72]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2687 a r:Inference; +skolem:lemma6012 a r:Inference; r:gives { - 2373 :numberToDigits (2 3 7 3). + 3373 :numberToDigits (3 3 7 3). }; r:evidence ( - [ a r:Fact; r:gives {(2373 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2373 1000) math:remainder 373}] + [ a r:Fact; r:gives {(3373 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3373 1000) math:remainder 373}] [ a r:Fact; r:gives {(373 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(373 100) math:remainder 73}] [ a r:Fact; r:gives {(73 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(73 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2373]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3373]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 373]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 73]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2688 a r:Inference; +skolem:lemma6013 a r:Inference; r:gives { - 2374 :numberToDigits (2 3 7 4). + 3374 :numberToDigits (3 3 7 4). }; r:evidence ( - [ a r:Fact; r:gives {(2374 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2374 1000) math:remainder 374}] + [ a r:Fact; r:gives {(3374 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3374 1000) math:remainder 374}] [ a r:Fact; r:gives {(374 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(374 100) math:remainder 74}] [ a r:Fact; r:gives {(74 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(74 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2374]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3374]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 374]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 74]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2689 a r:Inference; +skolem:lemma6014 a r:Inference; r:gives { - 2375 :numberToDigits (2 3 7 5). + 3375 :numberToDigits (3 3 7 5). }; r:evidence ( - [ a r:Fact; r:gives {(2375 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2375 1000) math:remainder 375}] + [ a r:Fact; r:gives {(3375 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3375 1000) math:remainder 375}] [ a r:Fact; r:gives {(375 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(375 100) math:remainder 75}] [ a r:Fact; r:gives {(75 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(75 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2375]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3375]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 375]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 75]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2690 a r:Inference; +skolem:lemma6015 a r:Inference; r:gives { - 2376 :numberToDigits (2 3 7 6). + 3376 :numberToDigits (3 3 7 6). }; r:evidence ( - [ a r:Fact; r:gives {(2376 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2376 1000) math:remainder 376}] + [ a r:Fact; r:gives {(3376 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3376 1000) math:remainder 376}] [ a r:Fact; r:gives {(376 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(376 100) math:remainder 76}] [ a r:Fact; r:gives {(76 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(76 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2376]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3376]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 376]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 76]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2691 a r:Inference; +skolem:lemma6016 a r:Inference; r:gives { - 2377 :numberToDigits (2 3 7 7). + 3377 :numberToDigits (3 3 7 7). }; r:evidence ( - [ a r:Fact; r:gives {(2377 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2377 1000) math:remainder 377}] + [ a r:Fact; r:gives {(3377 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3377 1000) math:remainder 377}] [ a r:Fact; r:gives {(377 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(377 100) math:remainder 77}] [ a r:Fact; r:gives {(77 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(77 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3377]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 377]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 77]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2692 a r:Inference; +skolem:lemma6017 a r:Inference; r:gives { - (2 3 7 7) :digitsToNumber 2377 . + (3 3 7 7) :digitsToNumber 3377 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(2000 300 70 7) math:sum 2377}] + [ a r:Fact; r:gives {(3000 300 70 7) math:sum 3377}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2377]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3377]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2693 a r:Inference; +skolem:lemma6018 a r:Inference; r:gives { - (7 7 3 2) :digitsToNumber 7732 . + (7 7 3 3) :digitsToNumber 7733 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(7 100) math:product 700}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(7000 700 30 2) math:sum 7732}] + [ a r:Fact; r:gives {(7000 700 30 3) math:sum 7733}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; @@ -64230,60 +141719,60 @@ skolem:lemma2693 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7732]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2694 a r:Inference; +skolem:lemma6019 a r:Inference; r:gives { - 2378 :numberToDigits (2 3 7 8). + 3378 :numberToDigits (3 3 7 8). }; r:evidence ( - [ a r:Fact; r:gives {(2378 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2378 1000) math:remainder 378}] + [ a r:Fact; r:gives {(3378 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3378 1000) math:remainder 378}] [ a r:Fact; r:gives {(378 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(378 100) math:remainder 78}] [ a r:Fact; r:gives {(78 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(78 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3378]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 378]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 78]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2695 a r:Inference; +skolem:lemma6020 a r:Inference; r:gives { - (2 3 7 8) :digitsToNumber 2378 . + (3 3 7 8) :digitsToNumber 3378 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(2000 300 70 8) math:sum 2378}] + [ a r:Fact; r:gives {(3000 300 70 8) math:sum 3378}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2378]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3378]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2696 a r:Inference; +skolem:lemma6021 a r:Inference; r:gives { - (8 7 3 2) :digitsToNumber 8732 . + (8 7 3 3) :digitsToNumber 8733 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(7 100) math:product 700}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(8000 700 30 2) math:sum 8732}] + [ a r:Fact; r:gives {(8000 700 30 3) math:sum 8733}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; @@ -64291,60 +141780,60 @@ skolem:lemma2696 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8732]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2697 a r:Inference; +skolem:lemma6022 a r:Inference; r:gives { - 2379 :numberToDigits (2 3 7 9). + 3379 :numberToDigits (3 3 7 9). }; r:evidence ( - [ a r:Fact; r:gives {(2379 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2379 1000) math:remainder 379}] + [ a r:Fact; r:gives {(3379 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3379 1000) math:remainder 379}] [ a r:Fact; r:gives {(379 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(379 100) math:remainder 79}] [ a r:Fact; r:gives {(79 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(79 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3379]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 379]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 79]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2698 a r:Inference; +skolem:lemma6023 a r:Inference; r:gives { - (2 3 7 9) :digitsToNumber 2379 . + (3 3 7 9) :digitsToNumber 3379 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(2000 300 70 9) math:sum 2379}] + [ a r:Fact; r:gives {(3000 300 70 9) math:sum 3379}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2379]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3379]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2699 a r:Inference; +skolem:lemma6024 a r:Inference; r:gives { - (9 7 3 2) :digitsToNumber 9732 . + (9 7 3 3) :digitsToNumber 9733 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(7 100) math:product 700}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(9000 700 30 2) math:sum 9732}] + [ a r:Fact; r:gives {(9000 700 30 3) math:sum 9733}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -64352,228 +141841,228 @@ skolem:lemma2699 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9732]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2700 a r:Inference; +skolem:lemma6025 a r:Inference; r:gives { - 2380 :numberToDigits (2 3 8 0). + 3380 :numberToDigits (3 3 8 0). }; r:evidence ( - [ a r:Fact; r:gives {(2380 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2380 1000) math:remainder 380}] + [ a r:Fact; r:gives {(3380 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3380 1000) math:remainder 380}] [ a r:Fact; r:gives {(380 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(380 100) math:remainder 80}] [ a r:Fact; r:gives {(80 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(80 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2380]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3380]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 380]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2701 a r:Inference; +skolem:lemma6026 a r:Inference; r:gives { - 2381 :numberToDigits (2 3 8 1). + 3381 :numberToDigits (3 3 8 1). }; r:evidence ( - [ a r:Fact; r:gives {(2381 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2381 1000) math:remainder 381}] + [ a r:Fact; r:gives {(3381 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3381 1000) math:remainder 381}] [ a r:Fact; r:gives {(381 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(381 100) math:remainder 81}] [ a r:Fact; r:gives {(81 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(81 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2381]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3381]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 381]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 81]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2702 a r:Inference; +skolem:lemma6027 a r:Inference; r:gives { - 2382 :numberToDigits (2 3 8 2). + 3382 :numberToDigits (3 3 8 2). }; r:evidence ( - [ a r:Fact; r:gives {(2382 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2382 1000) math:remainder 382}] + [ a r:Fact; r:gives {(3382 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3382 1000) math:remainder 382}] [ a r:Fact; r:gives {(382 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(382 100) math:remainder 82}] [ a r:Fact; r:gives {(82 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(82 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2382]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3382]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 382]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 82]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2703 a r:Inference; +skolem:lemma6028 a r:Inference; r:gives { - 2383 :numberToDigits (2 3 8 3). + 3383 :numberToDigits (3 3 8 3). }; r:evidence ( - [ a r:Fact; r:gives {(2383 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2383 1000) math:remainder 383}] + [ a r:Fact; r:gives {(3383 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3383 1000) math:remainder 383}] [ a r:Fact; r:gives {(383 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(383 100) math:remainder 83}] [ a r:Fact; r:gives {(83 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(83 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2383]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3383]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 383]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 83]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2704 a r:Inference; +skolem:lemma6029 a r:Inference; r:gives { - 2384 :numberToDigits (2 3 8 4). + 3384 :numberToDigits (3 3 8 4). }; r:evidence ( - [ a r:Fact; r:gives {(2384 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2384 1000) math:remainder 384}] + [ a r:Fact; r:gives {(3384 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3384 1000) math:remainder 384}] [ a r:Fact; r:gives {(384 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(384 100) math:remainder 84}] [ a r:Fact; r:gives {(84 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(84 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2384]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3384]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 384]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 84]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2705 a r:Inference; +skolem:lemma6030 a r:Inference; r:gives { - 2385 :numberToDigits (2 3 8 5). + 3385 :numberToDigits (3 3 8 5). }; r:evidence ( - [ a r:Fact; r:gives {(2385 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2385 1000) math:remainder 385}] + [ a r:Fact; r:gives {(3385 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3385 1000) math:remainder 385}] [ a r:Fact; r:gives {(385 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(385 100) math:remainder 85}] [ a r:Fact; r:gives {(85 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(85 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2385]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3385]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 385]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 85]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2706 a r:Inference; +skolem:lemma6031 a r:Inference; r:gives { - 2386 :numberToDigits (2 3 8 6). + 3386 :numberToDigits (3 3 8 6). }; r:evidence ( - [ a r:Fact; r:gives {(2386 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2386 1000) math:remainder 386}] + [ a r:Fact; r:gives {(3386 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3386 1000) math:remainder 386}] [ a r:Fact; r:gives {(386 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(386 100) math:remainder 86}] [ a r:Fact; r:gives {(86 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(86 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2386]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3386]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 386]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 86]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2707 a r:Inference; +skolem:lemma6032 a r:Inference; r:gives { - 2387 :numberToDigits (2 3 8 7). + 3387 :numberToDigits (3 3 8 7). }; r:evidence ( - [ a r:Fact; r:gives {(2387 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2387 1000) math:remainder 387}] + [ a r:Fact; r:gives {(3387 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3387 1000) math:remainder 387}] [ a r:Fact; r:gives {(387 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(387 100) math:remainder 87}] [ a r:Fact; r:gives {(87 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(87 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2387]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3387]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 387]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 87]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2708 a r:Inference; +skolem:lemma6033 a r:Inference; r:gives { - 2388 :numberToDigits (2 3 8 8). + 3388 :numberToDigits (3 3 8 8). }; r:evidence ( - [ a r:Fact; r:gives {(2388 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2388 1000) math:remainder 388}] + [ a r:Fact; r:gives {(3388 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3388 1000) math:remainder 388}] [ a r:Fact; r:gives {(388 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(388 100) math:remainder 88}] [ a r:Fact; r:gives {(88 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(88 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3388]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 388]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 88]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2709 a r:Inference; +skolem:lemma6034 a r:Inference; r:gives { - (2 3 8 8) :digitsToNumber 2388 . + (3 3 8 8) :digitsToNumber 3388 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(8 10) math:product 80}] - [ a r:Fact; r:gives {(2000 300 80 8) math:sum 2388}] + [ a r:Fact; r:gives {(3000 300 80 8) math:sum 3388}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2388]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3388]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2710 a r:Inference; +skolem:lemma6035 a r:Inference; r:gives { - (8 8 3 2) :digitsToNumber 8832 . + (8 8 3 3) :digitsToNumber 8833 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(8 100) math:product 800}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(8000 800 30 2) math:sum 8832}] + [ a r:Fact; r:gives {(8000 800 30 3) math:sum 8833}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; @@ -64581,60 +142070,60 @@ skolem:lemma2710 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8832]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8833]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2711 a r:Inference; +skolem:lemma6036 a r:Inference; r:gives { - 2389 :numberToDigits (2 3 8 9). + 3389 :numberToDigits (3 3 8 9). }; r:evidence ( - [ a r:Fact; r:gives {(2389 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2389 1000) math:remainder 389}] + [ a r:Fact; r:gives {(3389 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3389 1000) math:remainder 389}] [ a r:Fact; r:gives {(389 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(389 100) math:remainder 89}] [ a r:Fact; r:gives {(89 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(89 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3389]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 389]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 89]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2712 a r:Inference; +skolem:lemma6037 a r:Inference; r:gives { - (2 3 8 9) :digitsToNumber 2389 . + (3 3 8 9) :digitsToNumber 3389 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(8 10) math:product 80}] - [ a r:Fact; r:gives {(2000 300 80 9) math:sum 2389}] + [ a r:Fact; r:gives {(3000 300 80 9) math:sum 3389}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2389]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3389]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2713 a r:Inference; +skolem:lemma6038 a r:Inference; r:gives { - (9 8 3 2) :digitsToNumber 9832 . + (9 8 3 3) :digitsToNumber 9833 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(8 100) math:product 800}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(9000 800 30 2) math:sum 9832}] + [ a r:Fact; r:gives {(9000 800 30 3) math:sum 9833}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -64642,249 +142131,249 @@ skolem:lemma2713 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9832]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9833]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2714 a r:Inference; +skolem:lemma6039 a r:Inference; r:gives { - 2390 :numberToDigits (2 3 9 0). + 3390 :numberToDigits (3 3 9 0). }; r:evidence ( - [ a r:Fact; r:gives {(2390 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2390 1000) math:remainder 390}] + [ a r:Fact; r:gives {(3390 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3390 1000) math:remainder 390}] [ a r:Fact; r:gives {(390 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(390 100) math:remainder 90}] [ a r:Fact; r:gives {(90 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(90 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2390]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3390]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 390]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 90]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2715 a r:Inference; +skolem:lemma6040 a r:Inference; r:gives { - 2391 :numberToDigits (2 3 9 1). + 3391 :numberToDigits (3 3 9 1). }; r:evidence ( - [ a r:Fact; r:gives {(2391 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2391 1000) math:remainder 391}] + [ a r:Fact; r:gives {(3391 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3391 1000) math:remainder 391}] [ a r:Fact; r:gives {(391 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(391 100) math:remainder 91}] [ a r:Fact; r:gives {(91 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(91 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2391]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3391]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 391]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 91]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2716 a r:Inference; +skolem:lemma6041 a r:Inference; r:gives { - 2392 :numberToDigits (2 3 9 2). + 3392 :numberToDigits (3 3 9 2). }; r:evidence ( - [ a r:Fact; r:gives {(2392 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2392 1000) math:remainder 392}] + [ a r:Fact; r:gives {(3392 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3392 1000) math:remainder 392}] [ a r:Fact; r:gives {(392 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(392 100) math:remainder 92}] [ a r:Fact; r:gives {(92 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(92 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2392]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3392]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 392]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 92]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2717 a r:Inference; +skolem:lemma6042 a r:Inference; r:gives { - 2393 :numberToDigits (2 3 9 3). + 3393 :numberToDigits (3 3 9 3). }; r:evidence ( - [ a r:Fact; r:gives {(2393 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2393 1000) math:remainder 393}] + [ a r:Fact; r:gives {(3393 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3393 1000) math:remainder 393}] [ a r:Fact; r:gives {(393 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(393 100) math:remainder 93}] [ a r:Fact; r:gives {(93 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(93 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2393]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3393]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 393]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 93]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2718 a r:Inference; +skolem:lemma6043 a r:Inference; r:gives { - 2394 :numberToDigits (2 3 9 4). + 3394 :numberToDigits (3 3 9 4). }; r:evidence ( - [ a r:Fact; r:gives {(2394 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2394 1000) math:remainder 394}] + [ a r:Fact; r:gives {(3394 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3394 1000) math:remainder 394}] [ a r:Fact; r:gives {(394 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(394 100) math:remainder 94}] [ a r:Fact; r:gives {(94 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(94 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2394]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3394]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 394]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 94]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2719 a r:Inference; +skolem:lemma6044 a r:Inference; r:gives { - 2395 :numberToDigits (2 3 9 5). + 3395 :numberToDigits (3 3 9 5). }; r:evidence ( - [ a r:Fact; r:gives {(2395 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2395 1000) math:remainder 395}] + [ a r:Fact; r:gives {(3395 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3395 1000) math:remainder 395}] [ a r:Fact; r:gives {(395 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(395 100) math:remainder 95}] [ a r:Fact; r:gives {(95 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(95 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2395]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3395]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 395]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 95]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2720 a r:Inference; +skolem:lemma6045 a r:Inference; r:gives { - 2396 :numberToDigits (2 3 9 6). + 3396 :numberToDigits (3 3 9 6). }; r:evidence ( - [ a r:Fact; r:gives {(2396 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2396 1000) math:remainder 396}] + [ a r:Fact; r:gives {(3396 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3396 1000) math:remainder 396}] [ a r:Fact; r:gives {(396 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(396 100) math:remainder 96}] [ a r:Fact; r:gives {(96 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(96 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2396]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3396]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 396]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 96]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2721 a r:Inference; +skolem:lemma6046 a r:Inference; r:gives { - 2397 :numberToDigits (2 3 9 7). + 3397 :numberToDigits (3 3 9 7). }; r:evidence ( - [ a r:Fact; r:gives {(2397 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2397 1000) math:remainder 397}] + [ a r:Fact; r:gives {(3397 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3397 1000) math:remainder 397}] [ a r:Fact; r:gives {(397 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(397 100) math:remainder 97}] [ a r:Fact; r:gives {(97 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(97 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2397]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3397]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 397]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 97]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2722 a r:Inference; +skolem:lemma6047 a r:Inference; r:gives { - 2398 :numberToDigits (2 3 9 8). + 3398 :numberToDigits (3 3 9 8). }; r:evidence ( - [ a r:Fact; r:gives {(2398 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2398 1000) math:remainder 398}] + [ a r:Fact; r:gives {(3398 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3398 1000) math:remainder 398}] [ a r:Fact; r:gives {(398 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(398 100) math:remainder 98}] [ a r:Fact; r:gives {(98 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(98 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2398]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3398]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 398]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 98]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2723 a r:Inference; +skolem:lemma6048 a r:Inference; r:gives { - 2399 :numberToDigits (2 3 9 9). + 3399 :numberToDigits (3 3 9 9). }; r:evidence ( - [ a r:Fact; r:gives {(2399 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2399 1000) math:remainder 399}] + [ a r:Fact; r:gives {(3399 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3399 1000) math:remainder 399}] [ a r:Fact; r:gives {(399 100) math:integerQuotient 3}] [ a r:Fact; r:gives {(399 100) math:remainder 99}] [ a r:Fact; r:gives {(99 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(99 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3399]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 399]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 99]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2724 a r:Inference; +skolem:lemma6049 a r:Inference; r:gives { - (2 3 9 9) :digitsToNumber 2399 . + (3 3 9 9) :digitsToNumber 3399 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(3 100) math:product 300}] [ a r:Fact; r:gives {(9 10) math:product 90}] - [ a r:Fact; r:gives {(2000 300 90 9) math:sum 2399}] + [ a r:Fact; r:gives {(3000 300 90 9) math:sum 3399}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 300]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 90]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2399]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3399]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2725 a r:Inference; +skolem:lemma6050 a r:Inference; r:gives { - (9 9 3 2) :digitsToNumber 9932 . + (9 9 3 3) :digitsToNumber 9933 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(9 100) math:product 900}] [ a r:Fact; r:gives {(3 10) math:product 30}] - [ a r:Fact; r:gives {(9000 900 30 2) math:sum 9932}] + [ a r:Fact; r:gives {(9000 900 30 3) math:sum 9933}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -64892,984 +142381,984 @@ skolem:lemma2725 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9932]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9933]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2726 a r:Inference; +skolem:lemma6051 a r:Inference; r:gives { - 2400 :numberToDigits (2 4 0 0). + 3400 :numberToDigits (3 4 0 0). }; r:evidence ( - [ a r:Fact; r:gives {(2400 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2400 1000) math:remainder 400}] + [ a r:Fact; r:gives {(3400 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3400 1000) math:remainder 400}] [ a r:Fact; r:gives {(400 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(400 100) math:remainder 0}] [ a r:Fact; r:gives {(0 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(0 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2400]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2727 a r:Inference; +skolem:lemma6052 a r:Inference; r:gives { - 2401 :numberToDigits (2 4 0 1). + 3401 :numberToDigits (3 4 0 1). }; r:evidence ( - [ a r:Fact; r:gives {(2401 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2401 1000) math:remainder 401}] + [ a r:Fact; r:gives {(3401 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3401 1000) math:remainder 401}] [ a r:Fact; r:gives {(401 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(401 100) math:remainder 1}] [ a r:Fact; r:gives {(1 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(1 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2401]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3401]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 401]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2728 a r:Inference; +skolem:lemma6053 a r:Inference; r:gives { - 2402 :numberToDigits (2 4 0 2). + 3402 :numberToDigits (3 4 0 2). }; r:evidence ( - [ a r:Fact; r:gives {(2402 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2402 1000) math:remainder 402}] + [ a r:Fact; r:gives {(3402 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3402 1000) math:remainder 402}] [ a r:Fact; r:gives {(402 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(402 100) math:remainder 2}] [ a r:Fact; r:gives {(2 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(2 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2402]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3402]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 402]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2729 a r:Inference; +skolem:lemma6054 a r:Inference; r:gives { - 2403 :numberToDigits (2 4 0 3). + 3403 :numberToDigits (3 4 0 3). }; r:evidence ( - [ a r:Fact; r:gives {(2403 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2403 1000) math:remainder 403}] + [ a r:Fact; r:gives {(3403 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3403 1000) math:remainder 403}] [ a r:Fact; r:gives {(403 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(403 100) math:remainder 3}] [ a r:Fact; r:gives {(3 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(3 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2403]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3403]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 403]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2730 a r:Inference; +skolem:lemma6055 a r:Inference; r:gives { - 2404 :numberToDigits (2 4 0 4). + 3404 :numberToDigits (3 4 0 4). }; r:evidence ( - [ a r:Fact; r:gives {(2404 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2404 1000) math:remainder 404}] + [ a r:Fact; r:gives {(3404 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3404 1000) math:remainder 404}] [ a r:Fact; r:gives {(404 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(404 100) math:remainder 4}] [ a r:Fact; r:gives {(4 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(4 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2404]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3404]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 404]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2731 a r:Inference; +skolem:lemma6056 a r:Inference; r:gives { - 2405 :numberToDigits (2 4 0 5). + 3405 :numberToDigits (3 4 0 5). }; r:evidence ( - [ a r:Fact; r:gives {(2405 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2405 1000) math:remainder 405}] + [ a r:Fact; r:gives {(3405 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3405 1000) math:remainder 405}] [ a r:Fact; r:gives {(405 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(405 100) math:remainder 5}] [ a r:Fact; r:gives {(5 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(5 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2405]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3405]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 405]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2732 a r:Inference; +skolem:lemma6057 a r:Inference; r:gives { - 2406 :numberToDigits (2 4 0 6). + 3406 :numberToDigits (3 4 0 6). }; r:evidence ( - [ a r:Fact; r:gives {(2406 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2406 1000) math:remainder 406}] + [ a r:Fact; r:gives {(3406 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3406 1000) math:remainder 406}] [ a r:Fact; r:gives {(406 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(406 100) math:remainder 6}] [ a r:Fact; r:gives {(6 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(6 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2406]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3406]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 406]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2733 a r:Inference; +skolem:lemma6058 a r:Inference; r:gives { - 2407 :numberToDigits (2 4 0 7). + 3407 :numberToDigits (3 4 0 7). }; r:evidence ( - [ a r:Fact; r:gives {(2407 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2407 1000) math:remainder 407}] + [ a r:Fact; r:gives {(3407 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3407 1000) math:remainder 407}] [ a r:Fact; r:gives {(407 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(407 100) math:remainder 7}] [ a r:Fact; r:gives {(7 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(7 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2407]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3407]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 407]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2734 a r:Inference; +skolem:lemma6059 a r:Inference; r:gives { - 2408 :numberToDigits (2 4 0 8). + 3408 :numberToDigits (3 4 0 8). }; r:evidence ( - [ a r:Fact; r:gives {(2408 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2408 1000) math:remainder 408}] + [ a r:Fact; r:gives {(3408 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3408 1000) math:remainder 408}] [ a r:Fact; r:gives {(408 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(408 100) math:remainder 8}] [ a r:Fact; r:gives {(8 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(8 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2408]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3408]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 408]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2735 a r:Inference; +skolem:lemma6060 a r:Inference; r:gives { - 2409 :numberToDigits (2 4 0 9). + 3409 :numberToDigits (3 4 0 9). }; r:evidence ( - [ a r:Fact; r:gives {(2409 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2409 1000) math:remainder 409}] + [ a r:Fact; r:gives {(3409 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3409 1000) math:remainder 409}] [ a r:Fact; r:gives {(409 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(409 100) math:remainder 9}] [ a r:Fact; r:gives {(9 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(9 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2409]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3409]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 409]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2736 a r:Inference; +skolem:lemma6061 a r:Inference; r:gives { - 2410 :numberToDigits (2 4 1 0). + 3410 :numberToDigits (3 4 1 0). }; r:evidence ( - [ a r:Fact; r:gives {(2410 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2410 1000) math:remainder 410}] + [ a r:Fact; r:gives {(3410 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3410 1000) math:remainder 410}] [ a r:Fact; r:gives {(410 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(410 100) math:remainder 10}] [ a r:Fact; r:gives {(10 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(10 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2410]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3410]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 410]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2737 a r:Inference; +skolem:lemma6062 a r:Inference; r:gives { - 2411 :numberToDigits (2 4 1 1). + 3411 :numberToDigits (3 4 1 1). }; r:evidence ( - [ a r:Fact; r:gives {(2411 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2411 1000) math:remainder 411}] + [ a r:Fact; r:gives {(3411 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3411 1000) math:remainder 411}] [ a r:Fact; r:gives {(411 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(411 100) math:remainder 11}] [ a r:Fact; r:gives {(11 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(11 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2411]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3411]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 411]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 11]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2738 a r:Inference; +skolem:lemma6063 a r:Inference; r:gives { - 2412 :numberToDigits (2 4 1 2). + 3412 :numberToDigits (3 4 1 2). }; r:evidence ( - [ a r:Fact; r:gives {(2412 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2412 1000) math:remainder 412}] + [ a r:Fact; r:gives {(3412 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3412 1000) math:remainder 412}] [ a r:Fact; r:gives {(412 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(412 100) math:remainder 12}] [ a r:Fact; r:gives {(12 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(12 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2412]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3412]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 412]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2739 a r:Inference; +skolem:lemma6064 a r:Inference; r:gives { - 2413 :numberToDigits (2 4 1 3). + 3413 :numberToDigits (3 4 1 3). }; r:evidence ( - [ a r:Fact; r:gives {(2413 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2413 1000) math:remainder 413}] + [ a r:Fact; r:gives {(3413 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3413 1000) math:remainder 413}] [ a r:Fact; r:gives {(413 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(413 100) math:remainder 13}] [ a r:Fact; r:gives {(13 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(13 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2413]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3413]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 413]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 13]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2740 a r:Inference; +skolem:lemma6065 a r:Inference; r:gives { - 2414 :numberToDigits (2 4 1 4). + 3414 :numberToDigits (3 4 1 4). }; r:evidence ( - [ a r:Fact; r:gives {(2414 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2414 1000) math:remainder 414}] + [ a r:Fact; r:gives {(3414 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3414 1000) math:remainder 414}] [ a r:Fact; r:gives {(414 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(414 100) math:remainder 14}] [ a r:Fact; r:gives {(14 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(14 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2414]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3414]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 414]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 14]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2741 a r:Inference; +skolem:lemma6066 a r:Inference; r:gives { - 2415 :numberToDigits (2 4 1 5). + 3415 :numberToDigits (3 4 1 5). }; r:evidence ( - [ a r:Fact; r:gives {(2415 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2415 1000) math:remainder 415}] + [ a r:Fact; r:gives {(3415 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3415 1000) math:remainder 415}] [ a r:Fact; r:gives {(415 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(415 100) math:remainder 15}] [ a r:Fact; r:gives {(15 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(15 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2415]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3415]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 415]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 15]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2742 a r:Inference; +skolem:lemma6067 a r:Inference; r:gives { - 2416 :numberToDigits (2 4 1 6). + 3416 :numberToDigits (3 4 1 6). }; r:evidence ( - [ a r:Fact; r:gives {(2416 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2416 1000) math:remainder 416}] + [ a r:Fact; r:gives {(3416 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3416 1000) math:remainder 416}] [ a r:Fact; r:gives {(416 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(416 100) math:remainder 16}] [ a r:Fact; r:gives {(16 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(16 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2416]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3416]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 416]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 16]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2743 a r:Inference; +skolem:lemma6068 a r:Inference; r:gives { - 2417 :numberToDigits (2 4 1 7). + 3417 :numberToDigits (3 4 1 7). }; r:evidence ( - [ a r:Fact; r:gives {(2417 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2417 1000) math:remainder 417}] + [ a r:Fact; r:gives {(3417 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3417 1000) math:remainder 417}] [ a r:Fact; r:gives {(417 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(417 100) math:remainder 17}] [ a r:Fact; r:gives {(17 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(17 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2417]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3417]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 417]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 17]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2744 a r:Inference; +skolem:lemma6069 a r:Inference; r:gives { - 2418 :numberToDigits (2 4 1 8). + 3418 :numberToDigits (3 4 1 8). }; r:evidence ( - [ a r:Fact; r:gives {(2418 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2418 1000) math:remainder 418}] + [ a r:Fact; r:gives {(3418 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3418 1000) math:remainder 418}] [ a r:Fact; r:gives {(418 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(418 100) math:remainder 18}] [ a r:Fact; r:gives {(18 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(18 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2418]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3418]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 418]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 18]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2745 a r:Inference; +skolem:lemma6070 a r:Inference; r:gives { - 2419 :numberToDigits (2 4 1 9). + 3419 :numberToDigits (3 4 1 9). }; r:evidence ( - [ a r:Fact; r:gives {(2419 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2419 1000) math:remainder 419}] + [ a r:Fact; r:gives {(3419 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3419 1000) math:remainder 419}] [ a r:Fact; r:gives {(419 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(419 100) math:remainder 19}] [ a r:Fact; r:gives {(19 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(19 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2419]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3419]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 419]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 19]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2746 a r:Inference; +skolem:lemma6071 a r:Inference; r:gives { - 2420 :numberToDigits (2 4 2 0). + 3420 :numberToDigits (3 4 2 0). }; r:evidence ( - [ a r:Fact; r:gives {(2420 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2420 1000) math:remainder 420}] + [ a r:Fact; r:gives {(3420 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3420 1000) math:remainder 420}] [ a r:Fact; r:gives {(420 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(420 100) math:remainder 20}] [ a r:Fact; r:gives {(20 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(20 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2420]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3420]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 420]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 20]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2747 a r:Inference; +skolem:lemma6072 a r:Inference; r:gives { - 2421 :numberToDigits (2 4 2 1). + 3421 :numberToDigits (3 4 2 1). }; r:evidence ( - [ a r:Fact; r:gives {(2421 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2421 1000) math:remainder 421}] + [ a r:Fact; r:gives {(3421 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3421 1000) math:remainder 421}] [ a r:Fact; r:gives {(421 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(421 100) math:remainder 21}] [ a r:Fact; r:gives {(21 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(21 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2421]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3421]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 421]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 21]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2748 a r:Inference; +skolem:lemma6073 a r:Inference; r:gives { - 2422 :numberToDigits (2 4 2 2). + 3422 :numberToDigits (3 4 2 2). }; r:evidence ( - [ a r:Fact; r:gives {(2422 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2422 1000) math:remainder 422}] + [ a r:Fact; r:gives {(3422 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3422 1000) math:remainder 422}] [ a r:Fact; r:gives {(422 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(422 100) math:remainder 22}] [ a r:Fact; r:gives {(22 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(22 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2422]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3422]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 422]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2749 a r:Inference; +skolem:lemma6074 a r:Inference; r:gives { - 2423 :numberToDigits (2 4 2 3). + 3423 :numberToDigits (3 4 2 3). }; r:evidence ( - [ a r:Fact; r:gives {(2423 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2423 1000) math:remainder 423}] + [ a r:Fact; r:gives {(3423 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3423 1000) math:remainder 423}] [ a r:Fact; r:gives {(423 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(423 100) math:remainder 23}] [ a r:Fact; r:gives {(23 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(23 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2423]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3423]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 423]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2750 a r:Inference; +skolem:lemma6075 a r:Inference; r:gives { - 2424 :numberToDigits (2 4 2 4). + 3424 :numberToDigits (3 4 2 4). }; r:evidence ( - [ a r:Fact; r:gives {(2424 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2424 1000) math:remainder 424}] + [ a r:Fact; r:gives {(3424 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3424 1000) math:remainder 424}] [ a r:Fact; r:gives {(424 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(424 100) math:remainder 24}] [ a r:Fact; r:gives {(24 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(24 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2424]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3424]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 424]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2751 a r:Inference; +skolem:lemma6076 a r:Inference; r:gives { - 2425 :numberToDigits (2 4 2 5). + 3425 :numberToDigits (3 4 2 5). }; r:evidence ( - [ a r:Fact; r:gives {(2425 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2425 1000) math:remainder 425}] + [ a r:Fact; r:gives {(3425 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3425 1000) math:remainder 425}] [ a r:Fact; r:gives {(425 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(425 100) math:remainder 25}] [ a r:Fact; r:gives {(25 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(25 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2425]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3425]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 425]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2752 a r:Inference; +skolem:lemma6077 a r:Inference; r:gives { - 2426 :numberToDigits (2 4 2 6). + 3426 :numberToDigits (3 4 2 6). }; r:evidence ( - [ a r:Fact; r:gives {(2426 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2426 1000) math:remainder 426}] + [ a r:Fact; r:gives {(3426 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3426 1000) math:remainder 426}] [ a r:Fact; r:gives {(426 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(426 100) math:remainder 26}] [ a r:Fact; r:gives {(26 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(26 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2426]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3426]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 426]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2753 a r:Inference; +skolem:lemma6078 a r:Inference; r:gives { - 2427 :numberToDigits (2 4 2 7). + 3427 :numberToDigits (3 4 2 7). }; r:evidence ( - [ a r:Fact; r:gives {(2427 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2427 1000) math:remainder 427}] + [ a r:Fact; r:gives {(3427 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3427 1000) math:remainder 427}] [ a r:Fact; r:gives {(427 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(427 100) math:remainder 27}] [ a r:Fact; r:gives {(27 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(27 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2427]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3427]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 427]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2754 a r:Inference; +skolem:lemma6079 a r:Inference; r:gives { - 2428 :numberToDigits (2 4 2 8). + 3428 :numberToDigits (3 4 2 8). }; r:evidence ( - [ a r:Fact; r:gives {(2428 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2428 1000) math:remainder 428}] + [ a r:Fact; r:gives {(3428 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3428 1000) math:remainder 428}] [ a r:Fact; r:gives {(428 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(428 100) math:remainder 28}] [ a r:Fact; r:gives {(28 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(28 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2428]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3428]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 428]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2755 a r:Inference; +skolem:lemma6080 a r:Inference; r:gives { - 2429 :numberToDigits (2 4 2 9). + 3429 :numberToDigits (3 4 2 9). }; r:evidence ( - [ a r:Fact; r:gives {(2429 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2429 1000) math:remainder 429}] + [ a r:Fact; r:gives {(3429 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3429 1000) math:remainder 429}] [ a r:Fact; r:gives {(429 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(429 100) math:remainder 29}] [ a r:Fact; r:gives {(29 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(29 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2429]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3429]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 429]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2756 a r:Inference; +skolem:lemma6081 a r:Inference; r:gives { - 2430 :numberToDigits (2 4 3 0). + 3430 :numberToDigits (3 4 3 0). }; r:evidence ( - [ a r:Fact; r:gives {(2430 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2430 1000) math:remainder 430}] + [ a r:Fact; r:gives {(3430 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3430 1000) math:remainder 430}] [ a r:Fact; r:gives {(430 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(430 100) math:remainder 30}] [ a r:Fact; r:gives {(30 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(30 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2430]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3430]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 430]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2757 a r:Inference; +skolem:lemma6082 a r:Inference; r:gives { - 2431 :numberToDigits (2 4 3 1). + 3431 :numberToDigits (3 4 3 1). }; r:evidence ( - [ a r:Fact; r:gives {(2431 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2431 1000) math:remainder 431}] + [ a r:Fact; r:gives {(3431 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3431 1000) math:remainder 431}] [ a r:Fact; r:gives {(431 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(431 100) math:remainder 31}] [ a r:Fact; r:gives {(31 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(31 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2431]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3431]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 431]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 31]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2758 a r:Inference; +skolem:lemma6083 a r:Inference; r:gives { - 2432 :numberToDigits (2 4 3 2). + 3432 :numberToDigits (3 4 3 2). }; r:evidence ( - [ a r:Fact; r:gives {(2432 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2432 1000) math:remainder 432}] + [ a r:Fact; r:gives {(3432 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3432 1000) math:remainder 432}] [ a r:Fact; r:gives {(432 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(432 100) math:remainder 32}] [ a r:Fact; r:gives {(32 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(32 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2432]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3432]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 432]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 32]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2759 a r:Inference; +skolem:lemma6084 a r:Inference; r:gives { - 2433 :numberToDigits (2 4 3 3). + 3433 :numberToDigits (3 4 3 3). }; r:evidence ( - [ a r:Fact; r:gives {(2433 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2433 1000) math:remainder 433}] + [ a r:Fact; r:gives {(3433 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3433 1000) math:remainder 433}] [ a r:Fact; r:gives {(433 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(433 100) math:remainder 33}] [ a r:Fact; r:gives {(33 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(33 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2433]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3433]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 433]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 33]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2760 a r:Inference; +skolem:lemma6085 a r:Inference; r:gives { - 2434 :numberToDigits (2 4 3 4). + 3434 :numberToDigits (3 4 3 4). }; r:evidence ( - [ a r:Fact; r:gives {(2434 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2434 1000) math:remainder 434}] + [ a r:Fact; r:gives {(3434 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3434 1000) math:remainder 434}] [ a r:Fact; r:gives {(434 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(434 100) math:remainder 34}] [ a r:Fact; r:gives {(34 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(34 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2434]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3434]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 434]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 34]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2761 a r:Inference; +skolem:lemma6086 a r:Inference; r:gives { - 2435 :numberToDigits (2 4 3 5). + 3435 :numberToDigits (3 4 3 5). }; r:evidence ( - [ a r:Fact; r:gives {(2435 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2435 1000) math:remainder 435}] + [ a r:Fact; r:gives {(3435 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3435 1000) math:remainder 435}] [ a r:Fact; r:gives {(435 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(435 100) math:remainder 35}] [ a r:Fact; r:gives {(35 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(35 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2435]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3435]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 435]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 35]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2762 a r:Inference; +skolem:lemma6087 a r:Inference; r:gives { - 2436 :numberToDigits (2 4 3 6). + 3436 :numberToDigits (3 4 3 6). }; r:evidence ( - [ a r:Fact; r:gives {(2436 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2436 1000) math:remainder 436}] + [ a r:Fact; r:gives {(3436 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3436 1000) math:remainder 436}] [ a r:Fact; r:gives {(436 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(436 100) math:remainder 36}] [ a r:Fact; r:gives {(36 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(36 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2436]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3436]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 436]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 36]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2763 a r:Inference; +skolem:lemma6088 a r:Inference; r:gives { - 2437 :numberToDigits (2 4 3 7). + 3437 :numberToDigits (3 4 3 7). }; r:evidence ( - [ a r:Fact; r:gives {(2437 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2437 1000) math:remainder 437}] + [ a r:Fact; r:gives {(3437 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3437 1000) math:remainder 437}] [ a r:Fact; r:gives {(437 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(437 100) math:remainder 37}] [ a r:Fact; r:gives {(37 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(37 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2437]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3437]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 437]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 37]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2764 a r:Inference; +skolem:lemma6089 a r:Inference; r:gives { - 2438 :numberToDigits (2 4 3 8). + 3438 :numberToDigits (3 4 3 8). }; r:evidence ( - [ a r:Fact; r:gives {(2438 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2438 1000) math:remainder 438}] + [ a r:Fact; r:gives {(3438 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3438 1000) math:remainder 438}] [ a r:Fact; r:gives {(438 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(438 100) math:remainder 38}] [ a r:Fact; r:gives {(38 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(38 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2438]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3438]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 438]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 38]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2765 a r:Inference; +skolem:lemma6090 a r:Inference; r:gives { - 2439 :numberToDigits (2 4 3 9). + 3439 :numberToDigits (3 4 3 9). }; r:evidence ( - [ a r:Fact; r:gives {(2439 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2439 1000) math:remainder 439}] + [ a r:Fact; r:gives {(3439 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3439 1000) math:remainder 439}] [ a r:Fact; r:gives {(439 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(439 100) math:remainder 39}] [ a r:Fact; r:gives {(39 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(39 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2439]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3439]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 439]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 39]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2766 a r:Inference; +skolem:lemma6091 a r:Inference; r:gives { - 2440 :numberToDigits (2 4 4 0). + 3440 :numberToDigits (3 4 4 0). }; r:evidence ( - [ a r:Fact; r:gives {(2440 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2440 1000) math:remainder 440}] + [ a r:Fact; r:gives {(3440 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3440 1000) math:remainder 440}] [ a r:Fact; r:gives {(440 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(440 100) math:remainder 40}] [ a r:Fact; r:gives {(40 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(40 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2440]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3440]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 440]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2767 a r:Inference; +skolem:lemma6092 a r:Inference; r:gives { - 2441 :numberToDigits (2 4 4 1). + 3441 :numberToDigits (3 4 4 1). }; r:evidence ( - [ a r:Fact; r:gives {(2441 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2441 1000) math:remainder 441}] + [ a r:Fact; r:gives {(3441 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3441 1000) math:remainder 441}] [ a r:Fact; r:gives {(441 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(441 100) math:remainder 41}] [ a r:Fact; r:gives {(41 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(41 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2441]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3441]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 441]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 41]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2768 a r:Inference; +skolem:lemma6093 a r:Inference; r:gives { - 2442 :numberToDigits (2 4 4 2). + 3442 :numberToDigits (3 4 4 2). }; r:evidence ( - [ a r:Fact; r:gives {(2442 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2442 1000) math:remainder 442}] + [ a r:Fact; r:gives {(3442 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3442 1000) math:remainder 442}] [ a r:Fact; r:gives {(442 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(442 100) math:remainder 42}] [ a r:Fact; r:gives {(42 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(42 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2442]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3442]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 442]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 42]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2769 a r:Inference; +skolem:lemma6094 a r:Inference; r:gives { - 2443 :numberToDigits (2 4 4 3). + 3443 :numberToDigits (3 4 4 3). }; r:evidence ( - [ a r:Fact; r:gives {(2443 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2443 1000) math:remainder 443}] + [ a r:Fact; r:gives {(3443 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3443 1000) math:remainder 443}] [ a r:Fact; r:gives {(443 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(443 100) math:remainder 43}] [ a r:Fact; r:gives {(43 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(43 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3443]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 443]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 43]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2770 a r:Inference; +skolem:lemma6095 a r:Inference; r:gives { - 2444 :numberToDigits (2 4 4 4). + 3444 :numberToDigits (3 4 4 4). }; r:evidence ( - [ a r:Fact; r:gives {(2444 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2444 1000) math:remainder 444}] + [ a r:Fact; r:gives {(3444 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3444 1000) math:remainder 444}] [ a r:Fact; r:gives {(444 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(444 100) math:remainder 44}] [ a r:Fact; r:gives {(44 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(44 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3444]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 444]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 44]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2771 a r:Inference; +skolem:lemma6096 a r:Inference; r:gives { - (2 4 4 4) :digitsToNumber 2444 . + (3 4 4 4) :digitsToNumber 3444 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(2000 400 40 4) math:sum 2444}] + [ a r:Fact; r:gives {(3000 400 40 4) math:sum 3444}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2444]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3444]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2772 a r:Inference; +skolem:lemma6097 a r:Inference; r:gives { - (4 4 4 2) :digitsToNumber 4442 . + (4 4 4 3) :digitsToNumber 4443 . }; r:evidence ( [ a r:Fact; r:gives {(4 1000) math:product 4000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(4000 400 40 2) math:sum 4442}] + [ a r:Fact; r:gives {(4000 400 40 3) math:sum 4443}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 4000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 4]; @@ -65877,60 +143366,60 @@ skolem:lemma2772 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 4443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2773 a r:Inference; +skolem:lemma6098 a r:Inference; r:gives { - 2445 :numberToDigits (2 4 4 5). + 3445 :numberToDigits (3 4 4 5). }; r:evidence ( - [ a r:Fact; r:gives {(2445 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2445 1000) math:remainder 445}] + [ a r:Fact; r:gives {(3445 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3445 1000) math:remainder 445}] [ a r:Fact; r:gives {(445 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(445 100) math:remainder 45}] [ a r:Fact; r:gives {(45 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(45 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2445]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3445]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 445]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 45]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2774 a r:Inference; +skolem:lemma6099 a r:Inference; r:gives { - (2 4 4 5) :digitsToNumber 2445 . + (3 4 4 5) :digitsToNumber 3445 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(2000 400 40 5) math:sum 2445}] + [ a r:Fact; r:gives {(3000 400 40 5) math:sum 3445}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2445]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3445]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2775 a r:Inference; +skolem:lemma6100 a r:Inference; r:gives { - (5 4 4 2) :digitsToNumber 5442 . + (5 4 4 3) :digitsToNumber 5443 . }; r:evidence ( [ a r:Fact; r:gives {(5 1000) math:product 5000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(5000 400 40 2) math:sum 5442}] + [ a r:Fact; r:gives {(5000 400 40 3) math:sum 5443}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; @@ -65938,60 +143427,60 @@ skolem:lemma2775 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2776 a r:Inference; +skolem:lemma6101 a r:Inference; r:gives { - 2446 :numberToDigits (2 4 4 6). + 3446 :numberToDigits (3 4 4 6). }; r:evidence ( - [ a r:Fact; r:gives {(2446 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2446 1000) math:remainder 446}] + [ a r:Fact; r:gives {(3446 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3446 1000) math:remainder 446}] [ a r:Fact; r:gives {(446 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(446 100) math:remainder 46}] [ a r:Fact; r:gives {(46 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(46 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2446]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3446]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 446]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 46]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2777 a r:Inference; +skolem:lemma6102 a r:Inference; r:gives { - (2 4 4 6) :digitsToNumber 2446 . + (3 4 4 6) :digitsToNumber 3446 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(2000 400 40 6) math:sum 2446}] + [ a r:Fact; r:gives {(3000 400 40 6) math:sum 3446}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2446]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3446]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2778 a r:Inference; +skolem:lemma6103 a r:Inference; r:gives { - (6 4 4 2) :digitsToNumber 6442 . + (6 4 4 3) :digitsToNumber 6443 . }; r:evidence ( [ a r:Fact; r:gives {(6 1000) math:product 6000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(6000 400 40 2) math:sum 6442}] + [ a r:Fact; r:gives {(6000 400 40 3) math:sum 6443}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; @@ -65999,60 +143488,60 @@ skolem:lemma2778 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2779 a r:Inference; +skolem:lemma6104 a r:Inference; r:gives { - 2447 :numberToDigits (2 4 4 7). + 3447 :numberToDigits (3 4 4 7). }; r:evidence ( - [ a r:Fact; r:gives {(2447 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2447 1000) math:remainder 447}] + [ a r:Fact; r:gives {(3447 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3447 1000) math:remainder 447}] [ a r:Fact; r:gives {(447 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(447 100) math:remainder 47}] [ a r:Fact; r:gives {(47 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(47 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2447]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3447]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 447]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 47]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2780 a r:Inference; +skolem:lemma6105 a r:Inference; r:gives { - (2 4 4 7) :digitsToNumber 2447 . + (3 4 4 7) :digitsToNumber 3447 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(2000 400 40 7) math:sum 2447}] + [ a r:Fact; r:gives {(3000 400 40 7) math:sum 3447}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2447]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3447]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2781 a r:Inference; +skolem:lemma6106 a r:Inference; r:gives { - (7 4 4 2) :digitsToNumber 7442 . + (7 4 4 3) :digitsToNumber 7443 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(7000 400 40 2) math:sum 7442}] + [ a r:Fact; r:gives {(7000 400 40 3) math:sum 7443}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; @@ -66060,60 +143549,60 @@ skolem:lemma2781 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2782 a r:Inference; +skolem:lemma6107 a r:Inference; r:gives { - 2448 :numberToDigits (2 4 4 8). + 3448 :numberToDigits (3 4 4 8). }; r:evidence ( - [ a r:Fact; r:gives {(2448 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2448 1000) math:remainder 448}] + [ a r:Fact; r:gives {(3448 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3448 1000) math:remainder 448}] [ a r:Fact; r:gives {(448 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(448 100) math:remainder 48}] [ a r:Fact; r:gives {(48 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(48 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2448]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3448]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 448]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 48]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2783 a r:Inference; +skolem:lemma6108 a r:Inference; r:gives { - (2 4 4 8) :digitsToNumber 2448 . + (3 4 4 8) :digitsToNumber 3448 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(2000 400 40 8) math:sum 2448}] + [ a r:Fact; r:gives {(3000 400 40 8) math:sum 3448}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2448]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3448]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2784 a r:Inference; +skolem:lemma6109 a r:Inference; r:gives { - (8 4 4 2) :digitsToNumber 8442 . + (8 4 4 3) :digitsToNumber 8443 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(8000 400 40 2) math:sum 8442}] + [ a r:Fact; r:gives {(8000 400 40 3) math:sum 8443}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; @@ -66121,60 +143610,60 @@ skolem:lemma2784 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2785 a r:Inference; +skolem:lemma6110 a r:Inference; r:gives { - 2449 :numberToDigits (2 4 4 9). + 3449 :numberToDigits (3 4 4 9). }; r:evidence ( - [ a r:Fact; r:gives {(2449 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2449 1000) math:remainder 449}] + [ a r:Fact; r:gives {(3449 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3449 1000) math:remainder 449}] [ a r:Fact; r:gives {(449 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(449 100) math:remainder 49}] [ a r:Fact; r:gives {(49 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(49 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2449]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3449]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 449]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 49]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2786 a r:Inference; +skolem:lemma6111 a r:Inference; r:gives { - (2 4 4 9) :digitsToNumber 2449 . + (3 4 4 9) :digitsToNumber 3449 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(2000 400 40 9) math:sum 2449}] + [ a r:Fact; r:gives {(3000 400 40 9) math:sum 3449}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2449]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3449]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2787 a r:Inference; +skolem:lemma6112 a r:Inference; r:gives { - (9 4 4 2) :digitsToNumber 9442 . + (9 4 4 3) :digitsToNumber 9443 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(9000 400 40 2) math:sum 9442}] + [ a r:Fact; r:gives {(9000 400 40 3) math:sum 9443}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -66182,165 +143671,165 @@ skolem:lemma2787 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9442]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9443]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2788 a r:Inference; +skolem:lemma6113 a r:Inference; r:gives { - 2450 :numberToDigits (2 4 5 0). + 3450 :numberToDigits (3 4 5 0). }; r:evidence ( - [ a r:Fact; r:gives {(2450 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2450 1000) math:remainder 450}] + [ a r:Fact; r:gives {(3450 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3450 1000) math:remainder 450}] [ a r:Fact; r:gives {(450 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(450 100) math:remainder 50}] [ a r:Fact; r:gives {(50 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(50 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2450]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3450]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 450]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2789 a r:Inference; +skolem:lemma6114 a r:Inference; r:gives { - 2451 :numberToDigits (2 4 5 1). + 3451 :numberToDigits (3 4 5 1). }; r:evidence ( - [ a r:Fact; r:gives {(2451 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2451 1000) math:remainder 451}] + [ a r:Fact; r:gives {(3451 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3451 1000) math:remainder 451}] [ a r:Fact; r:gives {(451 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(451 100) math:remainder 51}] [ a r:Fact; r:gives {(51 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(51 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2451]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3451]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 451]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 51]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2790 a r:Inference; +skolem:lemma6115 a r:Inference; r:gives { - 2452 :numberToDigits (2 4 5 2). + 3452 :numberToDigits (3 4 5 2). }; r:evidence ( - [ a r:Fact; r:gives {(2452 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2452 1000) math:remainder 452}] + [ a r:Fact; r:gives {(3452 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3452 1000) math:remainder 452}] [ a r:Fact; r:gives {(452 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(452 100) math:remainder 52}] [ a r:Fact; r:gives {(52 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(52 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2452]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3452]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 452]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 52]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2791 a r:Inference; +skolem:lemma6116 a r:Inference; r:gives { - 2453 :numberToDigits (2 4 5 3). + 3453 :numberToDigits (3 4 5 3). }; r:evidence ( - [ a r:Fact; r:gives {(2453 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2453 1000) math:remainder 453}] + [ a r:Fact; r:gives {(3453 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3453 1000) math:remainder 453}] [ a r:Fact; r:gives {(453 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(453 100) math:remainder 53}] [ a r:Fact; r:gives {(53 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(53 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2453]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3453]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 453]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 53]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2792 a r:Inference; +skolem:lemma6117 a r:Inference; r:gives { - 2454 :numberToDigits (2 4 5 4). + 3454 :numberToDigits (3 4 5 4). }; r:evidence ( - [ a r:Fact; r:gives {(2454 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2454 1000) math:remainder 454}] + [ a r:Fact; r:gives {(3454 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3454 1000) math:remainder 454}] [ a r:Fact; r:gives {(454 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(454 100) math:remainder 54}] [ a r:Fact; r:gives {(54 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(54 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2454]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3454]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 454]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 54]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2793 a r:Inference; +skolem:lemma6118 a r:Inference; r:gives { - 2455 :numberToDigits (2 4 5 5). + 3455 :numberToDigits (3 4 5 5). }; r:evidence ( - [ a r:Fact; r:gives {(2455 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2455 1000) math:remainder 455}] + [ a r:Fact; r:gives {(3455 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3455 1000) math:remainder 455}] [ a r:Fact; r:gives {(455 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(455 100) math:remainder 55}] [ a r:Fact; r:gives {(55 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(55 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2455]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3455]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 455]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 55]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2794 a r:Inference; +skolem:lemma6119 a r:Inference; r:gives { - (2 4 5 5) :digitsToNumber 2455 . + (3 4 5 5) :digitsToNumber 3455 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(2000 400 50 5) math:sum 2455}] + [ a r:Fact; r:gives {(3000 400 50 5) math:sum 3455}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2455]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3455]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2795 a r:Inference; +skolem:lemma6120 a r:Inference; r:gives { - (5 5 4 2) :digitsToNumber 5542 . + (5 5 4 3) :digitsToNumber 5543 . }; r:evidence ( [ a r:Fact; r:gives {(5 1000) math:product 5000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(5000 500 40 2) math:sum 5542}] + [ a r:Fact; r:gives {(5000 500 40 3) math:sum 5543}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; @@ -66348,60 +143837,60 @@ skolem:lemma2795 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2796 a r:Inference; +skolem:lemma6121 a r:Inference; r:gives { - 2456 :numberToDigits (2 4 5 6). + 3456 :numberToDigits (3 4 5 6). }; r:evidence ( - [ a r:Fact; r:gives {(2456 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2456 1000) math:remainder 456}] + [ a r:Fact; r:gives {(3456 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3456 1000) math:remainder 456}] [ a r:Fact; r:gives {(456 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(456 100) math:remainder 56}] [ a r:Fact; r:gives {(56 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(56 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3456]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 456]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 56]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2797 a r:Inference; +skolem:lemma6122 a r:Inference; r:gives { - (2 4 5 6) :digitsToNumber 2456 . + (3 4 5 6) :digitsToNumber 3456 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(2000 400 50 6) math:sum 2456}] + [ a r:Fact; r:gives {(3000 400 50 6) math:sum 3456}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2456]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3456]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2798 a r:Inference; +skolem:lemma6123 a r:Inference; r:gives { - (6 5 4 2) :digitsToNumber 6542 . + (6 5 4 3) :digitsToNumber 6543 . }; r:evidence ( [ a r:Fact; r:gives {(6 1000) math:product 6000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(6000 500 40 2) math:sum 6542}] + [ a r:Fact; r:gives {(6000 500 40 3) math:sum 6543}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; @@ -66409,60 +143898,60 @@ skolem:lemma2798 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2799 a r:Inference; +skolem:lemma6124 a r:Inference; r:gives { - 2457 :numberToDigits (2 4 5 7). + 3457 :numberToDigits (3 4 5 7). }; r:evidence ( - [ a r:Fact; r:gives {(2457 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2457 1000) math:remainder 457}] + [ a r:Fact; r:gives {(3457 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3457 1000) math:remainder 457}] [ a r:Fact; r:gives {(457 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(457 100) math:remainder 57}] [ a r:Fact; r:gives {(57 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(57 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2457]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3457]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 457]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 57]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2800 a r:Inference; +skolem:lemma6125 a r:Inference; r:gives { - (2 4 5 7) :digitsToNumber 2457 . + (3 4 5 7) :digitsToNumber 3457 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(2000 400 50 7) math:sum 2457}] + [ a r:Fact; r:gives {(3000 400 50 7) math:sum 3457}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2457]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3457]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2801 a r:Inference; +skolem:lemma6126 a r:Inference; r:gives { - (7 5 4 2) :digitsToNumber 7542 . + (7 5 4 3) :digitsToNumber 7543 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(7000 500 40 2) math:sum 7542}] + [ a r:Fact; r:gives {(7000 500 40 3) math:sum 7543}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; @@ -66470,60 +143959,60 @@ skolem:lemma2801 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2802 a r:Inference; +skolem:lemma6127 a r:Inference; r:gives { - 2458 :numberToDigits (2 4 5 8). + 3458 :numberToDigits (3 4 5 8). }; r:evidence ( - [ a r:Fact; r:gives {(2458 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2458 1000) math:remainder 458}] + [ a r:Fact; r:gives {(3458 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3458 1000) math:remainder 458}] [ a r:Fact; r:gives {(458 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(458 100) math:remainder 58}] [ a r:Fact; r:gives {(58 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(58 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2458]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3458]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 458]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 58]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2803 a r:Inference; +skolem:lemma6128 a r:Inference; r:gives { - (2 4 5 8) :digitsToNumber 2458 . + (3 4 5 8) :digitsToNumber 3458 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(2000 400 50 8) math:sum 2458}] + [ a r:Fact; r:gives {(3000 400 50 8) math:sum 3458}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2458]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3458]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2804 a r:Inference; +skolem:lemma6129 a r:Inference; r:gives { - (8 5 4 2) :digitsToNumber 8542 . + (8 5 4 3) :digitsToNumber 8543 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(8000 500 40 2) math:sum 8542}] + [ a r:Fact; r:gives {(8000 500 40 3) math:sum 8543}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; @@ -66531,60 +144020,60 @@ skolem:lemma2804 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2805 a r:Inference; +skolem:lemma6130 a r:Inference; r:gives { - 2459 :numberToDigits (2 4 5 9). + 3459 :numberToDigits (3 4 5 9). }; r:evidence ( - [ a r:Fact; r:gives {(2459 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2459 1000) math:remainder 459}] + [ a r:Fact; r:gives {(3459 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3459 1000) math:remainder 459}] [ a r:Fact; r:gives {(459 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(459 100) math:remainder 59}] [ a r:Fact; r:gives {(59 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(59 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2459]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3459]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 459]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 59]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2806 a r:Inference; +skolem:lemma6131 a r:Inference; r:gives { - (2 4 5 9) :digitsToNumber 2459 . + (3 4 5 9) :digitsToNumber 3459 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(2000 400 50 9) math:sum 2459}] + [ a r:Fact; r:gives {(3000 400 50 9) math:sum 3459}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2459]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3459]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2807 a r:Inference; +skolem:lemma6132 a r:Inference; r:gives { - (9 5 4 2) :digitsToNumber 9542 . + (9 5 4 3) :digitsToNumber 9543 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(9000 500 40 2) math:sum 9542}] + [ a r:Fact; r:gives {(9000 500 40 3) math:sum 9543}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -66592,186 +144081,186 @@ skolem:lemma2807 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9542]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2808 a r:Inference; +skolem:lemma6133 a r:Inference; r:gives { - 2460 :numberToDigits (2 4 6 0). + 3460 :numberToDigits (3 4 6 0). }; r:evidence ( - [ a r:Fact; r:gives {(2460 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2460 1000) math:remainder 460}] + [ a r:Fact; r:gives {(3460 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3460 1000) math:remainder 460}] [ a r:Fact; r:gives {(460 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(460 100) math:remainder 60}] [ a r:Fact; r:gives {(60 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(60 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2460]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3460]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 460]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2809 a r:Inference; +skolem:lemma6134 a r:Inference; r:gives { - 2461 :numberToDigits (2 4 6 1). + 3461 :numberToDigits (3 4 6 1). }; r:evidence ( - [ a r:Fact; r:gives {(2461 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2461 1000) math:remainder 461}] + [ a r:Fact; r:gives {(3461 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3461 1000) math:remainder 461}] [ a r:Fact; r:gives {(461 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(461 100) math:remainder 61}] [ a r:Fact; r:gives {(61 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(61 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2461]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3461]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 461]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 61]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2810 a r:Inference; +skolem:lemma6135 a r:Inference; r:gives { - 2462 :numberToDigits (2 4 6 2). + 3462 :numberToDigits (3 4 6 2). }; r:evidence ( - [ a r:Fact; r:gives {(2462 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2462 1000) math:remainder 462}] + [ a r:Fact; r:gives {(3462 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3462 1000) math:remainder 462}] [ a r:Fact; r:gives {(462 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(462 100) math:remainder 62}] [ a r:Fact; r:gives {(62 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(62 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2462]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3462]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 462]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 62]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2811 a r:Inference; +skolem:lemma6136 a r:Inference; r:gives { - 2463 :numberToDigits (2 4 6 3). + 3463 :numberToDigits (3 4 6 3). }; r:evidence ( - [ a r:Fact; r:gives {(2463 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2463 1000) math:remainder 463}] + [ a r:Fact; r:gives {(3463 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3463 1000) math:remainder 463}] [ a r:Fact; r:gives {(463 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(463 100) math:remainder 63}] [ a r:Fact; r:gives {(63 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(63 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2463]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3463]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 463]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 63]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2812 a r:Inference; +skolem:lemma6137 a r:Inference; r:gives { - 2464 :numberToDigits (2 4 6 4). + 3464 :numberToDigits (3 4 6 4). }; r:evidence ( - [ a r:Fact; r:gives {(2464 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2464 1000) math:remainder 464}] + [ a r:Fact; r:gives {(3464 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3464 1000) math:remainder 464}] [ a r:Fact; r:gives {(464 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(464 100) math:remainder 64}] [ a r:Fact; r:gives {(64 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(64 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2464]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3464]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 464]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 64]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2813 a r:Inference; +skolem:lemma6138 a r:Inference; r:gives { - 2465 :numberToDigits (2 4 6 5). + 3465 :numberToDigits (3 4 6 5). }; r:evidence ( - [ a r:Fact; r:gives {(2465 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2465 1000) math:remainder 465}] + [ a r:Fact; r:gives {(3465 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3465 1000) math:remainder 465}] [ a r:Fact; r:gives {(465 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(465 100) math:remainder 65}] [ a r:Fact; r:gives {(65 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(65 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2465]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3465]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 465]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 65]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2814 a r:Inference; +skolem:lemma6139 a r:Inference; r:gives { - 2466 :numberToDigits (2 4 6 6). + 3466 :numberToDigits (3 4 6 6). }; r:evidence ( - [ a r:Fact; r:gives {(2466 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2466 1000) math:remainder 466}] + [ a r:Fact; r:gives {(3466 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3466 1000) math:remainder 466}] [ a r:Fact; r:gives {(466 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(466 100) math:remainder 66}] [ a r:Fact; r:gives {(66 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(66 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2466]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3466]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 466]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 66]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2815 a r:Inference; +skolem:lemma6140 a r:Inference; r:gives { - (2 4 6 6) :digitsToNumber 2466 . + (3 4 6 6) :digitsToNumber 3466 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(2000 400 60 6) math:sum 2466}] + [ a r:Fact; r:gives {(3000 400 60 6) math:sum 3466}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2466]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3466]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2816 a r:Inference; +skolem:lemma6141 a r:Inference; r:gives { - (6 6 4 2) :digitsToNumber 6642 . + (6 6 4 3) :digitsToNumber 6643 . }; r:evidence ( [ a r:Fact; r:gives {(6 1000) math:product 6000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(6000 600 40 2) math:sum 6642}] + [ a r:Fact; r:gives {(6000 600 40 3) math:sum 6643}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; @@ -66779,60 +144268,60 @@ skolem:lemma2816 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2817 a r:Inference; +skolem:lemma6142 a r:Inference; r:gives { - 2467 :numberToDigits (2 4 6 7). + 3467 :numberToDigits (3 4 6 7). }; r:evidence ( - [ a r:Fact; r:gives {(2467 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2467 1000) math:remainder 467}] + [ a r:Fact; r:gives {(3467 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3467 1000) math:remainder 467}] [ a r:Fact; r:gives {(467 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(467 100) math:remainder 67}] [ a r:Fact; r:gives {(67 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(67 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2467]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3467]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 467]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 67]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2818 a r:Inference; +skolem:lemma6143 a r:Inference; r:gives { - (2 4 6 7) :digitsToNumber 2467 . + (3 4 6 7) :digitsToNumber 3467 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(2000 400 60 7) math:sum 2467}] + [ a r:Fact; r:gives {(3000 400 60 7) math:sum 3467}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2467]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3467]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2819 a r:Inference; +skolem:lemma6144 a r:Inference; r:gives { - (7 6 4 2) :digitsToNumber 7642 . + (7 6 4 3) :digitsToNumber 7643 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(7000 600 40 2) math:sum 7642}] + [ a r:Fact; r:gives {(7000 600 40 3) math:sum 7643}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; @@ -66840,60 +144329,60 @@ skolem:lemma2819 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2820 a r:Inference; +skolem:lemma6145 a r:Inference; r:gives { - 2468 :numberToDigits (2 4 6 8). + 3468 :numberToDigits (3 4 6 8). }; r:evidence ( - [ a r:Fact; r:gives {(2468 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2468 1000) math:remainder 468}] + [ a r:Fact; r:gives {(3468 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3468 1000) math:remainder 468}] [ a r:Fact; r:gives {(468 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(468 100) math:remainder 68}] [ a r:Fact; r:gives {(68 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(68 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2468]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3468]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 468]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 68]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2821 a r:Inference; +skolem:lemma6146 a r:Inference; r:gives { - (2 4 6 8) :digitsToNumber 2468 . + (3 4 6 8) :digitsToNumber 3468 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(2000 400 60 8) math:sum 2468}] + [ a r:Fact; r:gives {(3000 400 60 8) math:sum 3468}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2468]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3468]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2822 a r:Inference; +skolem:lemma6147 a r:Inference; r:gives { - (8 6 4 2) :digitsToNumber 8642 . + (8 6 4 3) :digitsToNumber 8643 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(8000 600 40 2) math:sum 8642}] + [ a r:Fact; r:gives {(8000 600 40 3) math:sum 8643}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; @@ -66901,60 +144390,60 @@ skolem:lemma2822 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2823 a r:Inference; +skolem:lemma6148 a r:Inference; r:gives { - 2469 :numberToDigits (2 4 6 9). + 3469 :numberToDigits (3 4 6 9). }; r:evidence ( - [ a r:Fact; r:gives {(2469 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2469 1000) math:remainder 469}] + [ a r:Fact; r:gives {(3469 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3469 1000) math:remainder 469}] [ a r:Fact; r:gives {(469 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(469 100) math:remainder 69}] [ a r:Fact; r:gives {(69 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(69 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2469]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3469]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 469]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 69]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2824 a r:Inference; +skolem:lemma6149 a r:Inference; r:gives { - (2 4 6 9) :digitsToNumber 2469 . + (3 4 6 9) :digitsToNumber 3469 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(2000 400 60 9) math:sum 2469}] + [ a r:Fact; r:gives {(3000 400 60 9) math:sum 3469}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2469]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3469]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2825 a r:Inference; +skolem:lemma6150 a r:Inference; r:gives { - (9 6 4 2) :digitsToNumber 9642 . + (9 6 4 3) :digitsToNumber 9643 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(9000 600 40 2) math:sum 9642}] + [ a r:Fact; r:gives {(9000 600 40 3) math:sum 9643}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -66962,207 +144451,207 @@ skolem:lemma2825 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9642]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2826 a r:Inference; +skolem:lemma6151 a r:Inference; r:gives { - 2470 :numberToDigits (2 4 7 0). + 3470 :numberToDigits (3 4 7 0). }; r:evidence ( - [ a r:Fact; r:gives {(2470 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2470 1000) math:remainder 470}] + [ a r:Fact; r:gives {(3470 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3470 1000) math:remainder 470}] [ a r:Fact; r:gives {(470 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(470 100) math:remainder 70}] [ a r:Fact; r:gives {(70 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(70 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2470]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3470]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 470]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2827 a r:Inference; +skolem:lemma6152 a r:Inference; r:gives { - 2471 :numberToDigits (2 4 7 1). + 3471 :numberToDigits (3 4 7 1). }; r:evidence ( - [ a r:Fact; r:gives {(2471 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2471 1000) math:remainder 471}] + [ a r:Fact; r:gives {(3471 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3471 1000) math:remainder 471}] [ a r:Fact; r:gives {(471 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(471 100) math:remainder 71}] [ a r:Fact; r:gives {(71 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(71 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2471]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3471]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 471]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 71]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2828 a r:Inference; +skolem:lemma6153 a r:Inference; r:gives { - 2472 :numberToDigits (2 4 7 2). + 3472 :numberToDigits (3 4 7 2). }; r:evidence ( - [ a r:Fact; r:gives {(2472 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2472 1000) math:remainder 472}] + [ a r:Fact; r:gives {(3472 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3472 1000) math:remainder 472}] [ a r:Fact; r:gives {(472 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(472 100) math:remainder 72}] [ a r:Fact; r:gives {(72 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(72 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2472]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3472]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 472]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 72]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2829 a r:Inference; +skolem:lemma6154 a r:Inference; r:gives { - 2473 :numberToDigits (2 4 7 3). + 3473 :numberToDigits (3 4 7 3). }; r:evidence ( - [ a r:Fact; r:gives {(2473 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2473 1000) math:remainder 473}] + [ a r:Fact; r:gives {(3473 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3473 1000) math:remainder 473}] [ a r:Fact; r:gives {(473 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(473 100) math:remainder 73}] [ a r:Fact; r:gives {(73 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(73 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2473]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3473]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 473]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 73]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2830 a r:Inference; +skolem:lemma6155 a r:Inference; r:gives { - 2474 :numberToDigits (2 4 7 4). + 3474 :numberToDigits (3 4 7 4). }; r:evidence ( - [ a r:Fact; r:gives {(2474 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2474 1000) math:remainder 474}] + [ a r:Fact; r:gives {(3474 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3474 1000) math:remainder 474}] [ a r:Fact; r:gives {(474 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(474 100) math:remainder 74}] [ a r:Fact; r:gives {(74 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(74 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2474]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3474]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 474]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 74]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2831 a r:Inference; +skolem:lemma6156 a r:Inference; r:gives { - 2475 :numberToDigits (2 4 7 5). + 3475 :numberToDigits (3 4 7 5). }; r:evidence ( - [ a r:Fact; r:gives {(2475 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2475 1000) math:remainder 475}] + [ a r:Fact; r:gives {(3475 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3475 1000) math:remainder 475}] [ a r:Fact; r:gives {(475 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(475 100) math:remainder 75}] [ a r:Fact; r:gives {(75 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(75 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2475]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3475]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 475]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 75]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2832 a r:Inference; +skolem:lemma6157 a r:Inference; r:gives { - 2476 :numberToDigits (2 4 7 6). + 3476 :numberToDigits (3 4 7 6). }; r:evidence ( - [ a r:Fact; r:gives {(2476 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2476 1000) math:remainder 476}] + [ a r:Fact; r:gives {(3476 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3476 1000) math:remainder 476}] [ a r:Fact; r:gives {(476 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(476 100) math:remainder 76}] [ a r:Fact; r:gives {(76 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(76 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2476]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3476]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 476]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 76]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2833 a r:Inference; +skolem:lemma6158 a r:Inference; r:gives { - 2477 :numberToDigits (2 4 7 7). + 3477 :numberToDigits (3 4 7 7). }; r:evidence ( - [ a r:Fact; r:gives {(2477 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2477 1000) math:remainder 477}] + [ a r:Fact; r:gives {(3477 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3477 1000) math:remainder 477}] [ a r:Fact; r:gives {(477 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(477 100) math:remainder 77}] [ a r:Fact; r:gives {(77 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(77 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2477]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3477]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 477]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 77]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2834 a r:Inference; +skolem:lemma6159 a r:Inference; r:gives { - (2 4 7 7) :digitsToNumber 2477 . + (3 4 7 7) :digitsToNumber 3477 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(2000 400 70 7) math:sum 2477}] + [ a r:Fact; r:gives {(3000 400 70 7) math:sum 3477}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2477]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3477]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2835 a r:Inference; +skolem:lemma6160 a r:Inference; r:gives { - (7 7 4 2) :digitsToNumber 7742 . + (7 7 4 3) :digitsToNumber 7743 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(7 100) math:product 700}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(7000 700 40 2) math:sum 7742}] + [ a r:Fact; r:gives {(7000 700 40 3) math:sum 7743}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; @@ -67170,60 +144659,60 @@ skolem:lemma2835 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7742]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2836 a r:Inference; +skolem:lemma6161 a r:Inference; r:gives { - 2478 :numberToDigits (2 4 7 8). + 3478 :numberToDigits (3 4 7 8). }; r:evidence ( - [ a r:Fact; r:gives {(2478 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2478 1000) math:remainder 478}] + [ a r:Fact; r:gives {(3478 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3478 1000) math:remainder 478}] [ a r:Fact; r:gives {(478 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(478 100) math:remainder 78}] [ a r:Fact; r:gives {(78 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(78 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2478]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3478]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 478]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 78]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2837 a r:Inference; +skolem:lemma6162 a r:Inference; r:gives { - (2 4 7 8) :digitsToNumber 2478 . + (3 4 7 8) :digitsToNumber 3478 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(2000 400 70 8) math:sum 2478}] + [ a r:Fact; r:gives {(3000 400 70 8) math:sum 3478}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2478]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3478]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2838 a r:Inference; +skolem:lemma6163 a r:Inference; r:gives { - (8 7 4 2) :digitsToNumber 8742 . + (8 7 4 3) :digitsToNumber 8743 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(7 100) math:product 700}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(8000 700 40 2) math:sum 8742}] + [ a r:Fact; r:gives {(8000 700 40 3) math:sum 8743}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; @@ -67231,60 +144720,60 @@ skolem:lemma2838 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8742]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2839 a r:Inference; +skolem:lemma6164 a r:Inference; r:gives { - 2479 :numberToDigits (2 4 7 9). + 3479 :numberToDigits (3 4 7 9). }; r:evidence ( - [ a r:Fact; r:gives {(2479 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2479 1000) math:remainder 479}] + [ a r:Fact; r:gives {(3479 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3479 1000) math:remainder 479}] [ a r:Fact; r:gives {(479 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(479 100) math:remainder 79}] [ a r:Fact; r:gives {(79 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(79 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2479]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3479]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 479]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 79]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2840 a r:Inference; +skolem:lemma6165 a r:Inference; r:gives { - (2 4 7 9) :digitsToNumber 2479 . + (3 4 7 9) :digitsToNumber 3479 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(2000 400 70 9) math:sum 2479}] + [ a r:Fact; r:gives {(3000 400 70 9) math:sum 3479}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2479]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3479]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2841 a r:Inference; +skolem:lemma6166 a r:Inference; r:gives { - (9 7 4 2) :digitsToNumber 9742 . + (9 7 4 3) :digitsToNumber 9743 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(7 100) math:product 700}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(9000 700 40 2) math:sum 9742}] + [ a r:Fact; r:gives {(9000 700 40 3) math:sum 9743}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -67292,228 +144781,228 @@ skolem:lemma2841 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9742]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2842 a r:Inference; +skolem:lemma6167 a r:Inference; r:gives { - 2480 :numberToDigits (2 4 8 0). + 3480 :numberToDigits (3 4 8 0). }; r:evidence ( - [ a r:Fact; r:gives {(2480 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2480 1000) math:remainder 480}] + [ a r:Fact; r:gives {(3480 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3480 1000) math:remainder 480}] [ a r:Fact; r:gives {(480 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(480 100) math:remainder 80}] [ a r:Fact; r:gives {(80 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(80 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2480]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3480]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 480]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2843 a r:Inference; +skolem:lemma6168 a r:Inference; r:gives { - 2481 :numberToDigits (2 4 8 1). + 3481 :numberToDigits (3 4 8 1). }; r:evidence ( - [ a r:Fact; r:gives {(2481 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2481 1000) math:remainder 481}] + [ a r:Fact; r:gives {(3481 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3481 1000) math:remainder 481}] [ a r:Fact; r:gives {(481 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(481 100) math:remainder 81}] [ a r:Fact; r:gives {(81 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(81 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2481]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3481]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 481]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 81]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2844 a r:Inference; +skolem:lemma6169 a r:Inference; r:gives { - 2482 :numberToDigits (2 4 8 2). + 3482 :numberToDigits (3 4 8 2). }; r:evidence ( - [ a r:Fact; r:gives {(2482 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2482 1000) math:remainder 482}] + [ a r:Fact; r:gives {(3482 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3482 1000) math:remainder 482}] [ a r:Fact; r:gives {(482 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(482 100) math:remainder 82}] [ a r:Fact; r:gives {(82 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(82 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2482]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3482]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 482]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 82]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2845 a r:Inference; +skolem:lemma6170 a r:Inference; r:gives { - 2483 :numberToDigits (2 4 8 3). + 3483 :numberToDigits (3 4 8 3). }; r:evidence ( - [ a r:Fact; r:gives {(2483 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2483 1000) math:remainder 483}] + [ a r:Fact; r:gives {(3483 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3483 1000) math:remainder 483}] [ a r:Fact; r:gives {(483 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(483 100) math:remainder 83}] [ a r:Fact; r:gives {(83 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(83 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2483]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3483]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 483]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 83]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2846 a r:Inference; +skolem:lemma6171 a r:Inference; r:gives { - 2484 :numberToDigits (2 4 8 4). + 3484 :numberToDigits (3 4 8 4). }; r:evidence ( - [ a r:Fact; r:gives {(2484 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2484 1000) math:remainder 484}] + [ a r:Fact; r:gives {(3484 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3484 1000) math:remainder 484}] [ a r:Fact; r:gives {(484 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(484 100) math:remainder 84}] [ a r:Fact; r:gives {(84 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(84 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2484]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3484]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 484]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 84]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2847 a r:Inference; +skolem:lemma6172 a r:Inference; r:gives { - 2485 :numberToDigits (2 4 8 5). + 3485 :numberToDigits (3 4 8 5). }; r:evidence ( - [ a r:Fact; r:gives {(2485 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2485 1000) math:remainder 485}] + [ a r:Fact; r:gives {(3485 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3485 1000) math:remainder 485}] [ a r:Fact; r:gives {(485 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(485 100) math:remainder 85}] [ a r:Fact; r:gives {(85 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(85 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2485]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3485]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 485]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 85]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2848 a r:Inference; +skolem:lemma6173 a r:Inference; r:gives { - 2486 :numberToDigits (2 4 8 6). + 3486 :numberToDigits (3 4 8 6). }; r:evidence ( - [ a r:Fact; r:gives {(2486 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2486 1000) math:remainder 486}] + [ a r:Fact; r:gives {(3486 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3486 1000) math:remainder 486}] [ a r:Fact; r:gives {(486 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(486 100) math:remainder 86}] [ a r:Fact; r:gives {(86 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(86 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2486]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3486]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 486]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 86]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2849 a r:Inference; +skolem:lemma6174 a r:Inference; r:gives { - 2487 :numberToDigits (2 4 8 7). + 3487 :numberToDigits (3 4 8 7). }; r:evidence ( - [ a r:Fact; r:gives {(2487 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2487 1000) math:remainder 487}] + [ a r:Fact; r:gives {(3487 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3487 1000) math:remainder 487}] [ a r:Fact; r:gives {(487 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(487 100) math:remainder 87}] [ a r:Fact; r:gives {(87 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(87 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2487]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3487]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 487]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 87]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2850 a r:Inference; +skolem:lemma6175 a r:Inference; r:gives { - 2488 :numberToDigits (2 4 8 8). + 3488 :numberToDigits (3 4 8 8). }; r:evidence ( - [ a r:Fact; r:gives {(2488 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2488 1000) math:remainder 488}] + [ a r:Fact; r:gives {(3488 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3488 1000) math:remainder 488}] [ a r:Fact; r:gives {(488 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(488 100) math:remainder 88}] [ a r:Fact; r:gives {(88 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(88 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2488]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3488]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 488]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 88]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2851 a r:Inference; +skolem:lemma6176 a r:Inference; r:gives { - (2 4 8 8) :digitsToNumber 2488 . + (3 4 8 8) :digitsToNumber 3488 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(8 10) math:product 80}] - [ a r:Fact; r:gives {(2000 400 80 8) math:sum 2488}] + [ a r:Fact; r:gives {(3000 400 80 8) math:sum 3488}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2488]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3488]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2852 a r:Inference; +skolem:lemma6177 a r:Inference; r:gives { - (8 8 4 2) :digitsToNumber 8842 . + (8 8 4 3) :digitsToNumber 8843 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(8 100) math:product 800}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(8000 800 40 2) math:sum 8842}] + [ a r:Fact; r:gives {(8000 800 40 3) math:sum 8843}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; @@ -67521,60 +145010,60 @@ skolem:lemma2852 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8842]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8843]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2853 a r:Inference; +skolem:lemma6178 a r:Inference; r:gives { - 2489 :numberToDigits (2 4 8 9). + 3489 :numberToDigits (3 4 8 9). }; r:evidence ( - [ a r:Fact; r:gives {(2489 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2489 1000) math:remainder 489}] + [ a r:Fact; r:gives {(3489 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3489 1000) math:remainder 489}] [ a r:Fact; r:gives {(489 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(489 100) math:remainder 89}] [ a r:Fact; r:gives {(89 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(89 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2489]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3489]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 489]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 89]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2854 a r:Inference; +skolem:lemma6179 a r:Inference; r:gives { - (2 4 8 9) :digitsToNumber 2489 . + (3 4 8 9) :digitsToNumber 3489 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(8 10) math:product 80}] - [ a r:Fact; r:gives {(2000 400 80 9) math:sum 2489}] + [ a r:Fact; r:gives {(3000 400 80 9) math:sum 3489}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2489]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3489]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2855 a r:Inference; +skolem:lemma6180 a r:Inference; r:gives { - (9 8 4 2) :digitsToNumber 9842 . + (9 8 4 3) :digitsToNumber 9843 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(8 100) math:product 800}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(9000 800 40 2) math:sum 9842}] + [ a r:Fact; r:gives {(9000 800 40 3) math:sum 9843}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -67582,249 +145071,249 @@ skolem:lemma2855 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9842]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9843]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2856 a r:Inference; +skolem:lemma6181 a r:Inference; r:gives { - 2490 :numberToDigits (2 4 9 0). + 3490 :numberToDigits (3 4 9 0). }; r:evidence ( - [ a r:Fact; r:gives {(2490 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2490 1000) math:remainder 490}] + [ a r:Fact; r:gives {(3490 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3490 1000) math:remainder 490}] [ a r:Fact; r:gives {(490 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(490 100) math:remainder 90}] [ a r:Fact; r:gives {(90 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(90 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2490]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3490]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 490]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 90]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2857 a r:Inference; +skolem:lemma6182 a r:Inference; r:gives { - 2491 :numberToDigits (2 4 9 1). + 3491 :numberToDigits (3 4 9 1). }; r:evidence ( - [ a r:Fact; r:gives {(2491 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2491 1000) math:remainder 491}] + [ a r:Fact; r:gives {(3491 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3491 1000) math:remainder 491}] [ a r:Fact; r:gives {(491 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(491 100) math:remainder 91}] [ a r:Fact; r:gives {(91 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(91 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2491]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3491]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 491]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 91]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2858 a r:Inference; +skolem:lemma6183 a r:Inference; r:gives { - 2492 :numberToDigits (2 4 9 2). + 3492 :numberToDigits (3 4 9 2). }; r:evidence ( - [ a r:Fact; r:gives {(2492 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2492 1000) math:remainder 492}] + [ a r:Fact; r:gives {(3492 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3492 1000) math:remainder 492}] [ a r:Fact; r:gives {(492 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(492 100) math:remainder 92}] [ a r:Fact; r:gives {(92 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(92 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2492]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3492]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 492]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 92]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2859 a r:Inference; +skolem:lemma6184 a r:Inference; r:gives { - 2493 :numberToDigits (2 4 9 3). + 3493 :numberToDigits (3 4 9 3). }; r:evidence ( - [ a r:Fact; r:gives {(2493 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2493 1000) math:remainder 493}] + [ a r:Fact; r:gives {(3493 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3493 1000) math:remainder 493}] [ a r:Fact; r:gives {(493 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(493 100) math:remainder 93}] [ a r:Fact; r:gives {(93 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(93 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2493]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3493]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 493]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 93]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2860 a r:Inference; +skolem:lemma6185 a r:Inference; r:gives { - 2494 :numberToDigits (2 4 9 4). + 3494 :numberToDigits (3 4 9 4). }; r:evidence ( - [ a r:Fact; r:gives {(2494 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2494 1000) math:remainder 494}] + [ a r:Fact; r:gives {(3494 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3494 1000) math:remainder 494}] [ a r:Fact; r:gives {(494 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(494 100) math:remainder 94}] [ a r:Fact; r:gives {(94 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(94 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2494]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3494]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 494]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 94]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2861 a r:Inference; +skolem:lemma6186 a r:Inference; r:gives { - 2495 :numberToDigits (2 4 9 5). + 3495 :numberToDigits (3 4 9 5). }; r:evidence ( - [ a r:Fact; r:gives {(2495 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2495 1000) math:remainder 495}] + [ a r:Fact; r:gives {(3495 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3495 1000) math:remainder 495}] [ a r:Fact; r:gives {(495 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(495 100) math:remainder 95}] [ a r:Fact; r:gives {(95 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(95 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2495]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3495]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 495]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 95]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2862 a r:Inference; +skolem:lemma6187 a r:Inference; r:gives { - 2496 :numberToDigits (2 4 9 6). + 3496 :numberToDigits (3 4 9 6). }; r:evidence ( - [ a r:Fact; r:gives {(2496 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2496 1000) math:remainder 496}] + [ a r:Fact; r:gives {(3496 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3496 1000) math:remainder 496}] [ a r:Fact; r:gives {(496 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(496 100) math:remainder 96}] [ a r:Fact; r:gives {(96 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(96 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2496]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3496]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 496]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 96]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2863 a r:Inference; +skolem:lemma6188 a r:Inference; r:gives { - 2497 :numberToDigits (2 4 9 7). + 3497 :numberToDigits (3 4 9 7). }; r:evidence ( - [ a r:Fact; r:gives {(2497 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2497 1000) math:remainder 497}] + [ a r:Fact; r:gives {(3497 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3497 1000) math:remainder 497}] [ a r:Fact; r:gives {(497 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(497 100) math:remainder 97}] [ a r:Fact; r:gives {(97 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(97 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2497]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3497]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 497]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 97]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2864 a r:Inference; +skolem:lemma6189 a r:Inference; r:gives { - 2498 :numberToDigits (2 4 9 8). + 3498 :numberToDigits (3 4 9 8). }; r:evidence ( - [ a r:Fact; r:gives {(2498 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2498 1000) math:remainder 498}] + [ a r:Fact; r:gives {(3498 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3498 1000) math:remainder 498}] [ a r:Fact; r:gives {(498 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(498 100) math:remainder 98}] [ a r:Fact; r:gives {(98 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(98 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2498]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3498]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 498]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 98]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2865 a r:Inference; +skolem:lemma6190 a r:Inference; r:gives { - 2499 :numberToDigits (2 4 9 9). + 3499 :numberToDigits (3 4 9 9). }; r:evidence ( - [ a r:Fact; r:gives {(2499 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2499 1000) math:remainder 499}] + [ a r:Fact; r:gives {(3499 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3499 1000) math:remainder 499}] [ a r:Fact; r:gives {(499 100) math:integerQuotient 4}] [ a r:Fact; r:gives {(499 100) math:remainder 99}] [ a r:Fact; r:gives {(99 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(99 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2499]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3499]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 499]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 99]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2866 a r:Inference; +skolem:lemma6191 a r:Inference; r:gives { - (2 4 9 9) :digitsToNumber 2499 . + (3 4 9 9) :digitsToNumber 3499 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(4 100) math:product 400}] [ a r:Fact; r:gives {(9 10) math:product 90}] - [ a r:Fact; r:gives {(2000 400 90 9) math:sum 2499}] + [ a r:Fact; r:gives {(3000 400 90 9) math:sum 3499}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 400]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 90]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2499]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3499]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2867 a r:Inference; +skolem:lemma6192 a r:Inference; r:gives { - (9 9 4 2) :digitsToNumber 9942 . + (9 9 4 3) :digitsToNumber 9943 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(9 100) math:product 900}] [ a r:Fact; r:gives {(4 10) math:product 40}] - [ a r:Fact; r:gives {(9000 900 40 2) math:sum 9942}] + [ a r:Fact; r:gives {(9000 900 40 3) math:sum 9943}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -67832,1215 +145321,1215 @@ skolem:lemma2867 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9942]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9943]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2868 a r:Inference; +skolem:lemma6193 a r:Inference; r:gives { - 2500 :numberToDigits (2 5 0 0). + 3500 :numberToDigits (3 5 0 0). }; r:evidence ( - [ a r:Fact; r:gives {(2500 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2500 1000) math:remainder 500}] + [ a r:Fact; r:gives {(3500 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3500 1000) math:remainder 500}] [ a r:Fact; r:gives {(500 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(500 100) math:remainder 0}] [ a r:Fact; r:gives {(0 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(0 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2500]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2869 a r:Inference; +skolem:lemma6194 a r:Inference; r:gives { - 2501 :numberToDigits (2 5 0 1). + 3501 :numberToDigits (3 5 0 1). }; r:evidence ( - [ a r:Fact; r:gives {(2501 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2501 1000) math:remainder 501}] + [ a r:Fact; r:gives {(3501 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3501 1000) math:remainder 501}] [ a r:Fact; r:gives {(501 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(501 100) math:remainder 1}] [ a r:Fact; r:gives {(1 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(1 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2501]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3501]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 501]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2870 a r:Inference; +skolem:lemma6195 a r:Inference; r:gives { - 2502 :numberToDigits (2 5 0 2). + 3502 :numberToDigits (3 5 0 2). }; r:evidence ( - [ a r:Fact; r:gives {(2502 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2502 1000) math:remainder 502}] + [ a r:Fact; r:gives {(3502 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3502 1000) math:remainder 502}] [ a r:Fact; r:gives {(502 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(502 100) math:remainder 2}] [ a r:Fact; r:gives {(2 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(2 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2502]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3502]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 502]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2871 a r:Inference; +skolem:lemma6196 a r:Inference; r:gives { - 2503 :numberToDigits (2 5 0 3). + 3503 :numberToDigits (3 5 0 3). }; r:evidence ( - [ a r:Fact; r:gives {(2503 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2503 1000) math:remainder 503}] + [ a r:Fact; r:gives {(3503 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3503 1000) math:remainder 503}] [ a r:Fact; r:gives {(503 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(503 100) math:remainder 3}] [ a r:Fact; r:gives {(3 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(3 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2503]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3503]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 503]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2872 a r:Inference; +skolem:lemma6197 a r:Inference; r:gives { - 2504 :numberToDigits (2 5 0 4). + 3504 :numberToDigits (3 5 0 4). }; r:evidence ( - [ a r:Fact; r:gives {(2504 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2504 1000) math:remainder 504}] + [ a r:Fact; r:gives {(3504 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3504 1000) math:remainder 504}] [ a r:Fact; r:gives {(504 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(504 100) math:remainder 4}] [ a r:Fact; r:gives {(4 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(4 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2504]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3504]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 504]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2873 a r:Inference; +skolem:lemma6198 a r:Inference; r:gives { - 2505 :numberToDigits (2 5 0 5). + 3505 :numberToDigits (3 5 0 5). }; r:evidence ( - [ a r:Fact; r:gives {(2505 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2505 1000) math:remainder 505}] + [ a r:Fact; r:gives {(3505 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3505 1000) math:remainder 505}] [ a r:Fact; r:gives {(505 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(505 100) math:remainder 5}] [ a r:Fact; r:gives {(5 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(5 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2505]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3505]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 505]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2874 a r:Inference; +skolem:lemma6199 a r:Inference; r:gives { - 2506 :numberToDigits (2 5 0 6). + 3506 :numberToDigits (3 5 0 6). }; r:evidence ( - [ a r:Fact; r:gives {(2506 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2506 1000) math:remainder 506}] + [ a r:Fact; r:gives {(3506 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3506 1000) math:remainder 506}] [ a r:Fact; r:gives {(506 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(506 100) math:remainder 6}] [ a r:Fact; r:gives {(6 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(6 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2506]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3506]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 506]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2875 a r:Inference; +skolem:lemma6200 a r:Inference; r:gives { - 2507 :numberToDigits (2 5 0 7). + 3507 :numberToDigits (3 5 0 7). }; r:evidence ( - [ a r:Fact; r:gives {(2507 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2507 1000) math:remainder 507}] + [ a r:Fact; r:gives {(3507 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3507 1000) math:remainder 507}] [ a r:Fact; r:gives {(507 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(507 100) math:remainder 7}] [ a r:Fact; r:gives {(7 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(7 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2507]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3507]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 507]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2876 a r:Inference; +skolem:lemma6201 a r:Inference; r:gives { - 2508 :numberToDigits (2 5 0 8). + 3508 :numberToDigits (3 5 0 8). }; r:evidence ( - [ a r:Fact; r:gives {(2508 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2508 1000) math:remainder 508}] + [ a r:Fact; r:gives {(3508 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3508 1000) math:remainder 508}] [ a r:Fact; r:gives {(508 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(508 100) math:remainder 8}] [ a r:Fact; r:gives {(8 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(8 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2508]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3508]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 508]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2877 a r:Inference; +skolem:lemma6202 a r:Inference; r:gives { - 2509 :numberToDigits (2 5 0 9). + 3509 :numberToDigits (3 5 0 9). }; r:evidence ( - [ a r:Fact; r:gives {(2509 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2509 1000) math:remainder 509}] + [ a r:Fact; r:gives {(3509 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3509 1000) math:remainder 509}] [ a r:Fact; r:gives {(509 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(509 100) math:remainder 9}] [ a r:Fact; r:gives {(9 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(9 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2509]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3509]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 509]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2878 a r:Inference; +skolem:lemma6203 a r:Inference; r:gives { - 2510 :numberToDigits (2 5 1 0). + 3510 :numberToDigits (3 5 1 0). }; r:evidence ( - [ a r:Fact; r:gives {(2510 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2510 1000) math:remainder 510}] + [ a r:Fact; r:gives {(3510 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3510 1000) math:remainder 510}] [ a r:Fact; r:gives {(510 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(510 100) math:remainder 10}] [ a r:Fact; r:gives {(10 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(10 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2510]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3510]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 510]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2879 a r:Inference; +skolem:lemma6204 a r:Inference; r:gives { - 2511 :numberToDigits (2 5 1 1). + 3511 :numberToDigits (3 5 1 1). }; r:evidence ( - [ a r:Fact; r:gives {(2511 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2511 1000) math:remainder 511}] + [ a r:Fact; r:gives {(3511 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3511 1000) math:remainder 511}] [ a r:Fact; r:gives {(511 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(511 100) math:remainder 11}] [ a r:Fact; r:gives {(11 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(11 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2511]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3511]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 511]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 11]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2880 a r:Inference; +skolem:lemma6205 a r:Inference; r:gives { - 2512 :numberToDigits (2 5 1 2). + 3512 :numberToDigits (3 5 1 2). }; r:evidence ( - [ a r:Fact; r:gives {(2512 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2512 1000) math:remainder 512}] + [ a r:Fact; r:gives {(3512 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3512 1000) math:remainder 512}] [ a r:Fact; r:gives {(512 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(512 100) math:remainder 12}] [ a r:Fact; r:gives {(12 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(12 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2512]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3512]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 512]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2881 a r:Inference; +skolem:lemma6206 a r:Inference; r:gives { - 2513 :numberToDigits (2 5 1 3). + 3513 :numberToDigits (3 5 1 3). }; r:evidence ( - [ a r:Fact; r:gives {(2513 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2513 1000) math:remainder 513}] + [ a r:Fact; r:gives {(3513 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3513 1000) math:remainder 513}] [ a r:Fact; r:gives {(513 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(513 100) math:remainder 13}] [ a r:Fact; r:gives {(13 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(13 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2513]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3513]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 513]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 13]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2882 a r:Inference; +skolem:lemma6207 a r:Inference; r:gives { - 2514 :numberToDigits (2 5 1 4). + 3514 :numberToDigits (3 5 1 4). }; r:evidence ( - [ a r:Fact; r:gives {(2514 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2514 1000) math:remainder 514}] + [ a r:Fact; r:gives {(3514 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3514 1000) math:remainder 514}] [ a r:Fact; r:gives {(514 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(514 100) math:remainder 14}] [ a r:Fact; r:gives {(14 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(14 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2514]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3514]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 514]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 14]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2883 a r:Inference; +skolem:lemma6208 a r:Inference; r:gives { - 2515 :numberToDigits (2 5 1 5). + 3515 :numberToDigits (3 5 1 5). }; r:evidence ( - [ a r:Fact; r:gives {(2515 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2515 1000) math:remainder 515}] + [ a r:Fact; r:gives {(3515 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3515 1000) math:remainder 515}] [ a r:Fact; r:gives {(515 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(515 100) math:remainder 15}] [ a r:Fact; r:gives {(15 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(15 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2515]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3515]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 515]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 15]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2884 a r:Inference; +skolem:lemma6209 a r:Inference; r:gives { - 2516 :numberToDigits (2 5 1 6). + 3516 :numberToDigits (3 5 1 6). }; r:evidence ( - [ a r:Fact; r:gives {(2516 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2516 1000) math:remainder 516}] + [ a r:Fact; r:gives {(3516 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3516 1000) math:remainder 516}] [ a r:Fact; r:gives {(516 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(516 100) math:remainder 16}] [ a r:Fact; r:gives {(16 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(16 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2516]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3516]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 516]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 16]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2885 a r:Inference; +skolem:lemma6210 a r:Inference; r:gives { - 2517 :numberToDigits (2 5 1 7). + 3517 :numberToDigits (3 5 1 7). }; r:evidence ( - [ a r:Fact; r:gives {(2517 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2517 1000) math:remainder 517}] + [ a r:Fact; r:gives {(3517 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3517 1000) math:remainder 517}] [ a r:Fact; r:gives {(517 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(517 100) math:remainder 17}] [ a r:Fact; r:gives {(17 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(17 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2517]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3517]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 517]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 17]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2886 a r:Inference; +skolem:lemma6211 a r:Inference; r:gives { - 2518 :numberToDigits (2 5 1 8). + 3518 :numberToDigits (3 5 1 8). }; r:evidence ( - [ a r:Fact; r:gives {(2518 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2518 1000) math:remainder 518}] + [ a r:Fact; r:gives {(3518 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3518 1000) math:remainder 518}] [ a r:Fact; r:gives {(518 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(518 100) math:remainder 18}] [ a r:Fact; r:gives {(18 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(18 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2518]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3518]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 518]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 18]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2887 a r:Inference; +skolem:lemma6212 a r:Inference; r:gives { - 2519 :numberToDigits (2 5 1 9). + 3519 :numberToDigits (3 5 1 9). }; r:evidence ( - [ a r:Fact; r:gives {(2519 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2519 1000) math:remainder 519}] + [ a r:Fact; r:gives {(3519 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3519 1000) math:remainder 519}] [ a r:Fact; r:gives {(519 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(519 100) math:remainder 19}] [ a r:Fact; r:gives {(19 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(19 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2519]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3519]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 519]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 19]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2888 a r:Inference; +skolem:lemma6213 a r:Inference; r:gives { - 2520 :numberToDigits (2 5 2 0). + 3520 :numberToDigits (3 5 2 0). }; r:evidence ( - [ a r:Fact; r:gives {(2520 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2520 1000) math:remainder 520}] + [ a r:Fact; r:gives {(3520 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3520 1000) math:remainder 520}] [ a r:Fact; r:gives {(520 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(520 100) math:remainder 20}] [ a r:Fact; r:gives {(20 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(20 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2520]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3520]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 520]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 20]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2889 a r:Inference; +skolem:lemma6214 a r:Inference; r:gives { - 2521 :numberToDigits (2 5 2 1). + 3521 :numberToDigits (3 5 2 1). }; r:evidence ( - [ a r:Fact; r:gives {(2521 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2521 1000) math:remainder 521}] + [ a r:Fact; r:gives {(3521 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3521 1000) math:remainder 521}] [ a r:Fact; r:gives {(521 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(521 100) math:remainder 21}] [ a r:Fact; r:gives {(21 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(21 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2521]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3521]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 521]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 21]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2890 a r:Inference; +skolem:lemma6215 a r:Inference; r:gives { - 2522 :numberToDigits (2 5 2 2). + 3522 :numberToDigits (3 5 2 2). }; r:evidence ( - [ a r:Fact; r:gives {(2522 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2522 1000) math:remainder 522}] + [ a r:Fact; r:gives {(3522 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3522 1000) math:remainder 522}] [ a r:Fact; r:gives {(522 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(522 100) math:remainder 22}] [ a r:Fact; r:gives {(22 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(22 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2522]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3522]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 522]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2891 a r:Inference; +skolem:lemma6216 a r:Inference; r:gives { - 2523 :numberToDigits (2 5 2 3). + 3523 :numberToDigits (3 5 2 3). }; r:evidence ( - [ a r:Fact; r:gives {(2523 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2523 1000) math:remainder 523}] + [ a r:Fact; r:gives {(3523 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3523 1000) math:remainder 523}] [ a r:Fact; r:gives {(523 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(523 100) math:remainder 23}] [ a r:Fact; r:gives {(23 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(23 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2523]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3523]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 523]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2892 a r:Inference; +skolem:lemma6217 a r:Inference; r:gives { - 2524 :numberToDigits (2 5 2 4). + 3524 :numberToDigits (3 5 2 4). }; r:evidence ( - [ a r:Fact; r:gives {(2524 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2524 1000) math:remainder 524}] + [ a r:Fact; r:gives {(3524 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3524 1000) math:remainder 524}] [ a r:Fact; r:gives {(524 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(524 100) math:remainder 24}] [ a r:Fact; r:gives {(24 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(24 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2524]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3524]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 524]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2893 a r:Inference; +skolem:lemma6218 a r:Inference; r:gives { - 2525 :numberToDigits (2 5 2 5). + 3525 :numberToDigits (3 5 2 5). }; r:evidence ( - [ a r:Fact; r:gives {(2525 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2525 1000) math:remainder 525}] + [ a r:Fact; r:gives {(3525 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3525 1000) math:remainder 525}] [ a r:Fact; r:gives {(525 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(525 100) math:remainder 25}] [ a r:Fact; r:gives {(25 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(25 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2525]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3525]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 525]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2894 a r:Inference; +skolem:lemma6219 a r:Inference; r:gives { - 2526 :numberToDigits (2 5 2 6). + 3526 :numberToDigits (3 5 2 6). }; r:evidence ( - [ a r:Fact; r:gives {(2526 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2526 1000) math:remainder 526}] + [ a r:Fact; r:gives {(3526 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3526 1000) math:remainder 526}] [ a r:Fact; r:gives {(526 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(526 100) math:remainder 26}] [ a r:Fact; r:gives {(26 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(26 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2526]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3526]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 526]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2895 a r:Inference; +skolem:lemma6220 a r:Inference; r:gives { - 2527 :numberToDigits (2 5 2 7). + 3527 :numberToDigits (3 5 2 7). }; r:evidence ( - [ a r:Fact; r:gives {(2527 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2527 1000) math:remainder 527}] + [ a r:Fact; r:gives {(3527 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3527 1000) math:remainder 527}] [ a r:Fact; r:gives {(527 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(527 100) math:remainder 27}] [ a r:Fact; r:gives {(27 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(27 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2527]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3527]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 527]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2896 a r:Inference; +skolem:lemma6221 a r:Inference; r:gives { - 2528 :numberToDigits (2 5 2 8). + 3528 :numberToDigits (3 5 2 8). }; r:evidence ( - [ a r:Fact; r:gives {(2528 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2528 1000) math:remainder 528}] + [ a r:Fact; r:gives {(3528 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3528 1000) math:remainder 528}] [ a r:Fact; r:gives {(528 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(528 100) math:remainder 28}] [ a r:Fact; r:gives {(28 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(28 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2528]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3528]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 528]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2897 a r:Inference; +skolem:lemma6222 a r:Inference; r:gives { - 2529 :numberToDigits (2 5 2 9). + 3529 :numberToDigits (3 5 2 9). }; r:evidence ( - [ a r:Fact; r:gives {(2529 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2529 1000) math:remainder 529}] + [ a r:Fact; r:gives {(3529 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3529 1000) math:remainder 529}] [ a r:Fact; r:gives {(529 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(529 100) math:remainder 29}] [ a r:Fact; r:gives {(29 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(29 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2529]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3529]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 529]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2898 a r:Inference; +skolem:lemma6223 a r:Inference; r:gives { - 2530 :numberToDigits (2 5 3 0). + 3530 :numberToDigits (3 5 3 0). }; r:evidence ( - [ a r:Fact; r:gives {(2530 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2530 1000) math:remainder 530}] + [ a r:Fact; r:gives {(3530 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3530 1000) math:remainder 530}] [ a r:Fact; r:gives {(530 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(530 100) math:remainder 30}] [ a r:Fact; r:gives {(30 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(30 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2530]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3530]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 530]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2899 a r:Inference; +skolem:lemma6224 a r:Inference; r:gives { - 2531 :numberToDigits (2 5 3 1). + 3531 :numberToDigits (3 5 3 1). }; r:evidence ( - [ a r:Fact; r:gives {(2531 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2531 1000) math:remainder 531}] + [ a r:Fact; r:gives {(3531 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3531 1000) math:remainder 531}] [ a r:Fact; r:gives {(531 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(531 100) math:remainder 31}] [ a r:Fact; r:gives {(31 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(31 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2531]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3531]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 531]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 31]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2900 a r:Inference; +skolem:lemma6225 a r:Inference; r:gives { - 2532 :numberToDigits (2 5 3 2). + 3532 :numberToDigits (3 5 3 2). }; r:evidence ( - [ a r:Fact; r:gives {(2532 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2532 1000) math:remainder 532}] + [ a r:Fact; r:gives {(3532 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3532 1000) math:remainder 532}] [ a r:Fact; r:gives {(532 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(532 100) math:remainder 32}] [ a r:Fact; r:gives {(32 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(32 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2532]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3532]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 532]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 32]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2901 a r:Inference; +skolem:lemma6226 a r:Inference; r:gives { - 2533 :numberToDigits (2 5 3 3). + 3533 :numberToDigits (3 5 3 3). }; r:evidence ( - [ a r:Fact; r:gives {(2533 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2533 1000) math:remainder 533}] + [ a r:Fact; r:gives {(3533 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3533 1000) math:remainder 533}] [ a r:Fact; r:gives {(533 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(533 100) math:remainder 33}] [ a r:Fact; r:gives {(33 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(33 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2533]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3533]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 533]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 33]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2902 a r:Inference; +skolem:lemma6227 a r:Inference; r:gives { - 2534 :numberToDigits (2 5 3 4). + 3534 :numberToDigits (3 5 3 4). }; r:evidence ( - [ a r:Fact; r:gives {(2534 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2534 1000) math:remainder 534}] + [ a r:Fact; r:gives {(3534 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3534 1000) math:remainder 534}] [ a r:Fact; r:gives {(534 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(534 100) math:remainder 34}] [ a r:Fact; r:gives {(34 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(34 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2534]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3534]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 534]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 34]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2903 a r:Inference; +skolem:lemma6228 a r:Inference; r:gives { - 2535 :numberToDigits (2 5 3 5). + 3535 :numberToDigits (3 5 3 5). }; r:evidence ( - [ a r:Fact; r:gives {(2535 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2535 1000) math:remainder 535}] + [ a r:Fact; r:gives {(3535 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3535 1000) math:remainder 535}] [ a r:Fact; r:gives {(535 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(535 100) math:remainder 35}] [ a r:Fact; r:gives {(35 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(35 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2535]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3535]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 535]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 35]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2904 a r:Inference; +skolem:lemma6229 a r:Inference; r:gives { - 2536 :numberToDigits (2 5 3 6). + 3536 :numberToDigits (3 5 3 6). }; r:evidence ( - [ a r:Fact; r:gives {(2536 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2536 1000) math:remainder 536}] + [ a r:Fact; r:gives {(3536 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3536 1000) math:remainder 536}] [ a r:Fact; r:gives {(536 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(536 100) math:remainder 36}] [ a r:Fact; r:gives {(36 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(36 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2536]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3536]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 536]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 36]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2905 a r:Inference; +skolem:lemma6230 a r:Inference; r:gives { - 2537 :numberToDigits (2 5 3 7). + 3537 :numberToDigits (3 5 3 7). }; r:evidence ( - [ a r:Fact; r:gives {(2537 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2537 1000) math:remainder 537}] + [ a r:Fact; r:gives {(3537 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3537 1000) math:remainder 537}] [ a r:Fact; r:gives {(537 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(537 100) math:remainder 37}] [ a r:Fact; r:gives {(37 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(37 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2537]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3537]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 537]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 37]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2906 a r:Inference; +skolem:lemma6231 a r:Inference; r:gives { - 2538 :numberToDigits (2 5 3 8). + 3538 :numberToDigits (3 5 3 8). }; r:evidence ( - [ a r:Fact; r:gives {(2538 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2538 1000) math:remainder 538}] + [ a r:Fact; r:gives {(3538 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3538 1000) math:remainder 538}] [ a r:Fact; r:gives {(538 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(538 100) math:remainder 38}] [ a r:Fact; r:gives {(38 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(38 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2538]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3538]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 538]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 38]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2907 a r:Inference; +skolem:lemma6232 a r:Inference; r:gives { - 2539 :numberToDigits (2 5 3 9). + 3539 :numberToDigits (3 5 3 9). }; r:evidence ( - [ a r:Fact; r:gives {(2539 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2539 1000) math:remainder 539}] + [ a r:Fact; r:gives {(3539 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3539 1000) math:remainder 539}] [ a r:Fact; r:gives {(539 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(539 100) math:remainder 39}] [ a r:Fact; r:gives {(39 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(39 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2539]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3539]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 539]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 39]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2908 a r:Inference; +skolem:lemma6233 a r:Inference; r:gives { - 2540 :numberToDigits (2 5 4 0). + 3540 :numberToDigits (3 5 4 0). }; r:evidence ( - [ a r:Fact; r:gives {(2540 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2540 1000) math:remainder 540}] + [ a r:Fact; r:gives {(3540 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3540 1000) math:remainder 540}] [ a r:Fact; r:gives {(540 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(540 100) math:remainder 40}] [ a r:Fact; r:gives {(40 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(40 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2540]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3540]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 540]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2909 a r:Inference; +skolem:lemma6234 a r:Inference; r:gives { - 2541 :numberToDigits (2 5 4 1). + 3541 :numberToDigits (3 5 4 1). }; r:evidence ( - [ a r:Fact; r:gives {(2541 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2541 1000) math:remainder 541}] + [ a r:Fact; r:gives {(3541 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3541 1000) math:remainder 541}] [ a r:Fact; r:gives {(541 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(541 100) math:remainder 41}] [ a r:Fact; r:gives {(41 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(41 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2541]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3541]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 541]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 41]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2910 a r:Inference; +skolem:lemma6235 a r:Inference; r:gives { - 2542 :numberToDigits (2 5 4 2). + 3542 :numberToDigits (3 5 4 2). }; r:evidence ( - [ a r:Fact; r:gives {(2542 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2542 1000) math:remainder 542}] + [ a r:Fact; r:gives {(3542 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3542 1000) math:remainder 542}] [ a r:Fact; r:gives {(542 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(542 100) math:remainder 42}] [ a r:Fact; r:gives {(42 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(42 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2542]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3542]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 542]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 42]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2911 a r:Inference; +skolem:lemma6236 a r:Inference; r:gives { - 2543 :numberToDigits (2 5 4 3). + 3543 :numberToDigits (3 5 4 3). }; r:evidence ( - [ a r:Fact; r:gives {(2543 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2543 1000) math:remainder 543}] + [ a r:Fact; r:gives {(3543 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3543 1000) math:remainder 543}] [ a r:Fact; r:gives {(543 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(543 100) math:remainder 43}] [ a r:Fact; r:gives {(43 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(43 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2543]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3543]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 543]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 43]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2912 a r:Inference; +skolem:lemma6237 a r:Inference; r:gives { - 2544 :numberToDigits (2 5 4 4). + 3544 :numberToDigits (3 5 4 4). }; r:evidence ( - [ a r:Fact; r:gives {(2544 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2544 1000) math:remainder 544}] + [ a r:Fact; r:gives {(3544 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3544 1000) math:remainder 544}] [ a r:Fact; r:gives {(544 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(544 100) math:remainder 44}] [ a r:Fact; r:gives {(44 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(44 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2544]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3544]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 544]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 44]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2913 a r:Inference; +skolem:lemma6238 a r:Inference; r:gives { - 2545 :numberToDigits (2 5 4 5). + 3545 :numberToDigits (3 5 4 5). }; r:evidence ( - [ a r:Fact; r:gives {(2545 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2545 1000) math:remainder 545}] + [ a r:Fact; r:gives {(3545 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3545 1000) math:remainder 545}] [ a r:Fact; r:gives {(545 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(545 100) math:remainder 45}] [ a r:Fact; r:gives {(45 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(45 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2545]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3545]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 545]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 45]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2914 a r:Inference; +skolem:lemma6239 a r:Inference; r:gives { - 2546 :numberToDigits (2 5 4 6). + 3546 :numberToDigits (3 5 4 6). }; r:evidence ( - [ a r:Fact; r:gives {(2546 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2546 1000) math:remainder 546}] + [ a r:Fact; r:gives {(3546 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3546 1000) math:remainder 546}] [ a r:Fact; r:gives {(546 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(546 100) math:remainder 46}] [ a r:Fact; r:gives {(46 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(46 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2546]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3546]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 546]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 46]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2915 a r:Inference; +skolem:lemma6240 a r:Inference; r:gives { - 2547 :numberToDigits (2 5 4 7). + 3547 :numberToDigits (3 5 4 7). }; r:evidence ( - [ a r:Fact; r:gives {(2547 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2547 1000) math:remainder 547}] + [ a r:Fact; r:gives {(3547 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3547 1000) math:remainder 547}] [ a r:Fact; r:gives {(547 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(547 100) math:remainder 47}] [ a r:Fact; r:gives {(47 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(47 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2547]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3547]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 547]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 47]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2916 a r:Inference; +skolem:lemma6241 a r:Inference; r:gives { - 2548 :numberToDigits (2 5 4 8). + 3548 :numberToDigits (3 5 4 8). }; r:evidence ( - [ a r:Fact; r:gives {(2548 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2548 1000) math:remainder 548}] + [ a r:Fact; r:gives {(3548 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3548 1000) math:remainder 548}] [ a r:Fact; r:gives {(548 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(548 100) math:remainder 48}] [ a r:Fact; r:gives {(48 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(48 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2548]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3548]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 548]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 48]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2917 a r:Inference; +skolem:lemma6242 a r:Inference; r:gives { - 2549 :numberToDigits (2 5 4 9). + 3549 :numberToDigits (3 5 4 9). }; r:evidence ( - [ a r:Fact; r:gives {(2549 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2549 1000) math:remainder 549}] + [ a r:Fact; r:gives {(3549 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3549 1000) math:remainder 549}] [ a r:Fact; r:gives {(549 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(549 100) math:remainder 49}] [ a r:Fact; r:gives {(49 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(49 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2549]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3549]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 549]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 49]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2918 a r:Inference; +skolem:lemma6243 a r:Inference; r:gives { - 2550 :numberToDigits (2 5 5 0). + 3550 :numberToDigits (3 5 5 0). }; r:evidence ( - [ a r:Fact; r:gives {(2550 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2550 1000) math:remainder 550}] + [ a r:Fact; r:gives {(3550 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3550 1000) math:remainder 550}] [ a r:Fact; r:gives {(550 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(550 100) math:remainder 50}] [ a r:Fact; r:gives {(50 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(50 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2550]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3550]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 550]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2919 a r:Inference; +skolem:lemma6244 a r:Inference; r:gives { - 2551 :numberToDigits (2 5 5 1). + 3551 :numberToDigits (3 5 5 1). }; r:evidence ( - [ a r:Fact; r:gives {(2551 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2551 1000) math:remainder 551}] + [ a r:Fact; r:gives {(3551 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3551 1000) math:remainder 551}] [ a r:Fact; r:gives {(551 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(551 100) math:remainder 51}] [ a r:Fact; r:gives {(51 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(51 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2551]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3551]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 551]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 51]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2920 a r:Inference; +skolem:lemma6245 a r:Inference; r:gives { - 2552 :numberToDigits (2 5 5 2). + 3552 :numberToDigits (3 5 5 2). }; r:evidence ( - [ a r:Fact; r:gives {(2552 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2552 1000) math:remainder 552}] + [ a r:Fact; r:gives {(3552 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3552 1000) math:remainder 552}] [ a r:Fact; r:gives {(552 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(552 100) math:remainder 52}] [ a r:Fact; r:gives {(52 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(52 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2552]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3552]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 552]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 52]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2921 a r:Inference; +skolem:lemma6246 a r:Inference; r:gives { - 2553 :numberToDigits (2 5 5 3). + 3553 :numberToDigits (3 5 5 3). }; r:evidence ( - [ a r:Fact; r:gives {(2553 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2553 1000) math:remainder 553}] + [ a r:Fact; r:gives {(3553 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3553 1000) math:remainder 553}] [ a r:Fact; r:gives {(553 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(553 100) math:remainder 53}] [ a r:Fact; r:gives {(53 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(53 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3553]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 553]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 53]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2922 a r:Inference; +skolem:lemma6247 a r:Inference; r:gives { - 2554 :numberToDigits (2 5 5 4). + 3554 :numberToDigits (3 5 5 4). }; r:evidence ( - [ a r:Fact; r:gives {(2554 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2554 1000) math:remainder 554}] + [ a r:Fact; r:gives {(3554 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3554 1000) math:remainder 554}] [ a r:Fact; r:gives {(554 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(554 100) math:remainder 54}] [ a r:Fact; r:gives {(54 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(54 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2554]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3554]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 554]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 54]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2923 a r:Inference; +skolem:lemma6248 a r:Inference; r:gives { - 2555 :numberToDigits (2 5 5 5). + 3555 :numberToDigits (3 5 5 5). }; r:evidence ( - [ a r:Fact; r:gives {(2555 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2555 1000) math:remainder 555}] + [ a r:Fact; r:gives {(3555 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3555 1000) math:remainder 555}] [ a r:Fact; r:gives {(555 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(555 100) math:remainder 55}] [ a r:Fact; r:gives {(55 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(55 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2555]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3555]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 555]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 55]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2924 a r:Inference; +skolem:lemma6249 a r:Inference; r:gives { - (2 5 5 5) :digitsToNumber 2555 . + (3 5 5 5) :digitsToNumber 3555 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(2000 500 50 5) math:sum 2555}] + [ a r:Fact; r:gives {(3000 500 50 5) math:sum 3555}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2555]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3555]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2925 a r:Inference; +skolem:lemma6250 a r:Inference; r:gives { - (5 5 5 2) :digitsToNumber 5552 . + (5 5 5 3) :digitsToNumber 5553 . }; r:evidence ( [ a r:Fact; r:gives {(5 1000) math:product 5000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(5000 500 50 2) math:sum 5552}] + [ a r:Fact; r:gives {(5000 500 50 3) math:sum 5553}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 5000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 5]; @@ -69048,60 +146537,60 @@ skolem:lemma2925 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5552]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 5553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2926 a r:Inference; +skolem:lemma6251 a r:Inference; r:gives { - 2556 :numberToDigits (2 5 5 6). + 3556 :numberToDigits (3 5 5 6). }; r:evidence ( - [ a r:Fact; r:gives {(2556 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2556 1000) math:remainder 556}] + [ a r:Fact; r:gives {(3556 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3556 1000) math:remainder 556}] [ a r:Fact; r:gives {(556 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(556 100) math:remainder 56}] [ a r:Fact; r:gives {(56 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(56 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2556]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3556]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 556]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 56]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2927 a r:Inference; +skolem:lemma6252 a r:Inference; r:gives { - (2 5 5 6) :digitsToNumber 2556 . + (3 5 5 6) :digitsToNumber 3556 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(2000 500 50 6) math:sum 2556}] + [ a r:Fact; r:gives {(3000 500 50 6) math:sum 3556}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2556]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3556]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2928 a r:Inference; +skolem:lemma6253 a r:Inference; r:gives { - (6 5 5 2) :digitsToNumber 6552 . + (6 5 5 3) :digitsToNumber 6553 . }; r:evidence ( [ a r:Fact; r:gives {(6 1000) math:product 6000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(6000 500 50 2) math:sum 6552}] + [ a r:Fact; r:gives {(6000 500 50 3) math:sum 6553}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; @@ -69109,60 +146598,60 @@ skolem:lemma2928 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6552]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2929 a r:Inference; +skolem:lemma6254 a r:Inference; r:gives { - 2557 :numberToDigits (2 5 5 7). + 3557 :numberToDigits (3 5 5 7). }; r:evidence ( - [ a r:Fact; r:gives {(2557 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2557 1000) math:remainder 557}] + [ a r:Fact; r:gives {(3557 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3557 1000) math:remainder 557}] [ a r:Fact; r:gives {(557 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(557 100) math:remainder 57}] [ a r:Fact; r:gives {(57 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(57 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2557]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3557]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 557]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 57]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2930 a r:Inference; +skolem:lemma6255 a r:Inference; r:gives { - (2 5 5 7) :digitsToNumber 2557 . + (3 5 5 7) :digitsToNumber 3557 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(2000 500 50 7) math:sum 2557}] + [ a r:Fact; r:gives {(3000 500 50 7) math:sum 3557}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2557]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3557]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2931 a r:Inference; +skolem:lemma6256 a r:Inference; r:gives { - (7 5 5 2) :digitsToNumber 7552 . + (7 5 5 3) :digitsToNumber 7553 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(7000 500 50 2) math:sum 7552}] + [ a r:Fact; r:gives {(7000 500 50 3) math:sum 7553}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; @@ -69170,60 +146659,60 @@ skolem:lemma2931 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7552]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2932 a r:Inference; +skolem:lemma6257 a r:Inference; r:gives { - 2558 :numberToDigits (2 5 5 8). + 3558 :numberToDigits (3 5 5 8). }; r:evidence ( - [ a r:Fact; r:gives {(2558 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2558 1000) math:remainder 558}] + [ a r:Fact; r:gives {(3558 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3558 1000) math:remainder 558}] [ a r:Fact; r:gives {(558 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(558 100) math:remainder 58}] [ a r:Fact; r:gives {(58 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(58 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2558]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3558]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 558]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 58]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2933 a r:Inference; +skolem:lemma6258 a r:Inference; r:gives { - (2 5 5 8) :digitsToNumber 2558 . + (3 5 5 8) :digitsToNumber 3558 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(2000 500 50 8) math:sum 2558}] + [ a r:Fact; r:gives {(3000 500 50 8) math:sum 3558}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2558]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3558]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2934 a r:Inference; +skolem:lemma6259 a r:Inference; r:gives { - (8 5 5 2) :digitsToNumber 8552 . + (8 5 5 3) :digitsToNumber 8553 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(8000 500 50 2) math:sum 8552}] + [ a r:Fact; r:gives {(8000 500 50 3) math:sum 8553}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; @@ -69231,60 +146720,60 @@ skolem:lemma2934 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8552]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2935 a r:Inference; +skolem:lemma6260 a r:Inference; r:gives { - 2559 :numberToDigits (2 5 5 9). + 3559 :numberToDigits (3 5 5 9). }; r:evidence ( - [ a r:Fact; r:gives {(2559 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2559 1000) math:remainder 559}] + [ a r:Fact; r:gives {(3559 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3559 1000) math:remainder 559}] [ a r:Fact; r:gives {(559 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(559 100) math:remainder 59}] [ a r:Fact; r:gives {(59 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(59 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2559]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3559]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 559]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 59]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2936 a r:Inference; +skolem:lemma6261 a r:Inference; r:gives { - (2 5 5 9) :digitsToNumber 2559 . + (3 5 5 9) :digitsToNumber 3559 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(2000 500 50 9) math:sum 2559}] + [ a r:Fact; r:gives {(3000 500 50 9) math:sum 3559}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2559]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3559]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2937 a r:Inference; +skolem:lemma6262 a r:Inference; r:gives { - (9 5 5 2) :digitsToNumber 9552 . + (9 5 5 3) :digitsToNumber 9553 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(9000 500 50 2) math:sum 9552}] + [ a r:Fact; r:gives {(9000 500 50 3) math:sum 9553}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -69292,186 +146781,186 @@ skolem:lemma2937 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9552]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9553]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2938 a r:Inference; +skolem:lemma6263 a r:Inference; r:gives { - 2560 :numberToDigits (2 5 6 0). + 3560 :numberToDigits (3 5 6 0). }; r:evidence ( - [ a r:Fact; r:gives {(2560 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2560 1000) math:remainder 560}] + [ a r:Fact; r:gives {(3560 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3560 1000) math:remainder 560}] [ a r:Fact; r:gives {(560 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(560 100) math:remainder 60}] [ a r:Fact; r:gives {(60 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(60 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2560]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3560]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 560]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2939 a r:Inference; +skolem:lemma6264 a r:Inference; r:gives { - 2561 :numberToDigits (2 5 6 1). + 3561 :numberToDigits (3 5 6 1). }; r:evidence ( - [ a r:Fact; r:gives {(2561 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2561 1000) math:remainder 561}] + [ a r:Fact; r:gives {(3561 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3561 1000) math:remainder 561}] [ a r:Fact; r:gives {(561 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(561 100) math:remainder 61}] [ a r:Fact; r:gives {(61 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(61 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2561]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3561]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 561]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 61]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2940 a r:Inference; +skolem:lemma6265 a r:Inference; r:gives { - 2562 :numberToDigits (2 5 6 2). + 3562 :numberToDigits (3 5 6 2). }; r:evidence ( - [ a r:Fact; r:gives {(2562 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2562 1000) math:remainder 562}] + [ a r:Fact; r:gives {(3562 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3562 1000) math:remainder 562}] [ a r:Fact; r:gives {(562 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(562 100) math:remainder 62}] [ a r:Fact; r:gives {(62 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(62 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2562]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3562]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 562]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 62]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2941 a r:Inference; +skolem:lemma6266 a r:Inference; r:gives { - 2563 :numberToDigits (2 5 6 3). + 3563 :numberToDigits (3 5 6 3). }; r:evidence ( - [ a r:Fact; r:gives {(2563 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2563 1000) math:remainder 563}] + [ a r:Fact; r:gives {(3563 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3563 1000) math:remainder 563}] [ a r:Fact; r:gives {(563 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(563 100) math:remainder 63}] [ a r:Fact; r:gives {(63 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(63 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2563]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3563]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 563]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 63]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2942 a r:Inference; +skolem:lemma6267 a r:Inference; r:gives { - 2564 :numberToDigits (2 5 6 4). + 3564 :numberToDigits (3 5 6 4). }; r:evidence ( - [ a r:Fact; r:gives {(2564 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2564 1000) math:remainder 564}] + [ a r:Fact; r:gives {(3564 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3564 1000) math:remainder 564}] [ a r:Fact; r:gives {(564 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(564 100) math:remainder 64}] [ a r:Fact; r:gives {(64 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(64 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2564]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3564]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 564]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 64]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2943 a r:Inference; +skolem:lemma6268 a r:Inference; r:gives { - 2565 :numberToDigits (2 5 6 5). + 3565 :numberToDigits (3 5 6 5). }; r:evidence ( - [ a r:Fact; r:gives {(2565 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2565 1000) math:remainder 565}] + [ a r:Fact; r:gives {(3565 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3565 1000) math:remainder 565}] [ a r:Fact; r:gives {(565 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(565 100) math:remainder 65}] [ a r:Fact; r:gives {(65 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(65 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2565]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3565]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 565]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 65]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2944 a r:Inference; +skolem:lemma6269 a r:Inference; r:gives { - 2566 :numberToDigits (2 5 6 6). + 3566 :numberToDigits (3 5 6 6). }; r:evidence ( - [ a r:Fact; r:gives {(2566 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2566 1000) math:remainder 566}] + [ a r:Fact; r:gives {(3566 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3566 1000) math:remainder 566}] [ a r:Fact; r:gives {(566 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(566 100) math:remainder 66}] [ a r:Fact; r:gives {(66 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(66 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2566]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3566]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 566]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 66]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2945 a r:Inference; +skolem:lemma6270 a r:Inference; r:gives { - (2 5 6 6) :digitsToNumber 2566 . + (3 5 6 6) :digitsToNumber 3566 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(2000 500 60 6) math:sum 2566}] - ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + [ a r:Fact; r:gives {(3000 500 60 6) math:sum 3566}] + ); + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2566]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3566]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2946 a r:Inference; +skolem:lemma6271 a r:Inference; r:gives { - (6 6 5 2) :digitsToNumber 6652 . + (6 6 5 3) :digitsToNumber 6653 . }; r:evidence ( [ a r:Fact; r:gives {(6 1000) math:product 6000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(6000 600 50 2) math:sum 6652}] + [ a r:Fact; r:gives {(6000 600 50 3) math:sum 6653}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; @@ -69479,60 +146968,60 @@ skolem:lemma2946 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2947 a r:Inference; +skolem:lemma6272 a r:Inference; r:gives { - 2567 :numberToDigits (2 5 6 7). + 3567 :numberToDigits (3 5 6 7). }; r:evidence ( - [ a r:Fact; r:gives {(2567 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2567 1000) math:remainder 567}] + [ a r:Fact; r:gives {(3567 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3567 1000) math:remainder 567}] [ a r:Fact; r:gives {(567 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(567 100) math:remainder 67}] [ a r:Fact; r:gives {(67 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(67 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2567]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3567]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 567]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 67]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2948 a r:Inference; +skolem:lemma6273 a r:Inference; r:gives { - (2 5 6 7) :digitsToNumber 2567 . + (3 5 6 7) :digitsToNumber 3567 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(2000 500 60 7) math:sum 2567}] + [ a r:Fact; r:gives {(3000 500 60 7) math:sum 3567}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2567]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3567]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2949 a r:Inference; +skolem:lemma6274 a r:Inference; r:gives { - (7 6 5 2) :digitsToNumber 7652 . + (7 6 5 3) :digitsToNumber 7653 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(7000 600 50 2) math:sum 7652}] + [ a r:Fact; r:gives {(7000 600 50 3) math:sum 7653}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; @@ -69540,60 +147029,60 @@ skolem:lemma2949 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2950 a r:Inference; +skolem:lemma6275 a r:Inference; r:gives { - 2568 :numberToDigits (2 5 6 8). + 3568 :numberToDigits (3 5 6 8). }; r:evidence ( - [ a r:Fact; r:gives {(2568 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2568 1000) math:remainder 568}] + [ a r:Fact; r:gives {(3568 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3568 1000) math:remainder 568}] [ a r:Fact; r:gives {(568 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(568 100) math:remainder 68}] [ a r:Fact; r:gives {(68 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(68 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2568]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3568]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 568]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 68]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2951 a r:Inference; +skolem:lemma6276 a r:Inference; r:gives { - (2 5 6 8) :digitsToNumber 2568 . + (3 5 6 8) :digitsToNumber 3568 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(2000 500 60 8) math:sum 2568}] + [ a r:Fact; r:gives {(3000 500 60 8) math:sum 3568}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2568]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3568]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2952 a r:Inference; +skolem:lemma6277 a r:Inference; r:gives { - (8 6 5 2) :digitsToNumber 8652 . + (8 6 5 3) :digitsToNumber 8653 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(8000 600 50 2) math:sum 8652}] + [ a r:Fact; r:gives {(8000 600 50 3) math:sum 8653}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; @@ -69601,60 +147090,60 @@ skolem:lemma2952 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2953 a r:Inference; +skolem:lemma6278 a r:Inference; r:gives { - 2569 :numberToDigits (2 5 6 9). + 3569 :numberToDigits (3 5 6 9). }; r:evidence ( - [ a r:Fact; r:gives {(2569 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2569 1000) math:remainder 569}] + [ a r:Fact; r:gives {(3569 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3569 1000) math:remainder 569}] [ a r:Fact; r:gives {(569 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(569 100) math:remainder 69}] [ a r:Fact; r:gives {(69 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(69 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2569]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3569]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 569]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 69]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2954 a r:Inference; +skolem:lemma6279 a r:Inference; r:gives { - (2 5 6 9) :digitsToNumber 2569 . + (3 5 6 9) :digitsToNumber 3569 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(2000 500 60 9) math:sum 2569}] + [ a r:Fact; r:gives {(3000 500 60 9) math:sum 3569}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2569]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3569]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2955 a r:Inference; +skolem:lemma6280 a r:Inference; r:gives { - (9 6 5 2) :digitsToNumber 9652 . + (9 6 5 3) :digitsToNumber 9653 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(9000 600 50 2) math:sum 9652}] + [ a r:Fact; r:gives {(9000 600 50 3) math:sum 9653}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -69662,207 +147151,207 @@ skolem:lemma2955 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9652]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2956 a r:Inference; +skolem:lemma6281 a r:Inference; r:gives { - 2570 :numberToDigits (2 5 7 0). + 3570 :numberToDigits (3 5 7 0). }; r:evidence ( - [ a r:Fact; r:gives {(2570 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2570 1000) math:remainder 570}] + [ a r:Fact; r:gives {(3570 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3570 1000) math:remainder 570}] [ a r:Fact; r:gives {(570 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(570 100) math:remainder 70}] [ a r:Fact; r:gives {(70 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(70 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2570]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3570]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 570]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2957 a r:Inference; +skolem:lemma6282 a r:Inference; r:gives { - 2571 :numberToDigits (2 5 7 1). + 3571 :numberToDigits (3 5 7 1). }; r:evidence ( - [ a r:Fact; r:gives {(2571 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2571 1000) math:remainder 571}] + [ a r:Fact; r:gives {(3571 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3571 1000) math:remainder 571}] [ a r:Fact; r:gives {(571 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(571 100) math:remainder 71}] [ a r:Fact; r:gives {(71 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(71 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2571]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3571]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 571]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 71]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2958 a r:Inference; +skolem:lemma6283 a r:Inference; r:gives { - 2572 :numberToDigits (2 5 7 2). + 3572 :numberToDigits (3 5 7 2). }; r:evidence ( - [ a r:Fact; r:gives {(2572 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2572 1000) math:remainder 572}] + [ a r:Fact; r:gives {(3572 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3572 1000) math:remainder 572}] [ a r:Fact; r:gives {(572 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(572 100) math:remainder 72}] [ a r:Fact; r:gives {(72 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(72 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2572]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3572]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 572]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 72]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2959 a r:Inference; +skolem:lemma6284 a r:Inference; r:gives { - 2573 :numberToDigits (2 5 7 3). + 3573 :numberToDigits (3 5 7 3). }; r:evidence ( - [ a r:Fact; r:gives {(2573 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2573 1000) math:remainder 573}] + [ a r:Fact; r:gives {(3573 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3573 1000) math:remainder 573}] [ a r:Fact; r:gives {(573 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(573 100) math:remainder 73}] [ a r:Fact; r:gives {(73 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(73 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2573]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3573]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 573]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 73]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2960 a r:Inference; +skolem:lemma6285 a r:Inference; r:gives { - 2574 :numberToDigits (2 5 7 4). + 3574 :numberToDigits (3 5 7 4). }; r:evidence ( - [ a r:Fact; r:gives {(2574 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2574 1000) math:remainder 574}] + [ a r:Fact; r:gives {(3574 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3574 1000) math:remainder 574}] [ a r:Fact; r:gives {(574 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(574 100) math:remainder 74}] [ a r:Fact; r:gives {(74 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(74 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2574]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3574]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 574]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 74]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2961 a r:Inference; +skolem:lemma6286 a r:Inference; r:gives { - 2575 :numberToDigits (2 5 7 5). + 3575 :numberToDigits (3 5 7 5). }; r:evidence ( - [ a r:Fact; r:gives {(2575 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2575 1000) math:remainder 575}] + [ a r:Fact; r:gives {(3575 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3575 1000) math:remainder 575}] [ a r:Fact; r:gives {(575 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(575 100) math:remainder 75}] [ a r:Fact; r:gives {(75 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(75 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2575]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3575]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 575]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 75]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2962 a r:Inference; +skolem:lemma6287 a r:Inference; r:gives { - 2576 :numberToDigits (2 5 7 6). + 3576 :numberToDigits (3 5 7 6). }; r:evidence ( - [ a r:Fact; r:gives {(2576 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2576 1000) math:remainder 576}] + [ a r:Fact; r:gives {(3576 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3576 1000) math:remainder 576}] [ a r:Fact; r:gives {(576 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(576 100) math:remainder 76}] [ a r:Fact; r:gives {(76 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(76 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2576]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3576]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 576]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 76]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2963 a r:Inference; +skolem:lemma6288 a r:Inference; r:gives { - 2577 :numberToDigits (2 5 7 7). + 3577 :numberToDigits (3 5 7 7). }; r:evidence ( - [ a r:Fact; r:gives {(2577 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2577 1000) math:remainder 577}] + [ a r:Fact; r:gives {(3577 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3577 1000) math:remainder 577}] [ a r:Fact; r:gives {(577 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(577 100) math:remainder 77}] [ a r:Fact; r:gives {(77 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(77 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2577]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3577]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 577]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 77]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2964 a r:Inference; +skolem:lemma6289 a r:Inference; r:gives { - (2 5 7 7) :digitsToNumber 2577 . + (3 5 7 7) :digitsToNumber 3577 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(2000 500 70 7) math:sum 2577}] + [ a r:Fact; r:gives {(3000 500 70 7) math:sum 3577}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2577]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3577]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2965 a r:Inference; +skolem:lemma6290 a r:Inference; r:gives { - (7 7 5 2) :digitsToNumber 7752 . + (7 7 5 3) :digitsToNumber 7753 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(7 100) math:product 700}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(7000 700 50 2) math:sum 7752}] + [ a r:Fact; r:gives {(7000 700 50 3) math:sum 7753}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; @@ -69870,60 +147359,60 @@ skolem:lemma2965 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7752]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2966 a r:Inference; +skolem:lemma6291 a r:Inference; r:gives { - 2578 :numberToDigits (2 5 7 8). + 3578 :numberToDigits (3 5 7 8). }; r:evidence ( - [ a r:Fact; r:gives {(2578 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2578 1000) math:remainder 578}] + [ a r:Fact; r:gives {(3578 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3578 1000) math:remainder 578}] [ a r:Fact; r:gives {(578 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(578 100) math:remainder 78}] [ a r:Fact; r:gives {(78 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(78 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2578]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3578]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 578]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 78]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2967 a r:Inference; +skolem:lemma6292 a r:Inference; r:gives { - (2 5 7 8) :digitsToNumber 2578 . + (3 5 7 8) :digitsToNumber 3578 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(2000 500 70 8) math:sum 2578}] + [ a r:Fact; r:gives {(3000 500 70 8) math:sum 3578}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2578]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3578]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2968 a r:Inference; +skolem:lemma6293 a r:Inference; r:gives { - (8 7 5 2) :digitsToNumber 8752 . + (8 7 5 3) :digitsToNumber 8753 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(7 100) math:product 700}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(8000 700 50 2) math:sum 8752}] + [ a r:Fact; r:gives {(8000 700 50 3) math:sum 8753}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; @@ -69931,60 +147420,60 @@ skolem:lemma2968 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8752]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2969 a r:Inference; +skolem:lemma6294 a r:Inference; r:gives { - 2579 :numberToDigits (2 5 7 9). + 3579 :numberToDigits (3 5 7 9). }; r:evidence ( - [ a r:Fact; r:gives {(2579 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2579 1000) math:remainder 579}] + [ a r:Fact; r:gives {(3579 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3579 1000) math:remainder 579}] [ a r:Fact; r:gives {(579 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(579 100) math:remainder 79}] [ a r:Fact; r:gives {(79 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(79 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2579]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3579]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 579]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 79]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2970 a r:Inference; +skolem:lemma6295 a r:Inference; r:gives { - (2 5 7 9) :digitsToNumber 2579 . + (3 5 7 9) :digitsToNumber 3579 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(2000 500 70 9) math:sum 2579}] + [ a r:Fact; r:gives {(3000 500 70 9) math:sum 3579}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2579]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3579]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2971 a r:Inference; +skolem:lemma6296 a r:Inference; r:gives { - (9 7 5 2) :digitsToNumber 9752 . + (9 7 5 3) :digitsToNumber 9753 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(7 100) math:product 700}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(9000 700 50 2) math:sum 9752}] + [ a r:Fact; r:gives {(9000 700 50 3) math:sum 9753}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -69992,228 +147481,228 @@ skolem:lemma2971 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9752]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2972 a r:Inference; +skolem:lemma6297 a r:Inference; r:gives { - 2580 :numberToDigits (2 5 8 0). + 3580 :numberToDigits (3 5 8 0). }; r:evidence ( - [ a r:Fact; r:gives {(2580 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2580 1000) math:remainder 580}] + [ a r:Fact; r:gives {(3580 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3580 1000) math:remainder 580}] [ a r:Fact; r:gives {(580 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(580 100) math:remainder 80}] [ a r:Fact; r:gives {(80 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(80 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2580]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3580]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 580]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2973 a r:Inference; +skolem:lemma6298 a r:Inference; r:gives { - 2581 :numberToDigits (2 5 8 1). + 3581 :numberToDigits (3 5 8 1). }; r:evidence ( - [ a r:Fact; r:gives {(2581 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2581 1000) math:remainder 581}] + [ a r:Fact; r:gives {(3581 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3581 1000) math:remainder 581}] [ a r:Fact; r:gives {(581 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(581 100) math:remainder 81}] [ a r:Fact; r:gives {(81 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(81 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2581]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3581]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 581]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 81]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2974 a r:Inference; +skolem:lemma6299 a r:Inference; r:gives { - 2582 :numberToDigits (2 5 8 2). + 3582 :numberToDigits (3 5 8 2). }; r:evidence ( - [ a r:Fact; r:gives {(2582 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2582 1000) math:remainder 582}] + [ a r:Fact; r:gives {(3582 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3582 1000) math:remainder 582}] [ a r:Fact; r:gives {(582 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(582 100) math:remainder 82}] [ a r:Fact; r:gives {(82 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(82 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2582]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3582]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 582]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 82]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2975 a r:Inference; +skolem:lemma6300 a r:Inference; r:gives { - 2583 :numberToDigits (2 5 8 3). + 3583 :numberToDigits (3 5 8 3). }; r:evidence ( - [ a r:Fact; r:gives {(2583 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2583 1000) math:remainder 583}] + [ a r:Fact; r:gives {(3583 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3583 1000) math:remainder 583}] [ a r:Fact; r:gives {(583 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(583 100) math:remainder 83}] [ a r:Fact; r:gives {(83 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(83 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2583]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3583]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 583]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 83]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2976 a r:Inference; +skolem:lemma6301 a r:Inference; r:gives { - 2584 :numberToDigits (2 5 8 4). + 3584 :numberToDigits (3 5 8 4). }; r:evidence ( - [ a r:Fact; r:gives {(2584 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2584 1000) math:remainder 584}] + [ a r:Fact; r:gives {(3584 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3584 1000) math:remainder 584}] [ a r:Fact; r:gives {(584 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(584 100) math:remainder 84}] [ a r:Fact; r:gives {(84 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(84 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2584]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3584]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 584]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 84]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2977 a r:Inference; +skolem:lemma6302 a r:Inference; r:gives { - 2585 :numberToDigits (2 5 8 5). + 3585 :numberToDigits (3 5 8 5). }; r:evidence ( - [ a r:Fact; r:gives {(2585 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2585 1000) math:remainder 585}] + [ a r:Fact; r:gives {(3585 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3585 1000) math:remainder 585}] [ a r:Fact; r:gives {(585 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(585 100) math:remainder 85}] [ a r:Fact; r:gives {(85 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(85 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2585]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3585]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 585]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 85]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2978 a r:Inference; +skolem:lemma6303 a r:Inference; r:gives { - 2586 :numberToDigits (2 5 8 6). + 3586 :numberToDigits (3 5 8 6). }; r:evidence ( - [ a r:Fact; r:gives {(2586 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2586 1000) math:remainder 586}] + [ a r:Fact; r:gives {(3586 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3586 1000) math:remainder 586}] [ a r:Fact; r:gives {(586 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(586 100) math:remainder 86}] [ a r:Fact; r:gives {(86 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(86 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2586]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3586]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 586]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 86]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2979 a r:Inference; +skolem:lemma6304 a r:Inference; r:gives { - 2587 :numberToDigits (2 5 8 7). + 3587 :numberToDigits (3 5 8 7). }; r:evidence ( - [ a r:Fact; r:gives {(2587 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2587 1000) math:remainder 587}] + [ a r:Fact; r:gives {(3587 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3587 1000) math:remainder 587}] [ a r:Fact; r:gives {(587 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(587 100) math:remainder 87}] [ a r:Fact; r:gives {(87 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(87 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2587]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3587]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 587]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 87]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2980 a r:Inference; +skolem:lemma6305 a r:Inference; r:gives { - 2588 :numberToDigits (2 5 8 8). + 3588 :numberToDigits (3 5 8 8). }; r:evidence ( - [ a r:Fact; r:gives {(2588 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2588 1000) math:remainder 588}] + [ a r:Fact; r:gives {(3588 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3588 1000) math:remainder 588}] [ a r:Fact; r:gives {(588 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(588 100) math:remainder 88}] [ a r:Fact; r:gives {(88 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(88 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2588]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3588]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 588]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 88]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2981 a r:Inference; +skolem:lemma6306 a r:Inference; r:gives { - (2 5 8 8) :digitsToNumber 2588 . + (3 5 8 8) :digitsToNumber 3588 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(8 10) math:product 80}] - [ a r:Fact; r:gives {(2000 500 80 8) math:sum 2588}] + [ a r:Fact; r:gives {(3000 500 80 8) math:sum 3588}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2588]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3588]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2982 a r:Inference; +skolem:lemma6307 a r:Inference; r:gives { - (8 8 5 2) :digitsToNumber 8852 . + (8 8 5 3) :digitsToNumber 8853 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(8 100) math:product 800}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(8000 800 50 2) math:sum 8852}] + [ a r:Fact; r:gives {(8000 800 50 3) math:sum 8853}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; @@ -70221,60 +147710,60 @@ skolem:lemma2982 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8852]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8853]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2983 a r:Inference; +skolem:lemma6308 a r:Inference; r:gives { - 2589 :numberToDigits (2 5 8 9). + 3589 :numberToDigits (3 5 8 9). }; r:evidence ( - [ a r:Fact; r:gives {(2589 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2589 1000) math:remainder 589}] + [ a r:Fact; r:gives {(3589 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3589 1000) math:remainder 589}] [ a r:Fact; r:gives {(589 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(589 100) math:remainder 89}] [ a r:Fact; r:gives {(89 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(89 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2589]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3589]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 589]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 89]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2984 a r:Inference; +skolem:lemma6309 a r:Inference; r:gives { - (2 5 8 9) :digitsToNumber 2589 . + (3 5 8 9) :digitsToNumber 3589 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(8 10) math:product 80}] - [ a r:Fact; r:gives {(2000 500 80 9) math:sum 2589}] + [ a r:Fact; r:gives {(3000 500 80 9) math:sum 3589}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2589]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3589]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2985 a r:Inference; +skolem:lemma6310 a r:Inference; r:gives { - (9 8 5 2) :digitsToNumber 9852 . + (9 8 5 3) :digitsToNumber 9853 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(8 100) math:product 800}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(9000 800 50 2) math:sum 9852}] + [ a r:Fact; r:gives {(9000 800 50 3) math:sum 9853}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -70282,249 +147771,249 @@ skolem:lemma2985 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9852]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9853]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2986 a r:Inference; +skolem:lemma6311 a r:Inference; r:gives { - 2590 :numberToDigits (2 5 9 0). + 3590 :numberToDigits (3 5 9 0). }; r:evidence ( - [ a r:Fact; r:gives {(2590 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2590 1000) math:remainder 590}] + [ a r:Fact; r:gives {(3590 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3590 1000) math:remainder 590}] [ a r:Fact; r:gives {(590 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(590 100) math:remainder 90}] [ a r:Fact; r:gives {(90 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(90 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2590]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3590]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 590]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 90]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2987 a r:Inference; +skolem:lemma6312 a r:Inference; r:gives { - 2591 :numberToDigits (2 5 9 1). + 3591 :numberToDigits (3 5 9 1). }; r:evidence ( - [ a r:Fact; r:gives {(2591 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2591 1000) math:remainder 591}] + [ a r:Fact; r:gives {(3591 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3591 1000) math:remainder 591}] [ a r:Fact; r:gives {(591 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(591 100) math:remainder 91}] [ a r:Fact; r:gives {(91 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(91 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2591]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3591]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 591]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 91]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2988 a r:Inference; +skolem:lemma6313 a r:Inference; r:gives { - 2592 :numberToDigits (2 5 9 2). + 3592 :numberToDigits (3 5 9 2). }; r:evidence ( - [ a r:Fact; r:gives {(2592 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2592 1000) math:remainder 592}] + [ a r:Fact; r:gives {(3592 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3592 1000) math:remainder 592}] [ a r:Fact; r:gives {(592 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(592 100) math:remainder 92}] [ a r:Fact; r:gives {(92 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(92 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2592]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3592]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 592]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 92]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2989 a r:Inference; +skolem:lemma6314 a r:Inference; r:gives { - 2593 :numberToDigits (2 5 9 3). + 3593 :numberToDigits (3 5 9 3). }; r:evidence ( - [ a r:Fact; r:gives {(2593 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2593 1000) math:remainder 593}] + [ a r:Fact; r:gives {(3593 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3593 1000) math:remainder 593}] [ a r:Fact; r:gives {(593 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(593 100) math:remainder 93}] [ a r:Fact; r:gives {(93 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(93 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2593]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3593]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 593]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 93]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2990 a r:Inference; +skolem:lemma6315 a r:Inference; r:gives { - 2594 :numberToDigits (2 5 9 4). + 3594 :numberToDigits (3 5 9 4). }; r:evidence ( - [ a r:Fact; r:gives {(2594 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2594 1000) math:remainder 594}] + [ a r:Fact; r:gives {(3594 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3594 1000) math:remainder 594}] [ a r:Fact; r:gives {(594 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(594 100) math:remainder 94}] [ a r:Fact; r:gives {(94 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(94 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2594]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3594]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 594]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 94]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2991 a r:Inference; +skolem:lemma6316 a r:Inference; r:gives { - 2595 :numberToDigits (2 5 9 5). + 3595 :numberToDigits (3 5 9 5). }; r:evidence ( - [ a r:Fact; r:gives {(2595 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2595 1000) math:remainder 595}] + [ a r:Fact; r:gives {(3595 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3595 1000) math:remainder 595}] [ a r:Fact; r:gives {(595 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(595 100) math:remainder 95}] [ a r:Fact; r:gives {(95 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(95 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2595]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3595]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 595]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 95]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2992 a r:Inference; +skolem:lemma6317 a r:Inference; r:gives { - 2596 :numberToDigits (2 5 9 6). + 3596 :numberToDigits (3 5 9 6). }; r:evidence ( - [ a r:Fact; r:gives {(2596 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2596 1000) math:remainder 596}] + [ a r:Fact; r:gives {(3596 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3596 1000) math:remainder 596}] [ a r:Fact; r:gives {(596 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(596 100) math:remainder 96}] [ a r:Fact; r:gives {(96 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(96 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2596]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3596]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 596]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 96]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2993 a r:Inference; +skolem:lemma6318 a r:Inference; r:gives { - 2597 :numberToDigits (2 5 9 7). + 3597 :numberToDigits (3 5 9 7). }; r:evidence ( - [ a r:Fact; r:gives {(2597 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2597 1000) math:remainder 597}] + [ a r:Fact; r:gives {(3597 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3597 1000) math:remainder 597}] [ a r:Fact; r:gives {(597 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(597 100) math:remainder 97}] [ a r:Fact; r:gives {(97 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(97 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2597]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3597]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 597]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 97]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2994 a r:Inference; +skolem:lemma6319 a r:Inference; r:gives { - 2598 :numberToDigits (2 5 9 8). + 3598 :numberToDigits (3 5 9 8). }; r:evidence ( - [ a r:Fact; r:gives {(2598 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2598 1000) math:remainder 598}] + [ a r:Fact; r:gives {(3598 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3598 1000) math:remainder 598}] [ a r:Fact; r:gives {(598 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(598 100) math:remainder 98}] [ a r:Fact; r:gives {(98 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(98 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2598]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3598]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 598]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 98]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2995 a r:Inference; +skolem:lemma6320 a r:Inference; r:gives { - 2599 :numberToDigits (2 5 9 9). + 3599 :numberToDigits (3 5 9 9). }; r:evidence ( - [ a r:Fact; r:gives {(2599 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2599 1000) math:remainder 599}] + [ a r:Fact; r:gives {(3599 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3599 1000) math:remainder 599}] [ a r:Fact; r:gives {(599 100) math:integerQuotient 5}] [ a r:Fact; r:gives {(599 100) math:remainder 99}] [ a r:Fact; r:gives {(99 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(99 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2599]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3599]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 599]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 99]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2996 a r:Inference; +skolem:lemma6321 a r:Inference; r:gives { - (2 5 9 9) :digitsToNumber 2599 . + (3 5 9 9) :digitsToNumber 3599 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(5 100) math:product 500}] [ a r:Fact; r:gives {(9 10) math:product 90}] - [ a r:Fact; r:gives {(2000 500 90 9) math:sum 2599}] + [ a r:Fact; r:gives {(3000 500 90 9) math:sum 3599}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 500]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 90]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2599]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3599]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma2997 a r:Inference; +skolem:lemma6322 a r:Inference; r:gives { - (9 9 5 2) :digitsToNumber 9952 . + (9 9 5 3) :digitsToNumber 9953 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(9 100) math:product 900}] [ a r:Fact; r:gives {(5 10) math:product 50}] - [ a r:Fact; r:gives {(9000 900 50 2) math:sum 9952}] + [ a r:Fact; r:gives {(9000 900 50 3) math:sum 9953}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -70532,1446 +148021,1446 @@ skolem:lemma2997 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9952]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9953]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma2998 a r:Inference; +skolem:lemma6323 a r:Inference; r:gives { - 2600 :numberToDigits (2 6 0 0). + 3600 :numberToDigits (3 6 0 0). }; r:evidence ( - [ a r:Fact; r:gives {(2600 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2600 1000) math:remainder 600}] + [ a r:Fact; r:gives {(3600 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3600 1000) math:remainder 600}] [ a r:Fact; r:gives {(600 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(600 100) math:remainder 0}] [ a r:Fact; r:gives {(0 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(0 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2600]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3600]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 600]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma2999 a r:Inference; +skolem:lemma6324 a r:Inference; r:gives { - 2601 :numberToDigits (2 6 0 1). + 3601 :numberToDigits (3 6 0 1). }; r:evidence ( - [ a r:Fact; r:gives {(2601 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2601 1000) math:remainder 601}] + [ a r:Fact; r:gives {(3601 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3601 1000) math:remainder 601}] [ a r:Fact; r:gives {(601 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(601 100) math:remainder 1}] [ a r:Fact; r:gives {(1 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(1 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2601]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3601]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 601]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3000 a r:Inference; +skolem:lemma6325 a r:Inference; r:gives { - 2602 :numberToDigits (2 6 0 2). + 3602 :numberToDigits (3 6 0 2). }; r:evidence ( - [ a r:Fact; r:gives {(2602 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2602 1000) math:remainder 602}] + [ a r:Fact; r:gives {(3602 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3602 1000) math:remainder 602}] [ a r:Fact; r:gives {(602 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(602 100) math:remainder 2}] [ a r:Fact; r:gives {(2 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(2 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2602]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3602]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 602]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3001 a r:Inference; +skolem:lemma6326 a r:Inference; r:gives { - 2603 :numberToDigits (2 6 0 3). + 3603 :numberToDigits (3 6 0 3). }; r:evidence ( - [ a r:Fact; r:gives {(2603 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2603 1000) math:remainder 603}] + [ a r:Fact; r:gives {(3603 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3603 1000) math:remainder 603}] [ a r:Fact; r:gives {(603 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(603 100) math:remainder 3}] [ a r:Fact; r:gives {(3 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(3 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2603]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3603]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 603]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3002 a r:Inference; +skolem:lemma6327 a r:Inference; r:gives { - 2604 :numberToDigits (2 6 0 4). + 3604 :numberToDigits (3 6 0 4). }; r:evidence ( - [ a r:Fact; r:gives {(2604 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2604 1000) math:remainder 604}] + [ a r:Fact; r:gives {(3604 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3604 1000) math:remainder 604}] [ a r:Fact; r:gives {(604 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(604 100) math:remainder 4}] [ a r:Fact; r:gives {(4 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(4 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2604]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3604]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 604]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3003 a r:Inference; +skolem:lemma6328 a r:Inference; r:gives { - 2605 :numberToDigits (2 6 0 5). + 3605 :numberToDigits (3 6 0 5). }; r:evidence ( - [ a r:Fact; r:gives {(2605 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2605 1000) math:remainder 605}] + [ a r:Fact; r:gives {(3605 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3605 1000) math:remainder 605}] [ a r:Fact; r:gives {(605 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(605 100) math:remainder 5}] [ a r:Fact; r:gives {(5 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(5 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2605]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3605]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 605]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3004 a r:Inference; +skolem:lemma6329 a r:Inference; r:gives { - 2606 :numberToDigits (2 6 0 6). + 3606 :numberToDigits (3 6 0 6). }; r:evidence ( - [ a r:Fact; r:gives {(2606 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2606 1000) math:remainder 606}] + [ a r:Fact; r:gives {(3606 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3606 1000) math:remainder 606}] [ a r:Fact; r:gives {(606 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(606 100) math:remainder 6}] [ a r:Fact; r:gives {(6 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(6 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2606]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3606]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 606]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3005 a r:Inference; +skolem:lemma6330 a r:Inference; r:gives { - 2607 :numberToDigits (2 6 0 7). + 3607 :numberToDigits (3 6 0 7). }; r:evidence ( - [ a r:Fact; r:gives {(2607 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2607 1000) math:remainder 607}] + [ a r:Fact; r:gives {(3607 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3607 1000) math:remainder 607}] [ a r:Fact; r:gives {(607 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(607 100) math:remainder 7}] [ a r:Fact; r:gives {(7 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(7 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2607]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3607]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 607]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3006 a r:Inference; +skolem:lemma6331 a r:Inference; r:gives { - 2608 :numberToDigits (2 6 0 8). + 3608 :numberToDigits (3 6 0 8). }; r:evidence ( - [ a r:Fact; r:gives {(2608 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2608 1000) math:remainder 608}] + [ a r:Fact; r:gives {(3608 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3608 1000) math:remainder 608}] [ a r:Fact; r:gives {(608 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(608 100) math:remainder 8}] [ a r:Fact; r:gives {(8 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(8 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2608]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3608]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 608]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3007 a r:Inference; +skolem:lemma6332 a r:Inference; r:gives { - 2609 :numberToDigits (2 6 0 9). + 3609 :numberToDigits (3 6 0 9). }; r:evidence ( - [ a r:Fact; r:gives {(2609 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2609 1000) math:remainder 609}] + [ a r:Fact; r:gives {(3609 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3609 1000) math:remainder 609}] [ a r:Fact; r:gives {(609 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(609 100) math:remainder 9}] [ a r:Fact; r:gives {(9 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(9 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2609]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3609]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 609]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3008 a r:Inference; +skolem:lemma6333 a r:Inference; r:gives { - 2610 :numberToDigits (2 6 1 0). + 3610 :numberToDigits (3 6 1 0). }; r:evidence ( - [ a r:Fact; r:gives {(2610 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2610 1000) math:remainder 610}] + [ a r:Fact; r:gives {(3610 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3610 1000) math:remainder 610}] [ a r:Fact; r:gives {(610 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(610 100) math:remainder 10}] [ a r:Fact; r:gives {(10 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(10 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2610]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3610]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 610]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3009 a r:Inference; +skolem:lemma6334 a r:Inference; r:gives { - 2611 :numberToDigits (2 6 1 1). + 3611 :numberToDigits (3 6 1 1). }; r:evidence ( - [ a r:Fact; r:gives {(2611 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2611 1000) math:remainder 611}] + [ a r:Fact; r:gives {(3611 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3611 1000) math:remainder 611}] [ a r:Fact; r:gives {(611 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(611 100) math:remainder 11}] [ a r:Fact; r:gives {(11 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(11 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2611]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3611]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 611]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 11]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3010 a r:Inference; +skolem:lemma6335 a r:Inference; r:gives { - 2612 :numberToDigits (2 6 1 2). + 3612 :numberToDigits (3 6 1 2). }; r:evidence ( - [ a r:Fact; r:gives {(2612 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2612 1000) math:remainder 612}] + [ a r:Fact; r:gives {(3612 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3612 1000) math:remainder 612}] [ a r:Fact; r:gives {(612 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(612 100) math:remainder 12}] [ a r:Fact; r:gives {(12 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(12 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2612]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3612]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 612]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3011 a r:Inference; +skolem:lemma6336 a r:Inference; r:gives { - 2613 :numberToDigits (2 6 1 3). + 3613 :numberToDigits (3 6 1 3). }; r:evidence ( - [ a r:Fact; r:gives {(2613 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2613 1000) math:remainder 613}] + [ a r:Fact; r:gives {(3613 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3613 1000) math:remainder 613}] [ a r:Fact; r:gives {(613 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(613 100) math:remainder 13}] [ a r:Fact; r:gives {(13 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(13 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2613]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3613]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 613]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 13]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3012 a r:Inference; +skolem:lemma6337 a r:Inference; r:gives { - 2614 :numberToDigits (2 6 1 4). + 3614 :numberToDigits (3 6 1 4). }; r:evidence ( - [ a r:Fact; r:gives {(2614 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2614 1000) math:remainder 614}] + [ a r:Fact; r:gives {(3614 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3614 1000) math:remainder 614}] [ a r:Fact; r:gives {(614 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(614 100) math:remainder 14}] [ a r:Fact; r:gives {(14 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(14 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2614]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3614]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 614]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 14]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3013 a r:Inference; +skolem:lemma6338 a r:Inference; r:gives { - 2615 :numberToDigits (2 6 1 5). + 3615 :numberToDigits (3 6 1 5). }; r:evidence ( - [ a r:Fact; r:gives {(2615 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2615 1000) math:remainder 615}] + [ a r:Fact; r:gives {(3615 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3615 1000) math:remainder 615}] [ a r:Fact; r:gives {(615 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(615 100) math:remainder 15}] [ a r:Fact; r:gives {(15 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(15 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2615]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3615]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 615]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 15]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3014 a r:Inference; +skolem:lemma6339 a r:Inference; r:gives { - 2616 :numberToDigits (2 6 1 6). + 3616 :numberToDigits (3 6 1 6). }; r:evidence ( - [ a r:Fact; r:gives {(2616 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2616 1000) math:remainder 616}] + [ a r:Fact; r:gives {(3616 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3616 1000) math:remainder 616}] [ a r:Fact; r:gives {(616 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(616 100) math:remainder 16}] [ a r:Fact; r:gives {(16 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(16 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2616]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3616]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 616]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 16]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3015 a r:Inference; +skolem:lemma6340 a r:Inference; r:gives { - 2617 :numberToDigits (2 6 1 7). + 3617 :numberToDigits (3 6 1 7). }; r:evidence ( - [ a r:Fact; r:gives {(2617 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2617 1000) math:remainder 617}] + [ a r:Fact; r:gives {(3617 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3617 1000) math:remainder 617}] [ a r:Fact; r:gives {(617 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(617 100) math:remainder 17}] [ a r:Fact; r:gives {(17 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(17 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2617]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3617]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 617]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 17]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3016 a r:Inference; +skolem:lemma6341 a r:Inference; r:gives { - 2618 :numberToDigits (2 6 1 8). + 3618 :numberToDigits (3 6 1 8). }; r:evidence ( - [ a r:Fact; r:gives {(2618 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2618 1000) math:remainder 618}] + [ a r:Fact; r:gives {(3618 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3618 1000) math:remainder 618}] [ a r:Fact; r:gives {(618 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(618 100) math:remainder 18}] [ a r:Fact; r:gives {(18 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(18 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2618]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3618]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 618]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 18]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3017 a r:Inference; +skolem:lemma6342 a r:Inference; r:gives { - 2619 :numberToDigits (2 6 1 9). + 3619 :numberToDigits (3 6 1 9). }; r:evidence ( - [ a r:Fact; r:gives {(2619 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2619 1000) math:remainder 619}] + [ a r:Fact; r:gives {(3619 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3619 1000) math:remainder 619}] [ a r:Fact; r:gives {(619 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(619 100) math:remainder 19}] [ a r:Fact; r:gives {(19 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(19 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2619]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3619]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 619]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 19]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3018 a r:Inference; +skolem:lemma6343 a r:Inference; r:gives { - 2620 :numberToDigits (2 6 2 0). + 3620 :numberToDigits (3 6 2 0). }; r:evidence ( - [ a r:Fact; r:gives {(2620 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2620 1000) math:remainder 620}] + [ a r:Fact; r:gives {(3620 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3620 1000) math:remainder 620}] [ a r:Fact; r:gives {(620 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(620 100) math:remainder 20}] [ a r:Fact; r:gives {(20 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(20 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2620]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3620]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 620]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 20]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3019 a r:Inference; +skolem:lemma6344 a r:Inference; r:gives { - 2621 :numberToDigits (2 6 2 1). + 3621 :numberToDigits (3 6 2 1). }; r:evidence ( - [ a r:Fact; r:gives {(2621 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2621 1000) math:remainder 621}] + [ a r:Fact; r:gives {(3621 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3621 1000) math:remainder 621}] [ a r:Fact; r:gives {(621 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(621 100) math:remainder 21}] [ a r:Fact; r:gives {(21 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(21 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2621]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3621]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 621]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 21]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3020 a r:Inference; +skolem:lemma6345 a r:Inference; r:gives { - 2622 :numberToDigits (2 6 2 2). + 3622 :numberToDigits (3 6 2 2). }; r:evidence ( - [ a r:Fact; r:gives {(2622 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2622 1000) math:remainder 622}] + [ a r:Fact; r:gives {(3622 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3622 1000) math:remainder 622}] [ a r:Fact; r:gives {(622 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(622 100) math:remainder 22}] [ a r:Fact; r:gives {(22 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(22 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2622]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3622]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 622]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3021 a r:Inference; +skolem:lemma6346 a r:Inference; r:gives { - 2623 :numberToDigits (2 6 2 3). + 3623 :numberToDigits (3 6 2 3). }; r:evidence ( - [ a r:Fact; r:gives {(2623 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2623 1000) math:remainder 623}] + [ a r:Fact; r:gives {(3623 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3623 1000) math:remainder 623}] [ a r:Fact; r:gives {(623 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(623 100) math:remainder 23}] [ a r:Fact; r:gives {(23 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(23 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2623]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3623]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 623]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3022 a r:Inference; +skolem:lemma6347 a r:Inference; r:gives { - 2624 :numberToDigits (2 6 2 4). + 3624 :numberToDigits (3 6 2 4). }; r:evidence ( - [ a r:Fact; r:gives {(2624 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2624 1000) math:remainder 624}] + [ a r:Fact; r:gives {(3624 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3624 1000) math:remainder 624}] [ a r:Fact; r:gives {(624 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(624 100) math:remainder 24}] [ a r:Fact; r:gives {(24 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(24 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2624]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3624]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 624]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3023 a r:Inference; +skolem:lemma6348 a r:Inference; r:gives { - 2625 :numberToDigits (2 6 2 5). + 3625 :numberToDigits (3 6 2 5). }; r:evidence ( - [ a r:Fact; r:gives {(2625 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2625 1000) math:remainder 625}] + [ a r:Fact; r:gives {(3625 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3625 1000) math:remainder 625}] [ a r:Fact; r:gives {(625 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(625 100) math:remainder 25}] [ a r:Fact; r:gives {(25 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(25 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2625]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3625]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 625]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3024 a r:Inference; +skolem:lemma6349 a r:Inference; r:gives { - 2626 :numberToDigits (2 6 2 6). + 3626 :numberToDigits (3 6 2 6). }; r:evidence ( - [ a r:Fact; r:gives {(2626 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2626 1000) math:remainder 626}] + [ a r:Fact; r:gives {(3626 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3626 1000) math:remainder 626}] [ a r:Fact; r:gives {(626 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(626 100) math:remainder 26}] [ a r:Fact; r:gives {(26 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(26 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2626]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3626]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 626]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3025 a r:Inference; +skolem:lemma6350 a r:Inference; r:gives { - 2627 :numberToDigits (2 6 2 7). + 3627 :numberToDigits (3 6 2 7). }; r:evidence ( - [ a r:Fact; r:gives {(2627 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2627 1000) math:remainder 627}] + [ a r:Fact; r:gives {(3627 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3627 1000) math:remainder 627}] [ a r:Fact; r:gives {(627 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(627 100) math:remainder 27}] [ a r:Fact; r:gives {(27 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(27 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2627]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3627]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 627]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3026 a r:Inference; +skolem:lemma6351 a r:Inference; r:gives { - 2628 :numberToDigits (2 6 2 8). + 3628 :numberToDigits (3 6 2 8). }; r:evidence ( - [ a r:Fact; r:gives {(2628 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2628 1000) math:remainder 628}] + [ a r:Fact; r:gives {(3628 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3628 1000) math:remainder 628}] [ a r:Fact; r:gives {(628 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(628 100) math:remainder 28}] [ a r:Fact; r:gives {(28 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(28 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2628]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3628]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 628]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3027 a r:Inference; +skolem:lemma6352 a r:Inference; r:gives { - 2629 :numberToDigits (2 6 2 9). + 3629 :numberToDigits (3 6 2 9). }; r:evidence ( - [ a r:Fact; r:gives {(2629 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2629 1000) math:remainder 629}] + [ a r:Fact; r:gives {(3629 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3629 1000) math:remainder 629}] [ a r:Fact; r:gives {(629 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(629 100) math:remainder 29}] [ a r:Fact; r:gives {(29 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(29 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2629]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3629]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 629]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3028 a r:Inference; +skolem:lemma6353 a r:Inference; r:gives { - 2630 :numberToDigits (2 6 3 0). + 3630 :numberToDigits (3 6 3 0). }; r:evidence ( - [ a r:Fact; r:gives {(2630 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2630 1000) math:remainder 630}] + [ a r:Fact; r:gives {(3630 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3630 1000) math:remainder 630}] [ a r:Fact; r:gives {(630 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(630 100) math:remainder 30}] [ a r:Fact; r:gives {(30 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(30 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2630]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3630]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 630]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3029 a r:Inference; +skolem:lemma6354 a r:Inference; r:gives { - 2631 :numberToDigits (2 6 3 1). + 3631 :numberToDigits (3 6 3 1). }; r:evidence ( - [ a r:Fact; r:gives {(2631 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2631 1000) math:remainder 631}] + [ a r:Fact; r:gives {(3631 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3631 1000) math:remainder 631}] [ a r:Fact; r:gives {(631 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(631 100) math:remainder 31}] [ a r:Fact; r:gives {(31 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(31 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2631]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3631]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 631]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 31]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3030 a r:Inference; +skolem:lemma6355 a r:Inference; r:gives { - 2632 :numberToDigits (2 6 3 2). + 3632 :numberToDigits (3 6 3 2). }; r:evidence ( - [ a r:Fact; r:gives {(2632 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2632 1000) math:remainder 632}] + [ a r:Fact; r:gives {(3632 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3632 1000) math:remainder 632}] [ a r:Fact; r:gives {(632 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(632 100) math:remainder 32}] [ a r:Fact; r:gives {(32 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(32 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2632]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3632]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 632]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 32]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3031 a r:Inference; +skolem:lemma6356 a r:Inference; r:gives { - 2633 :numberToDigits (2 6 3 3). + 3633 :numberToDigits (3 6 3 3). }; r:evidence ( - [ a r:Fact; r:gives {(2633 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2633 1000) math:remainder 633}] + [ a r:Fact; r:gives {(3633 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3633 1000) math:remainder 633}] [ a r:Fact; r:gives {(633 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(633 100) math:remainder 33}] [ a r:Fact; r:gives {(33 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(33 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2633]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3633]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 633]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 33]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3032 a r:Inference; +skolem:lemma6357 a r:Inference; r:gives { - 2634 :numberToDigits (2 6 3 4). + 3634 :numberToDigits (3 6 3 4). }; r:evidence ( - [ a r:Fact; r:gives {(2634 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2634 1000) math:remainder 634}] + [ a r:Fact; r:gives {(3634 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3634 1000) math:remainder 634}] [ a r:Fact; r:gives {(634 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(634 100) math:remainder 34}] [ a r:Fact; r:gives {(34 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(34 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2634]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3634]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 634]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 34]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3033 a r:Inference; +skolem:lemma6358 a r:Inference; r:gives { - 2635 :numberToDigits (2 6 3 5). + 3635 :numberToDigits (3 6 3 5). }; r:evidence ( - [ a r:Fact; r:gives {(2635 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2635 1000) math:remainder 635}] + [ a r:Fact; r:gives {(3635 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3635 1000) math:remainder 635}] [ a r:Fact; r:gives {(635 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(635 100) math:remainder 35}] [ a r:Fact; r:gives {(35 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(35 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2635]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3635]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 635]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 35]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3034 a r:Inference; +skolem:lemma6359 a r:Inference; r:gives { - 2636 :numberToDigits (2 6 3 6). + 3636 :numberToDigits (3 6 3 6). }; r:evidence ( - [ a r:Fact; r:gives {(2636 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2636 1000) math:remainder 636}] + [ a r:Fact; r:gives {(3636 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3636 1000) math:remainder 636}] [ a r:Fact; r:gives {(636 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(636 100) math:remainder 36}] [ a r:Fact; r:gives {(36 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(36 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2636]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3636]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 636]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 36]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3035 a r:Inference; +skolem:lemma6360 a r:Inference; r:gives { - 2637 :numberToDigits (2 6 3 7). + 3637 :numberToDigits (3 6 3 7). }; r:evidence ( - [ a r:Fact; r:gives {(2637 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2637 1000) math:remainder 637}] + [ a r:Fact; r:gives {(3637 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3637 1000) math:remainder 637}] [ a r:Fact; r:gives {(637 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(637 100) math:remainder 37}] [ a r:Fact; r:gives {(37 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(37 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2637]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3637]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 637]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 37]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3036 a r:Inference; +skolem:lemma6361 a r:Inference; r:gives { - 2638 :numberToDigits (2 6 3 8). + 3638 :numberToDigits (3 6 3 8). }; r:evidence ( - [ a r:Fact; r:gives {(2638 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2638 1000) math:remainder 638}] + [ a r:Fact; r:gives {(3638 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3638 1000) math:remainder 638}] [ a r:Fact; r:gives {(638 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(638 100) math:remainder 38}] [ a r:Fact; r:gives {(38 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(38 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2638]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3638]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 638]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 38]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3037 a r:Inference; +skolem:lemma6362 a r:Inference; r:gives { - 2639 :numberToDigits (2 6 3 9). + 3639 :numberToDigits (3 6 3 9). }; r:evidence ( - [ a r:Fact; r:gives {(2639 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2639 1000) math:remainder 639}] + [ a r:Fact; r:gives {(3639 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3639 1000) math:remainder 639}] [ a r:Fact; r:gives {(639 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(639 100) math:remainder 39}] [ a r:Fact; r:gives {(39 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(39 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2639]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3639]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 639]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 39]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3038 a r:Inference; +skolem:lemma6363 a r:Inference; r:gives { - 2640 :numberToDigits (2 6 4 0). + 3640 :numberToDigits (3 6 4 0). }; r:evidence ( - [ a r:Fact; r:gives {(2640 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2640 1000) math:remainder 640}] + [ a r:Fact; r:gives {(3640 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3640 1000) math:remainder 640}] [ a r:Fact; r:gives {(640 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(640 100) math:remainder 40}] [ a r:Fact; r:gives {(40 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(40 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2640]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3640]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 640]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3039 a r:Inference; +skolem:lemma6364 a r:Inference; r:gives { - 2641 :numberToDigits (2 6 4 1). + 3641 :numberToDigits (3 6 4 1). }; r:evidence ( - [ a r:Fact; r:gives {(2641 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2641 1000) math:remainder 641}] + [ a r:Fact; r:gives {(3641 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3641 1000) math:remainder 641}] [ a r:Fact; r:gives {(641 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(641 100) math:remainder 41}] [ a r:Fact; r:gives {(41 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(41 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2641]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3641]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 641]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 41]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3040 a r:Inference; +skolem:lemma6365 a r:Inference; r:gives { - 2642 :numberToDigits (2 6 4 2). + 3642 :numberToDigits (3 6 4 2). }; r:evidence ( - [ a r:Fact; r:gives {(2642 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2642 1000) math:remainder 642}] + [ a r:Fact; r:gives {(3642 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3642 1000) math:remainder 642}] [ a r:Fact; r:gives {(642 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(642 100) math:remainder 42}] [ a r:Fact; r:gives {(42 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(42 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2642]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3642]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 642]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 42]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3041 a r:Inference; +skolem:lemma6366 a r:Inference; r:gives { - 2643 :numberToDigits (2 6 4 3). + 3643 :numberToDigits (3 6 4 3). }; r:evidence ( - [ a r:Fact; r:gives {(2643 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2643 1000) math:remainder 643}] + [ a r:Fact; r:gives {(3643 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3643 1000) math:remainder 643}] [ a r:Fact; r:gives {(643 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(643 100) math:remainder 43}] [ a r:Fact; r:gives {(43 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(43 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2643]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3643]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 643]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 43]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3042 a r:Inference; +skolem:lemma6367 a r:Inference; r:gives { - 2644 :numberToDigits (2 6 4 4). + 3644 :numberToDigits (3 6 4 4). }; r:evidence ( - [ a r:Fact; r:gives {(2644 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2644 1000) math:remainder 644}] + [ a r:Fact; r:gives {(3644 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3644 1000) math:remainder 644}] [ a r:Fact; r:gives {(644 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(644 100) math:remainder 44}] [ a r:Fact; r:gives {(44 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(44 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2644]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3644]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 644]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 44]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3043 a r:Inference; +skolem:lemma6368 a r:Inference; r:gives { - 2645 :numberToDigits (2 6 4 5). + 3645 :numberToDigits (3 6 4 5). }; r:evidence ( - [ a r:Fact; r:gives {(2645 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2645 1000) math:remainder 645}] + [ a r:Fact; r:gives {(3645 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3645 1000) math:remainder 645}] [ a r:Fact; r:gives {(645 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(645 100) math:remainder 45}] [ a r:Fact; r:gives {(45 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(45 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2645]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3645]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 645]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 45]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3044 a r:Inference; +skolem:lemma6369 a r:Inference; r:gives { - 2646 :numberToDigits (2 6 4 6). + 3646 :numberToDigits (3 6 4 6). }; r:evidence ( - [ a r:Fact; r:gives {(2646 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2646 1000) math:remainder 646}] + [ a r:Fact; r:gives {(3646 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3646 1000) math:remainder 646}] [ a r:Fact; r:gives {(646 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(646 100) math:remainder 46}] [ a r:Fact; r:gives {(46 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(46 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2646]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3646]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 646]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 46]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3045 a r:Inference; +skolem:lemma6370 a r:Inference; r:gives { - 2647 :numberToDigits (2 6 4 7). + 3647 :numberToDigits (3 6 4 7). }; r:evidence ( - [ a r:Fact; r:gives {(2647 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2647 1000) math:remainder 647}] + [ a r:Fact; r:gives {(3647 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3647 1000) math:remainder 647}] [ a r:Fact; r:gives {(647 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(647 100) math:remainder 47}] [ a r:Fact; r:gives {(47 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(47 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2647]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3647]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 647]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 47]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3046 a r:Inference; +skolem:lemma6371 a r:Inference; r:gives { - 2648 :numberToDigits (2 6 4 8). + 3648 :numberToDigits (3 6 4 8). }; r:evidence ( - [ a r:Fact; r:gives {(2648 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2648 1000) math:remainder 648}] + [ a r:Fact; r:gives {(3648 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3648 1000) math:remainder 648}] [ a r:Fact; r:gives {(648 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(648 100) math:remainder 48}] [ a r:Fact; r:gives {(48 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(48 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2648]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3648]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 648]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 48]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3047 a r:Inference; +skolem:lemma6372 a r:Inference; r:gives { - 2649 :numberToDigits (2 6 4 9). + 3649 :numberToDigits (3 6 4 9). }; r:evidence ( - [ a r:Fact; r:gives {(2649 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2649 1000) math:remainder 649}] + [ a r:Fact; r:gives {(3649 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3649 1000) math:remainder 649}] [ a r:Fact; r:gives {(649 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(649 100) math:remainder 49}] [ a r:Fact; r:gives {(49 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(49 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2649]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3649]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 649]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 49]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3048 a r:Inference; +skolem:lemma6373 a r:Inference; r:gives { - 2650 :numberToDigits (2 6 5 0). + 3650 :numberToDigits (3 6 5 0). }; r:evidence ( - [ a r:Fact; r:gives {(2650 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2650 1000) math:remainder 650}] + [ a r:Fact; r:gives {(3650 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3650 1000) math:remainder 650}] [ a r:Fact; r:gives {(650 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(650 100) math:remainder 50}] [ a r:Fact; r:gives {(50 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(50 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2650]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3650]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 650]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3049 a r:Inference; +skolem:lemma6374 a r:Inference; r:gives { - 2651 :numberToDigits (2 6 5 1). + 3651 :numberToDigits (3 6 5 1). }; r:evidence ( - [ a r:Fact; r:gives {(2651 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2651 1000) math:remainder 651}] + [ a r:Fact; r:gives {(3651 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3651 1000) math:remainder 651}] [ a r:Fact; r:gives {(651 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(651 100) math:remainder 51}] [ a r:Fact; r:gives {(51 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(51 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2651]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3651]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 651]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 51]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3050 a r:Inference; +skolem:lemma6375 a r:Inference; r:gives { - 2652 :numberToDigits (2 6 5 2). + 3652 :numberToDigits (3 6 5 2). }; r:evidence ( - [ a r:Fact; r:gives {(2652 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2652 1000) math:remainder 652}] + [ a r:Fact; r:gives {(3652 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3652 1000) math:remainder 652}] [ a r:Fact; r:gives {(652 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(652 100) math:remainder 52}] [ a r:Fact; r:gives {(52 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(52 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2652]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3652]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 652]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 52]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3051 a r:Inference; +skolem:lemma6376 a r:Inference; r:gives { - 2653 :numberToDigits (2 6 5 3). + 3653 :numberToDigits (3 6 5 3). }; r:evidence ( - [ a r:Fact; r:gives {(2653 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2653 1000) math:remainder 653}] + [ a r:Fact; r:gives {(3653 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3653 1000) math:remainder 653}] [ a r:Fact; r:gives {(653 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(653 100) math:remainder 53}] [ a r:Fact; r:gives {(53 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(53 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2653]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3653]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 653]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 53]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3052 a r:Inference; +skolem:lemma6377 a r:Inference; r:gives { - 2654 :numberToDigits (2 6 5 4). + 3654 :numberToDigits (3 6 5 4). }; r:evidence ( - [ a r:Fact; r:gives {(2654 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2654 1000) math:remainder 654}] + [ a r:Fact; r:gives {(3654 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3654 1000) math:remainder 654}] [ a r:Fact; r:gives {(654 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(654 100) math:remainder 54}] [ a r:Fact; r:gives {(54 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(54 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2654]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3654]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 654]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 54]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3053 a r:Inference; +skolem:lemma6378 a r:Inference; r:gives { - 2655 :numberToDigits (2 6 5 5). + 3655 :numberToDigits (3 6 5 5). }; r:evidence ( - [ a r:Fact; r:gives {(2655 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2655 1000) math:remainder 655}] + [ a r:Fact; r:gives {(3655 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3655 1000) math:remainder 655}] [ a r:Fact; r:gives {(655 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(655 100) math:remainder 55}] [ a r:Fact; r:gives {(55 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(55 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2655]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3655]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 655]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 55]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3054 a r:Inference; +skolem:lemma6379 a r:Inference; r:gives { - 2656 :numberToDigits (2 6 5 6). + 3656 :numberToDigits (3 6 5 6). }; r:evidence ( - [ a r:Fact; r:gives {(2656 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2656 1000) math:remainder 656}] + [ a r:Fact; r:gives {(3656 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3656 1000) math:remainder 656}] [ a r:Fact; r:gives {(656 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(656 100) math:remainder 56}] [ a r:Fact; r:gives {(56 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(56 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2656]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3656]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 656]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 56]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3055 a r:Inference; +skolem:lemma6380 a r:Inference; r:gives { - 2657 :numberToDigits (2 6 5 7). + 3657 :numberToDigits (3 6 5 7). }; r:evidence ( - [ a r:Fact; r:gives {(2657 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2657 1000) math:remainder 657}] + [ a r:Fact; r:gives {(3657 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3657 1000) math:remainder 657}] [ a r:Fact; r:gives {(657 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(657 100) math:remainder 57}] [ a r:Fact; r:gives {(57 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(57 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2657]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3657]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 657]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 57]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3056 a r:Inference; +skolem:lemma6381 a r:Inference; r:gives { - 2658 :numberToDigits (2 6 5 8). + 3658 :numberToDigits (3 6 5 8). }; r:evidence ( - [ a r:Fact; r:gives {(2658 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2658 1000) math:remainder 658}] + [ a r:Fact; r:gives {(3658 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3658 1000) math:remainder 658}] [ a r:Fact; r:gives {(658 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(658 100) math:remainder 58}] [ a r:Fact; r:gives {(58 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(58 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2658]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3658]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 658]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 58]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3057 a r:Inference; +skolem:lemma6382 a r:Inference; r:gives { - 2659 :numberToDigits (2 6 5 9). + 3659 :numberToDigits (3 6 5 9). }; r:evidence ( - [ a r:Fact; r:gives {(2659 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2659 1000) math:remainder 659}] + [ a r:Fact; r:gives {(3659 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3659 1000) math:remainder 659}] [ a r:Fact; r:gives {(659 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(659 100) math:remainder 59}] [ a r:Fact; r:gives {(59 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(59 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2659]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3659]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 659]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 59]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3058 a r:Inference; +skolem:lemma6383 a r:Inference; r:gives { - 2660 :numberToDigits (2 6 6 0). + 3660 :numberToDigits (3 6 6 0). }; r:evidence ( - [ a r:Fact; r:gives {(2660 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2660 1000) math:remainder 660}] + [ a r:Fact; r:gives {(3660 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3660 1000) math:remainder 660}] [ a r:Fact; r:gives {(660 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(660 100) math:remainder 60}] [ a r:Fact; r:gives {(60 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(60 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2660]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3660]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 660]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3059 a r:Inference; +skolem:lemma6384 a r:Inference; r:gives { - 2661 :numberToDigits (2 6 6 1). + 3661 :numberToDigits (3 6 6 1). }; r:evidence ( - [ a r:Fact; r:gives {(2661 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2661 1000) math:remainder 661}] + [ a r:Fact; r:gives {(3661 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3661 1000) math:remainder 661}] [ a r:Fact; r:gives {(661 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(661 100) math:remainder 61}] [ a r:Fact; r:gives {(61 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(61 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2661]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3661]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 661]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 61]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3060 a r:Inference; +skolem:lemma6385 a r:Inference; r:gives { - 2662 :numberToDigits (2 6 6 2). + 3662 :numberToDigits (3 6 6 2). }; r:evidence ( - [ a r:Fact; r:gives {(2662 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2662 1000) math:remainder 662}] + [ a r:Fact; r:gives {(3662 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3662 1000) math:remainder 662}] [ a r:Fact; r:gives {(662 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(662 100) math:remainder 62}] [ a r:Fact; r:gives {(62 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(62 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2662]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3662]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 662]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 62]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3061 a r:Inference; +skolem:lemma6386 a r:Inference; r:gives { - 2663 :numberToDigits (2 6 6 3). + 3663 :numberToDigits (3 6 6 3). }; r:evidence ( - [ a r:Fact; r:gives {(2663 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2663 1000) math:remainder 663}] + [ a r:Fact; r:gives {(3663 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3663 1000) math:remainder 663}] [ a r:Fact; r:gives {(663 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(663 100) math:remainder 63}] [ a r:Fact; r:gives {(63 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(63 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2663]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3663]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 663]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 63]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3062 a r:Inference; +skolem:lemma6387 a r:Inference; r:gives { - 2664 :numberToDigits (2 6 6 4). + 3664 :numberToDigits (3 6 6 4). }; r:evidence ( - [ a r:Fact; r:gives {(2664 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2664 1000) math:remainder 664}] + [ a r:Fact; r:gives {(3664 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3664 1000) math:remainder 664}] [ a r:Fact; r:gives {(664 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(664 100) math:remainder 64}] [ a r:Fact; r:gives {(64 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(64 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2664]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3664]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 664]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 64]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3063 a r:Inference; +skolem:lemma6388 a r:Inference; r:gives { - 2665 :numberToDigits (2 6 6 5). + 3665 :numberToDigits (3 6 6 5). }; r:evidence ( - [ a r:Fact; r:gives {(2665 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2665 1000) math:remainder 665}] + [ a r:Fact; r:gives {(3665 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3665 1000) math:remainder 665}] [ a r:Fact; r:gives {(665 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(665 100) math:remainder 65}] [ a r:Fact; r:gives {(65 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(65 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2665]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3665]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 665]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 65]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3064 a r:Inference; +skolem:lemma6389 a r:Inference; r:gives { - 2666 :numberToDigits (2 6 6 6). + 3666 :numberToDigits (3 6 6 6). }; r:evidence ( - [ a r:Fact; r:gives {(2666 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2666 1000) math:remainder 666}] + [ a r:Fact; r:gives {(3666 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3666 1000) math:remainder 666}] [ a r:Fact; r:gives {(666 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(666 100) math:remainder 66}] [ a r:Fact; r:gives {(66 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(66 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2666]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3666]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 666]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 66]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3065 a r:Inference; +skolem:lemma6390 a r:Inference; r:gives { - (2 6 6 6) :digitsToNumber 2666 . + (3 6 6 6) :digitsToNumber 3666 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(2000 600 60 6) math:sum 2666}] + [ a r:Fact; r:gives {(3000 600 60 6) math:sum 3666}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2666]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3666]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma3066 a r:Inference; +skolem:lemma6391 a r:Inference; r:gives { - (6 6 6 2) :digitsToNumber 6662 . + (6 6 6 3) :digitsToNumber 6663 . }; r:evidence ( [ a r:Fact; r:gives {(6 1000) math:product 6000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(6000 600 60 2) math:sum 6662}] + [ a r:Fact; r:gives {(6000 600 60 3) math:sum 6663}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 6000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 6]; @@ -71979,60 +149468,60 @@ skolem:lemma3066 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6662]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 6663]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma3067 a r:Inference; +skolem:lemma6392 a r:Inference; r:gives { - 2667 :numberToDigits (2 6 6 7). + 3667 :numberToDigits (3 6 6 7). }; r:evidence ( - [ a r:Fact; r:gives {(2667 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2667 1000) math:remainder 667}] + [ a r:Fact; r:gives {(3667 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3667 1000) math:remainder 667}] [ a r:Fact; r:gives {(667 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(667 100) math:remainder 67}] [ a r:Fact; r:gives {(67 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(67 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2667]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3667]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 667]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 67]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3068 a r:Inference; +skolem:lemma6393 a r:Inference; r:gives { - (2 6 6 7) :digitsToNumber 2667 . + (3 6 6 7) :digitsToNumber 3667 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(2000 600 60 7) math:sum 2667}] + [ a r:Fact; r:gives {(3000 600 60 7) math:sum 3667}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2667]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3667]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma3069 a r:Inference; +skolem:lemma6394 a r:Inference; r:gives { - (7 6 6 2) :digitsToNumber 7662 . + (7 6 6 3) :digitsToNumber 7663 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(7000 600 60 2) math:sum 7662}] + [ a r:Fact; r:gives {(7000 600 60 3) math:sum 7663}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; @@ -72040,60 +149529,60 @@ skolem:lemma3069 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7662]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7663]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma3070 a r:Inference; +skolem:lemma6395 a r:Inference; r:gives { - 2668 :numberToDigits (2 6 6 8). + 3668 :numberToDigits (3 6 6 8). }; r:evidence ( - [ a r:Fact; r:gives {(2668 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2668 1000) math:remainder 668}] + [ a r:Fact; r:gives {(3668 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3668 1000) math:remainder 668}] [ a r:Fact; r:gives {(668 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(668 100) math:remainder 68}] [ a r:Fact; r:gives {(68 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(68 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2668]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3668]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 668]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 68]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3071 a r:Inference; +skolem:lemma6396 a r:Inference; r:gives { - (2 6 6 8) :digitsToNumber 2668 . + (3 6 6 8) :digitsToNumber 3668 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(2000 600 60 8) math:sum 2668}] + [ a r:Fact; r:gives {(3000 600 60 8) math:sum 3668}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2668]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3668]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma3072 a r:Inference; +skolem:lemma6397 a r:Inference; r:gives { - (8 6 6 2) :digitsToNumber 8662 . + (8 6 6 3) :digitsToNumber 8663 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(8000 600 60 2) math:sum 8662}] + [ a r:Fact; r:gives {(8000 600 60 3) math:sum 8663}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; @@ -72101,60 +149590,60 @@ skolem:lemma3072 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8662]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8663]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma3073 a r:Inference; +skolem:lemma6398 a r:Inference; r:gives { - 2669 :numberToDigits (2 6 6 9). + 3669 :numberToDigits (3 6 6 9). }; r:evidence ( - [ a r:Fact; r:gives {(2669 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2669 1000) math:remainder 669}] + [ a r:Fact; r:gives {(3669 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3669 1000) math:remainder 669}] [ a r:Fact; r:gives {(669 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(669 100) math:remainder 69}] [ a r:Fact; r:gives {(69 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(69 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2669]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3669]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 669]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 69]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3074 a r:Inference; +skolem:lemma6399 a r:Inference; r:gives { - (2 6 6 9) :digitsToNumber 2669 . + (3 6 6 9) :digitsToNumber 3669 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(2000 600 60 9) math:sum 2669}] + [ a r:Fact; r:gives {(3000 600 60 9) math:sum 3669}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2669]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3669]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma3075 a r:Inference; +skolem:lemma6400 a r:Inference; r:gives { - (9 6 6 2) :digitsToNumber 9662 . + (9 6 6 3) :digitsToNumber 9663 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(9000 600 60 2) math:sum 9662}] + [ a r:Fact; r:gives {(9000 600 60 3) math:sum 9663}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -72162,207 +149651,207 @@ skolem:lemma3075 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9662]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9663]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma3076 a r:Inference; +skolem:lemma6401 a r:Inference; r:gives { - 2670 :numberToDigits (2 6 7 0). + 3670 :numberToDigits (3 6 7 0). }; r:evidence ( - [ a r:Fact; r:gives {(2670 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2670 1000) math:remainder 670}] + [ a r:Fact; r:gives {(3670 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3670 1000) math:remainder 670}] [ a r:Fact; r:gives {(670 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(670 100) math:remainder 70}] [ a r:Fact; r:gives {(70 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(70 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2670]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3670]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 670]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3077 a r:Inference; +skolem:lemma6402 a r:Inference; r:gives { - 2671 :numberToDigits (2 6 7 1). + 3671 :numberToDigits (3 6 7 1). }; r:evidence ( - [ a r:Fact; r:gives {(2671 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2671 1000) math:remainder 671}] + [ a r:Fact; r:gives {(3671 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3671 1000) math:remainder 671}] [ a r:Fact; r:gives {(671 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(671 100) math:remainder 71}] [ a r:Fact; r:gives {(71 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(71 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2671]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3671]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 671]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 71]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3078 a r:Inference; +skolem:lemma6403 a r:Inference; r:gives { - 2672 :numberToDigits (2 6 7 2). + 3672 :numberToDigits (3 6 7 2). }; r:evidence ( - [ a r:Fact; r:gives {(2672 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2672 1000) math:remainder 672}] + [ a r:Fact; r:gives {(3672 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3672 1000) math:remainder 672}] [ a r:Fact; r:gives {(672 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(672 100) math:remainder 72}] [ a r:Fact; r:gives {(72 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(72 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2672]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3672]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 672]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 72]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3079 a r:Inference; +skolem:lemma6404 a r:Inference; r:gives { - 2673 :numberToDigits (2 6 7 3). + 3673 :numberToDigits (3 6 7 3). }; r:evidence ( - [ a r:Fact; r:gives {(2673 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2673 1000) math:remainder 673}] + [ a r:Fact; r:gives {(3673 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3673 1000) math:remainder 673}] [ a r:Fact; r:gives {(673 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(673 100) math:remainder 73}] [ a r:Fact; r:gives {(73 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(73 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2673]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3673]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 673]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 73]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3080 a r:Inference; +skolem:lemma6405 a r:Inference; r:gives { - 2674 :numberToDigits (2 6 7 4). + 3674 :numberToDigits (3 6 7 4). }; r:evidence ( - [ a r:Fact; r:gives {(2674 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2674 1000) math:remainder 674}] + [ a r:Fact; r:gives {(3674 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3674 1000) math:remainder 674}] [ a r:Fact; r:gives {(674 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(674 100) math:remainder 74}] [ a r:Fact; r:gives {(74 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(74 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2674]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3674]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 674]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 74]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3081 a r:Inference; +skolem:lemma6406 a r:Inference; r:gives { - 2675 :numberToDigits (2 6 7 5). + 3675 :numberToDigits (3 6 7 5). }; r:evidence ( - [ a r:Fact; r:gives {(2675 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2675 1000) math:remainder 675}] + [ a r:Fact; r:gives {(3675 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3675 1000) math:remainder 675}] [ a r:Fact; r:gives {(675 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(675 100) math:remainder 75}] [ a r:Fact; r:gives {(75 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(75 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2675]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3675]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 675]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 75]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3082 a r:Inference; +skolem:lemma6407 a r:Inference; r:gives { - 2676 :numberToDigits (2 6 7 6). + 3676 :numberToDigits (3 6 7 6). }; r:evidence ( - [ a r:Fact; r:gives {(2676 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2676 1000) math:remainder 676}] + [ a r:Fact; r:gives {(3676 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3676 1000) math:remainder 676}] [ a r:Fact; r:gives {(676 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(676 100) math:remainder 76}] [ a r:Fact; r:gives {(76 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(76 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2676]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3676]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 676]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 76]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3083 a r:Inference; +skolem:lemma6408 a r:Inference; r:gives { - 2677 :numberToDigits (2 6 7 7). + 3677 :numberToDigits (3 6 7 7). }; r:evidence ( - [ a r:Fact; r:gives {(2677 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2677 1000) math:remainder 677}] + [ a r:Fact; r:gives {(3677 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3677 1000) math:remainder 677}] [ a r:Fact; r:gives {(677 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(677 100) math:remainder 77}] [ a r:Fact; r:gives {(77 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(77 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2677]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3677]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 677]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 77]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3084 a r:Inference; +skolem:lemma6409 a r:Inference; r:gives { - (2 6 7 7) :digitsToNumber 2677 . + (3 6 7 7) :digitsToNumber 3677 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(2000 600 70 7) math:sum 2677}] + [ a r:Fact; r:gives {(3000 600 70 7) math:sum 3677}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2677]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3677]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma3085 a r:Inference; +skolem:lemma6410 a r:Inference; r:gives { - (7 7 6 2) :digitsToNumber 7762 . + (7 7 6 3) :digitsToNumber 7763 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(7 100) math:product 700}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(7000 700 60 2) math:sum 7762}] + [ a r:Fact; r:gives {(7000 700 60 3) math:sum 7763}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; @@ -72370,60 +149859,60 @@ skolem:lemma3085 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7762]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma3086 a r:Inference; +skolem:lemma6411 a r:Inference; r:gives { - 2678 :numberToDigits (2 6 7 8). + 3678 :numberToDigits (3 6 7 8). }; r:evidence ( - [ a r:Fact; r:gives {(2678 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2678 1000) math:remainder 678}] + [ a r:Fact; r:gives {(3678 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3678 1000) math:remainder 678}] [ a r:Fact; r:gives {(678 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(678 100) math:remainder 78}] [ a r:Fact; r:gives {(78 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(78 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2678]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3678]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 678]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 78]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3087 a r:Inference; +skolem:lemma6412 a r:Inference; r:gives { - (2 6 7 8) :digitsToNumber 2678 . + (3 6 7 8) :digitsToNumber 3678 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(2000 600 70 8) math:sum 2678}] + [ a r:Fact; r:gives {(3000 600 70 8) math:sum 3678}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2678]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3678]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma3088 a r:Inference; +skolem:lemma6413 a r:Inference; r:gives { - (8 7 6 2) :digitsToNumber 8762 . + (8 7 6 3) :digitsToNumber 8763 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(7 100) math:product 700}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(8000 700 60 2) math:sum 8762}] + [ a r:Fact; r:gives {(8000 700 60 3) math:sum 8763}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; @@ -72431,60 +149920,60 @@ skolem:lemma3088 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8762]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma3089 a r:Inference; +skolem:lemma6414 a r:Inference; r:gives { - 2679 :numberToDigits (2 6 7 9). + 3679 :numberToDigits (3 6 7 9). }; r:evidence ( - [ a r:Fact; r:gives {(2679 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2679 1000) math:remainder 679}] + [ a r:Fact; r:gives {(3679 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3679 1000) math:remainder 679}] [ a r:Fact; r:gives {(679 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(679 100) math:remainder 79}] [ a r:Fact; r:gives {(79 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(79 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2679]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3679]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 679]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 79]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3090 a r:Inference; +skolem:lemma6415 a r:Inference; r:gives { - (2 6 7 9) :digitsToNumber 2679 . + (3 6 7 9) :digitsToNumber 3679 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(2000 600 70 9) math:sum 2679}] + [ a r:Fact; r:gives {(3000 600 70 9) math:sum 3679}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2679]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3679]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma3091 a r:Inference; +skolem:lemma6416 a r:Inference; r:gives { - (9 7 6 2) :digitsToNumber 9762 . + (9 7 6 3) :digitsToNumber 9763 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(7 100) math:product 700}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(9000 700 60 2) math:sum 9762}] + [ a r:Fact; r:gives {(9000 700 60 3) math:sum 9763}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -72492,228 +149981,228 @@ skolem:lemma3091 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9762]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma3092 a r:Inference; +skolem:lemma6417 a r:Inference; r:gives { - 2680 :numberToDigits (2 6 8 0). + 3680 :numberToDigits (3 6 8 0). }; r:evidence ( - [ a r:Fact; r:gives {(2680 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2680 1000) math:remainder 680}] + [ a r:Fact; r:gives {(3680 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3680 1000) math:remainder 680}] [ a r:Fact; r:gives {(680 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(680 100) math:remainder 80}] [ a r:Fact; r:gives {(80 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(80 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2680]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3680]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 680]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3093 a r:Inference; +skolem:lemma6418 a r:Inference; r:gives { - 2681 :numberToDigits (2 6 8 1). + 3681 :numberToDigits (3 6 8 1). }; r:evidence ( - [ a r:Fact; r:gives {(2681 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2681 1000) math:remainder 681}] + [ a r:Fact; r:gives {(3681 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3681 1000) math:remainder 681}] [ a r:Fact; r:gives {(681 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(681 100) math:remainder 81}] [ a r:Fact; r:gives {(81 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(81 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2681]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3681]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 681]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 81]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3094 a r:Inference; +skolem:lemma6419 a r:Inference; r:gives { - 2682 :numberToDigits (2 6 8 2). + 3682 :numberToDigits (3 6 8 2). }; r:evidence ( - [ a r:Fact; r:gives {(2682 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2682 1000) math:remainder 682}] + [ a r:Fact; r:gives {(3682 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3682 1000) math:remainder 682}] [ a r:Fact; r:gives {(682 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(682 100) math:remainder 82}] [ a r:Fact; r:gives {(82 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(82 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2682]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3682]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 682]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 82]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3095 a r:Inference; +skolem:lemma6420 a r:Inference; r:gives { - 2683 :numberToDigits (2 6 8 3). + 3683 :numberToDigits (3 6 8 3). }; r:evidence ( - [ a r:Fact; r:gives {(2683 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2683 1000) math:remainder 683}] + [ a r:Fact; r:gives {(3683 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3683 1000) math:remainder 683}] [ a r:Fact; r:gives {(683 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(683 100) math:remainder 83}] [ a r:Fact; r:gives {(83 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(83 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2683]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3683]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 683]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 83]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3096 a r:Inference; +skolem:lemma6421 a r:Inference; r:gives { - 2684 :numberToDigits (2 6 8 4). + 3684 :numberToDigits (3 6 8 4). }; r:evidence ( - [ a r:Fact; r:gives {(2684 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2684 1000) math:remainder 684}] + [ a r:Fact; r:gives {(3684 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3684 1000) math:remainder 684}] [ a r:Fact; r:gives {(684 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(684 100) math:remainder 84}] [ a r:Fact; r:gives {(84 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(84 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2684]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3684]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 684]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 84]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3097 a r:Inference; +skolem:lemma6422 a r:Inference; r:gives { - 2685 :numberToDigits (2 6 8 5). + 3685 :numberToDigits (3 6 8 5). }; r:evidence ( - [ a r:Fact; r:gives {(2685 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2685 1000) math:remainder 685}] + [ a r:Fact; r:gives {(3685 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3685 1000) math:remainder 685}] [ a r:Fact; r:gives {(685 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(685 100) math:remainder 85}] [ a r:Fact; r:gives {(85 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(85 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2685]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3685]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 685]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 85]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3098 a r:Inference; +skolem:lemma6423 a r:Inference; r:gives { - 2686 :numberToDigits (2 6 8 6). + 3686 :numberToDigits (3 6 8 6). }; r:evidence ( - [ a r:Fact; r:gives {(2686 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2686 1000) math:remainder 686}] + [ a r:Fact; r:gives {(3686 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3686 1000) math:remainder 686}] [ a r:Fact; r:gives {(686 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(686 100) math:remainder 86}] [ a r:Fact; r:gives {(86 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(86 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2686]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3686]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 686]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 86]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3099 a r:Inference; +skolem:lemma6424 a r:Inference; r:gives { - 2687 :numberToDigits (2 6 8 7). + 3687 :numberToDigits (3 6 8 7). }; r:evidence ( - [ a r:Fact; r:gives {(2687 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2687 1000) math:remainder 687}] + [ a r:Fact; r:gives {(3687 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3687 1000) math:remainder 687}] [ a r:Fact; r:gives {(687 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(687 100) math:remainder 87}] [ a r:Fact; r:gives {(87 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(87 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2687]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3687]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 687]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 87]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3100 a r:Inference; +skolem:lemma6425 a r:Inference; r:gives { - 2688 :numberToDigits (2 6 8 8). + 3688 :numberToDigits (3 6 8 8). }; r:evidence ( - [ a r:Fact; r:gives {(2688 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2688 1000) math:remainder 688}] + [ a r:Fact; r:gives {(3688 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3688 1000) math:remainder 688}] [ a r:Fact; r:gives {(688 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(688 100) math:remainder 88}] [ a r:Fact; r:gives {(88 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(88 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2688]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3688]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 688]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 88]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3101 a r:Inference; +skolem:lemma6426 a r:Inference; r:gives { - (2 6 8 8) :digitsToNumber 2688 . + (3 6 8 8) :digitsToNumber 3688 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(8 10) math:product 80}] - [ a r:Fact; r:gives {(2000 600 80 8) math:sum 2688}] + [ a r:Fact; r:gives {(3000 600 80 8) math:sum 3688}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2688]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3688]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma3102 a r:Inference; +skolem:lemma6427 a r:Inference; r:gives { - (8 8 6 2) :digitsToNumber 8862 . + (8 8 6 3) :digitsToNumber 8863 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(8 100) math:product 800}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(8000 800 60 2) math:sum 8862}] + [ a r:Fact; r:gives {(8000 800 60 3) math:sum 8863}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; @@ -72721,60 +150210,60 @@ skolem:lemma3102 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8862]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8863]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma3103 a r:Inference; +skolem:lemma6428 a r:Inference; r:gives { - 2689 :numberToDigits (2 6 8 9). + 3689 :numberToDigits (3 6 8 9). }; r:evidence ( - [ a r:Fact; r:gives {(2689 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2689 1000) math:remainder 689}] + [ a r:Fact; r:gives {(3689 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3689 1000) math:remainder 689}] [ a r:Fact; r:gives {(689 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(689 100) math:remainder 89}] [ a r:Fact; r:gives {(89 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(89 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2689]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3689]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 689]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 89]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3104 a r:Inference; +skolem:lemma6429 a r:Inference; r:gives { - (2 6 8 9) :digitsToNumber 2689 . + (3 6 8 9) :digitsToNumber 3689 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(8 10) math:product 80}] - [ a r:Fact; r:gives {(2000 600 80 9) math:sum 2689}] + [ a r:Fact; r:gives {(3000 600 80 9) math:sum 3689}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2689]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3689]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma3105 a r:Inference; +skolem:lemma6430 a r:Inference; r:gives { - (9 8 6 2) :digitsToNumber 9862 . + (9 8 6 3) :digitsToNumber 9863 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(8 100) math:product 800}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(9000 800 60 2) math:sum 9862}] + [ a r:Fact; r:gives {(9000 800 60 3) math:sum 9863}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -72782,249 +150271,249 @@ skolem:lemma3105 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9862]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9863]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma3106 a r:Inference; +skolem:lemma6431 a r:Inference; r:gives { - 2690 :numberToDigits (2 6 9 0). + 3690 :numberToDigits (3 6 9 0). }; r:evidence ( - [ a r:Fact; r:gives {(2690 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2690 1000) math:remainder 690}] + [ a r:Fact; r:gives {(3690 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3690 1000) math:remainder 690}] [ a r:Fact; r:gives {(690 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(690 100) math:remainder 90}] [ a r:Fact; r:gives {(90 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(90 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2690]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3690]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 690]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 90]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3107 a r:Inference; +skolem:lemma6432 a r:Inference; r:gives { - 2691 :numberToDigits (2 6 9 1). + 3691 :numberToDigits (3 6 9 1). }; r:evidence ( - [ a r:Fact; r:gives {(2691 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2691 1000) math:remainder 691}] + [ a r:Fact; r:gives {(3691 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3691 1000) math:remainder 691}] [ a r:Fact; r:gives {(691 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(691 100) math:remainder 91}] [ a r:Fact; r:gives {(91 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(91 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2691]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3691]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 691]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 91]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3108 a r:Inference; +skolem:lemma6433 a r:Inference; r:gives { - 2692 :numberToDigits (2 6 9 2). + 3692 :numberToDigits (3 6 9 2). }; r:evidence ( - [ a r:Fact; r:gives {(2692 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2692 1000) math:remainder 692}] + [ a r:Fact; r:gives {(3692 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3692 1000) math:remainder 692}] [ a r:Fact; r:gives {(692 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(692 100) math:remainder 92}] [ a r:Fact; r:gives {(92 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(92 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2692]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3692]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 692]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 92]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3109 a r:Inference; +skolem:lemma6434 a r:Inference; r:gives { - 2693 :numberToDigits (2 6 9 3). + 3693 :numberToDigits (3 6 9 3). }; r:evidence ( - [ a r:Fact; r:gives {(2693 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2693 1000) math:remainder 693}] + [ a r:Fact; r:gives {(3693 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3693 1000) math:remainder 693}] [ a r:Fact; r:gives {(693 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(693 100) math:remainder 93}] [ a r:Fact; r:gives {(93 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(93 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2693]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3693]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 693]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 93]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3110 a r:Inference; +skolem:lemma6435 a r:Inference; r:gives { - 2694 :numberToDigits (2 6 9 4). + 3694 :numberToDigits (3 6 9 4). }; r:evidence ( - [ a r:Fact; r:gives {(2694 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2694 1000) math:remainder 694}] + [ a r:Fact; r:gives {(3694 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3694 1000) math:remainder 694}] [ a r:Fact; r:gives {(694 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(694 100) math:remainder 94}] [ a r:Fact; r:gives {(94 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(94 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2694]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3694]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 694]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 94]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3111 a r:Inference; +skolem:lemma6436 a r:Inference; r:gives { - 2695 :numberToDigits (2 6 9 5). + 3695 :numberToDigits (3 6 9 5). }; r:evidence ( - [ a r:Fact; r:gives {(2695 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2695 1000) math:remainder 695}] + [ a r:Fact; r:gives {(3695 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3695 1000) math:remainder 695}] [ a r:Fact; r:gives {(695 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(695 100) math:remainder 95}] [ a r:Fact; r:gives {(95 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(95 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2695]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3695]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 695]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 95]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3112 a r:Inference; +skolem:lemma6437 a r:Inference; r:gives { - 2696 :numberToDigits (2 6 9 6). + 3696 :numberToDigits (3 6 9 6). }; r:evidence ( - [ a r:Fact; r:gives {(2696 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2696 1000) math:remainder 696}] + [ a r:Fact; r:gives {(3696 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3696 1000) math:remainder 696}] [ a r:Fact; r:gives {(696 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(696 100) math:remainder 96}] [ a r:Fact; r:gives {(96 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(96 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2696]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3696]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 696]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 96]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3113 a r:Inference; +skolem:lemma6438 a r:Inference; r:gives { - 2697 :numberToDigits (2 6 9 7). + 3697 :numberToDigits (3 6 9 7). }; r:evidence ( - [ a r:Fact; r:gives {(2697 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2697 1000) math:remainder 697}] + [ a r:Fact; r:gives {(3697 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3697 1000) math:remainder 697}] [ a r:Fact; r:gives {(697 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(697 100) math:remainder 97}] [ a r:Fact; r:gives {(97 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(97 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2697]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3697]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 697]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 97]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3114 a r:Inference; +skolem:lemma6439 a r:Inference; r:gives { - 2698 :numberToDigits (2 6 9 8). + 3698 :numberToDigits (3 6 9 8). }; r:evidence ( - [ a r:Fact; r:gives {(2698 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2698 1000) math:remainder 698}] + [ a r:Fact; r:gives {(3698 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3698 1000) math:remainder 698}] [ a r:Fact; r:gives {(698 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(698 100) math:remainder 98}] [ a r:Fact; r:gives {(98 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(98 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2698]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3698]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 698]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 98]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3115 a r:Inference; +skolem:lemma6440 a r:Inference; r:gives { - 2699 :numberToDigits (2 6 9 9). + 3699 :numberToDigits (3 6 9 9). }; r:evidence ( - [ a r:Fact; r:gives {(2699 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2699 1000) math:remainder 699}] + [ a r:Fact; r:gives {(3699 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3699 1000) math:remainder 699}] [ a r:Fact; r:gives {(699 100) math:integerQuotient 6}] [ a r:Fact; r:gives {(699 100) math:remainder 99}] [ a r:Fact; r:gives {(99 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(99 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2699]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3699]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 699]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 99]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3116 a r:Inference; +skolem:lemma6441 a r:Inference; r:gives { - (2 6 9 9) :digitsToNumber 2699 . + (3 6 9 9) :digitsToNumber 3699 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(6 100) math:product 600}] [ a r:Fact; r:gives {(9 10) math:product 90}] - [ a r:Fact; r:gives {(2000 600 90 9) math:sum 2699}] + [ a r:Fact; r:gives {(3000 600 90 9) math:sum 3699}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 600]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 90]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2699]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3699]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma3117 a r:Inference; +skolem:lemma6442 a r:Inference; r:gives { - (9 9 6 2) :digitsToNumber 9962 . + (9 9 6 3) :digitsToNumber 9963 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(9 100) math:product 900}] [ a r:Fact; r:gives {(6 10) math:product 60}] - [ a r:Fact; r:gives {(9000 900 60 2) math:sum 9962}] + [ a r:Fact; r:gives {(9000 900 60 3) math:sum 9963}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -73032,1677 +150521,1677 @@ skolem:lemma3117 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9962]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9963]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma3118 a r:Inference; +skolem:lemma6443 a r:Inference; r:gives { - 2700 :numberToDigits (2 7 0 0). + 3700 :numberToDigits (3 7 0 0). }; r:evidence ( - [ a r:Fact; r:gives {(2700 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2700 1000) math:remainder 700}] + [ a r:Fact; r:gives {(3700 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3700 1000) math:remainder 700}] [ a r:Fact; r:gives {(700 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(700 100) math:remainder 0}] [ a r:Fact; r:gives {(0 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(0 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2700]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3700]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 700]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3119 a r:Inference; +skolem:lemma6444 a r:Inference; r:gives { - 2701 :numberToDigits (2 7 0 1). + 3701 :numberToDigits (3 7 0 1). }; r:evidence ( - [ a r:Fact; r:gives {(2701 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2701 1000) math:remainder 701}] + [ a r:Fact; r:gives {(3701 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3701 1000) math:remainder 701}] [ a r:Fact; r:gives {(701 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(701 100) math:remainder 1}] [ a r:Fact; r:gives {(1 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(1 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2701]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3701]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 701]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3120 a r:Inference; +skolem:lemma6445 a r:Inference; r:gives { - 2702 :numberToDigits (2 7 0 2). + 3702 :numberToDigits (3 7 0 2). }; r:evidence ( - [ a r:Fact; r:gives {(2702 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2702 1000) math:remainder 702}] + [ a r:Fact; r:gives {(3702 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3702 1000) math:remainder 702}] [ a r:Fact; r:gives {(702 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(702 100) math:remainder 2}] [ a r:Fact; r:gives {(2 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(2 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2702]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3702]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 702]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3121 a r:Inference; +skolem:lemma6446 a r:Inference; r:gives { - 2703 :numberToDigits (2 7 0 3). + 3703 :numberToDigits (3 7 0 3). }; r:evidence ( - [ a r:Fact; r:gives {(2703 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2703 1000) math:remainder 703}] + [ a r:Fact; r:gives {(3703 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3703 1000) math:remainder 703}] [ a r:Fact; r:gives {(703 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(703 100) math:remainder 3}] [ a r:Fact; r:gives {(3 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(3 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2703]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3703]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 703]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3122 a r:Inference; +skolem:lemma6447 a r:Inference; r:gives { - 2704 :numberToDigits (2 7 0 4). + 3704 :numberToDigits (3 7 0 4). }; r:evidence ( - [ a r:Fact; r:gives {(2704 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2704 1000) math:remainder 704}] + [ a r:Fact; r:gives {(3704 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3704 1000) math:remainder 704}] [ a r:Fact; r:gives {(704 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(704 100) math:remainder 4}] [ a r:Fact; r:gives {(4 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(4 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2704]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3704]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 704]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3123 a r:Inference; +skolem:lemma6448 a r:Inference; r:gives { - 2705 :numberToDigits (2 7 0 5). + 3705 :numberToDigits (3 7 0 5). }; r:evidence ( - [ a r:Fact; r:gives {(2705 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2705 1000) math:remainder 705}] + [ a r:Fact; r:gives {(3705 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3705 1000) math:remainder 705}] [ a r:Fact; r:gives {(705 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(705 100) math:remainder 5}] [ a r:Fact; r:gives {(5 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(5 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2705]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3705]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 705]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3124 a r:Inference; +skolem:lemma6449 a r:Inference; r:gives { - 2706 :numberToDigits (2 7 0 6). + 3706 :numberToDigits (3 7 0 6). }; r:evidence ( - [ a r:Fact; r:gives {(2706 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2706 1000) math:remainder 706}] + [ a r:Fact; r:gives {(3706 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3706 1000) math:remainder 706}] [ a r:Fact; r:gives {(706 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(706 100) math:remainder 6}] [ a r:Fact; r:gives {(6 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(6 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2706]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3706]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 706]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3125 a r:Inference; +skolem:lemma6450 a r:Inference; r:gives { - 2707 :numberToDigits (2 7 0 7). + 3707 :numberToDigits (3 7 0 7). }; r:evidence ( - [ a r:Fact; r:gives {(2707 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2707 1000) math:remainder 707}] + [ a r:Fact; r:gives {(3707 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3707 1000) math:remainder 707}] [ a r:Fact; r:gives {(707 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(707 100) math:remainder 7}] [ a r:Fact; r:gives {(7 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(7 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2707]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3707]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 707]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3126 a r:Inference; +skolem:lemma6451 a r:Inference; r:gives { - 2708 :numberToDigits (2 7 0 8). + 3708 :numberToDigits (3 7 0 8). }; r:evidence ( - [ a r:Fact; r:gives {(2708 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2708 1000) math:remainder 708}] + [ a r:Fact; r:gives {(3708 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3708 1000) math:remainder 708}] [ a r:Fact; r:gives {(708 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(708 100) math:remainder 8}] [ a r:Fact; r:gives {(8 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(8 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2708]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3708]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 708]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3127 a r:Inference; +skolem:lemma6452 a r:Inference; r:gives { - 2709 :numberToDigits (2 7 0 9). + 3709 :numberToDigits (3 7 0 9). }; r:evidence ( - [ a r:Fact; r:gives {(2709 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2709 1000) math:remainder 709}] + [ a r:Fact; r:gives {(3709 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3709 1000) math:remainder 709}] [ a r:Fact; r:gives {(709 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(709 100) math:remainder 9}] [ a r:Fact; r:gives {(9 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(9 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2709]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3709]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 709]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3128 a r:Inference; +skolem:lemma6453 a r:Inference; r:gives { - 2710 :numberToDigits (2 7 1 0). + 3710 :numberToDigits (3 7 1 0). }; r:evidence ( - [ a r:Fact; r:gives {(2710 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2710 1000) math:remainder 710}] + [ a r:Fact; r:gives {(3710 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3710 1000) math:remainder 710}] [ a r:Fact; r:gives {(710 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(710 100) math:remainder 10}] [ a r:Fact; r:gives {(10 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(10 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2710]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3710]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 710]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3129 a r:Inference; +skolem:lemma6454 a r:Inference; r:gives { - 2711 :numberToDigits (2 7 1 1). + 3711 :numberToDigits (3 7 1 1). }; r:evidence ( - [ a r:Fact; r:gives {(2711 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2711 1000) math:remainder 711}] + [ a r:Fact; r:gives {(3711 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3711 1000) math:remainder 711}] [ a r:Fact; r:gives {(711 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(711 100) math:remainder 11}] [ a r:Fact; r:gives {(11 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(11 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2711]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3711]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 711]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 11]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3130 a r:Inference; +skolem:lemma6455 a r:Inference; r:gives { - 2712 :numberToDigits (2 7 1 2). + 3712 :numberToDigits (3 7 1 2). }; r:evidence ( - [ a r:Fact; r:gives {(2712 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2712 1000) math:remainder 712}] + [ a r:Fact; r:gives {(3712 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3712 1000) math:remainder 712}] [ a r:Fact; r:gives {(712 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(712 100) math:remainder 12}] [ a r:Fact; r:gives {(12 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(12 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2712]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3712]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 712]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3131 a r:Inference; +skolem:lemma6456 a r:Inference; r:gives { - 2713 :numberToDigits (2 7 1 3). + 3713 :numberToDigits (3 7 1 3). }; r:evidence ( - [ a r:Fact; r:gives {(2713 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2713 1000) math:remainder 713}] + [ a r:Fact; r:gives {(3713 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3713 1000) math:remainder 713}] [ a r:Fact; r:gives {(713 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(713 100) math:remainder 13}] [ a r:Fact; r:gives {(13 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(13 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2713]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3713]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 713]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 13]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3132 a r:Inference; +skolem:lemma6457 a r:Inference; r:gives { - 2714 :numberToDigits (2 7 1 4). + 3714 :numberToDigits (3 7 1 4). }; r:evidence ( - [ a r:Fact; r:gives {(2714 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2714 1000) math:remainder 714}] + [ a r:Fact; r:gives {(3714 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3714 1000) math:remainder 714}] [ a r:Fact; r:gives {(714 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(714 100) math:remainder 14}] [ a r:Fact; r:gives {(14 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(14 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2714]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3714]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 714]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 14]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3133 a r:Inference; +skolem:lemma6458 a r:Inference; r:gives { - 2715 :numberToDigits (2 7 1 5). + 3715 :numberToDigits (3 7 1 5). }; r:evidence ( - [ a r:Fact; r:gives {(2715 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2715 1000) math:remainder 715}] + [ a r:Fact; r:gives {(3715 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3715 1000) math:remainder 715}] [ a r:Fact; r:gives {(715 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(715 100) math:remainder 15}] [ a r:Fact; r:gives {(15 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(15 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2715]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3715]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 715]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 15]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3134 a r:Inference; +skolem:lemma6459 a r:Inference; r:gives { - 2716 :numberToDigits (2 7 1 6). + 3716 :numberToDigits (3 7 1 6). }; r:evidence ( - [ a r:Fact; r:gives {(2716 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2716 1000) math:remainder 716}] + [ a r:Fact; r:gives {(3716 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3716 1000) math:remainder 716}] [ a r:Fact; r:gives {(716 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(716 100) math:remainder 16}] [ a r:Fact; r:gives {(16 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(16 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2716]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3716]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 716]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 16]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3135 a r:Inference; +skolem:lemma6460 a r:Inference; r:gives { - 2717 :numberToDigits (2 7 1 7). + 3717 :numberToDigits (3 7 1 7). }; r:evidence ( - [ a r:Fact; r:gives {(2717 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2717 1000) math:remainder 717}] + [ a r:Fact; r:gives {(3717 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3717 1000) math:remainder 717}] [ a r:Fact; r:gives {(717 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(717 100) math:remainder 17}] [ a r:Fact; r:gives {(17 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(17 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2717]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3717]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 717]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 17]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3136 a r:Inference; +skolem:lemma6461 a r:Inference; r:gives { - 2718 :numberToDigits (2 7 1 8). + 3718 :numberToDigits (3 7 1 8). }; r:evidence ( - [ a r:Fact; r:gives {(2718 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2718 1000) math:remainder 718}] + [ a r:Fact; r:gives {(3718 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3718 1000) math:remainder 718}] [ a r:Fact; r:gives {(718 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(718 100) math:remainder 18}] [ a r:Fact; r:gives {(18 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(18 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2718]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3718]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 718]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 18]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3137 a r:Inference; +skolem:lemma6462 a r:Inference; r:gives { - 2719 :numberToDigits (2 7 1 9). + 3719 :numberToDigits (3 7 1 9). }; r:evidence ( - [ a r:Fact; r:gives {(2719 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2719 1000) math:remainder 719}] + [ a r:Fact; r:gives {(3719 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3719 1000) math:remainder 719}] [ a r:Fact; r:gives {(719 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(719 100) math:remainder 19}] [ a r:Fact; r:gives {(19 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(19 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2719]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3719]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 719]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 19]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3138 a r:Inference; +skolem:lemma6463 a r:Inference; r:gives { - 2720 :numberToDigits (2 7 2 0). + 3720 :numberToDigits (3 7 2 0). }; r:evidence ( - [ a r:Fact; r:gives {(2720 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2720 1000) math:remainder 720}] + [ a r:Fact; r:gives {(3720 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3720 1000) math:remainder 720}] [ a r:Fact; r:gives {(720 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(720 100) math:remainder 20}] [ a r:Fact; r:gives {(20 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(20 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2720]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3720]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 720]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 20]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3139 a r:Inference; +skolem:lemma6464 a r:Inference; r:gives { - 2721 :numberToDigits (2 7 2 1). + 3721 :numberToDigits (3 7 2 1). }; r:evidence ( - [ a r:Fact; r:gives {(2721 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2721 1000) math:remainder 721}] + [ a r:Fact; r:gives {(3721 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3721 1000) math:remainder 721}] [ a r:Fact; r:gives {(721 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(721 100) math:remainder 21}] [ a r:Fact; r:gives {(21 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(21 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2721]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3721]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 721]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 21]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3140 a r:Inference; +skolem:lemma6465 a r:Inference; r:gives { - 2722 :numberToDigits (2 7 2 2). + 3722 :numberToDigits (3 7 2 2). }; r:evidence ( - [ a r:Fact; r:gives {(2722 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2722 1000) math:remainder 722}] + [ a r:Fact; r:gives {(3722 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3722 1000) math:remainder 722}] [ a r:Fact; r:gives {(722 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(722 100) math:remainder 22}] [ a r:Fact; r:gives {(22 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(22 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2722]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3722]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 722]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3141 a r:Inference; +skolem:lemma6466 a r:Inference; r:gives { - 2723 :numberToDigits (2 7 2 3). + 3723 :numberToDigits (3 7 2 3). }; r:evidence ( - [ a r:Fact; r:gives {(2723 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2723 1000) math:remainder 723}] + [ a r:Fact; r:gives {(3723 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3723 1000) math:remainder 723}] [ a r:Fact; r:gives {(723 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(723 100) math:remainder 23}] [ a r:Fact; r:gives {(23 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(23 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2723]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3723]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 723]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3142 a r:Inference; +skolem:lemma6467 a r:Inference; r:gives { - 2724 :numberToDigits (2 7 2 4). + 3724 :numberToDigits (3 7 2 4). }; r:evidence ( - [ a r:Fact; r:gives {(2724 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2724 1000) math:remainder 724}] + [ a r:Fact; r:gives {(3724 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3724 1000) math:remainder 724}] [ a r:Fact; r:gives {(724 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(724 100) math:remainder 24}] [ a r:Fact; r:gives {(24 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(24 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2724]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3724]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 724]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3143 a r:Inference; +skolem:lemma6468 a r:Inference; r:gives { - 2725 :numberToDigits (2 7 2 5). + 3725 :numberToDigits (3 7 2 5). }; r:evidence ( - [ a r:Fact; r:gives {(2725 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2725 1000) math:remainder 725}] + [ a r:Fact; r:gives {(3725 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3725 1000) math:remainder 725}] [ a r:Fact; r:gives {(725 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(725 100) math:remainder 25}] [ a r:Fact; r:gives {(25 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(25 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2725]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3725]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 725]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3144 a r:Inference; +skolem:lemma6469 a r:Inference; r:gives { - 2726 :numberToDigits (2 7 2 6). + 3726 :numberToDigits (3 7 2 6). }; r:evidence ( - [ a r:Fact; r:gives {(2726 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2726 1000) math:remainder 726}] + [ a r:Fact; r:gives {(3726 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3726 1000) math:remainder 726}] [ a r:Fact; r:gives {(726 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(726 100) math:remainder 26}] [ a r:Fact; r:gives {(26 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(26 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2726]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3726]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 726]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3145 a r:Inference; +skolem:lemma6470 a r:Inference; r:gives { - 2727 :numberToDigits (2 7 2 7). + 3727 :numberToDigits (3 7 2 7). }; r:evidence ( - [ a r:Fact; r:gives {(2727 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2727 1000) math:remainder 727}] + [ a r:Fact; r:gives {(3727 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3727 1000) math:remainder 727}] [ a r:Fact; r:gives {(727 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(727 100) math:remainder 27}] [ a r:Fact; r:gives {(27 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(27 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2727]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3727]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 727]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3146 a r:Inference; +skolem:lemma6471 a r:Inference; r:gives { - 2728 :numberToDigits (2 7 2 8). + 3728 :numberToDigits (3 7 2 8). }; r:evidence ( - [ a r:Fact; r:gives {(2728 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2728 1000) math:remainder 728}] + [ a r:Fact; r:gives {(3728 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3728 1000) math:remainder 728}] [ a r:Fact; r:gives {(728 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(728 100) math:remainder 28}] [ a r:Fact; r:gives {(28 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(28 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2728]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3728]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 728]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3147 a r:Inference; +skolem:lemma6472 a r:Inference; r:gives { - 2729 :numberToDigits (2 7 2 9). + 3729 :numberToDigits (3 7 2 9). }; r:evidence ( - [ a r:Fact; r:gives {(2729 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2729 1000) math:remainder 729}] + [ a r:Fact; r:gives {(3729 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3729 1000) math:remainder 729}] [ a r:Fact; r:gives {(729 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(729 100) math:remainder 29}] [ a r:Fact; r:gives {(29 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(29 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2729]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3729]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 729]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3148 a r:Inference; +skolem:lemma6473 a r:Inference; r:gives { - 2730 :numberToDigits (2 7 3 0). + 3730 :numberToDigits (3 7 3 0). }; r:evidence ( - [ a r:Fact; r:gives {(2730 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2730 1000) math:remainder 730}] + [ a r:Fact; r:gives {(3730 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3730 1000) math:remainder 730}] [ a r:Fact; r:gives {(730 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(730 100) math:remainder 30}] [ a r:Fact; r:gives {(30 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(30 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2730]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3730]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 730]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3149 a r:Inference; +skolem:lemma6474 a r:Inference; r:gives { - 2731 :numberToDigits (2 7 3 1). + 3731 :numberToDigits (3 7 3 1). }; r:evidence ( - [ a r:Fact; r:gives {(2731 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2731 1000) math:remainder 731}] + [ a r:Fact; r:gives {(3731 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3731 1000) math:remainder 731}] [ a r:Fact; r:gives {(731 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(731 100) math:remainder 31}] [ a r:Fact; r:gives {(31 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(31 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2731]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3731]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 731]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 31]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3150 a r:Inference; +skolem:lemma6475 a r:Inference; r:gives { - 2732 :numberToDigits (2 7 3 2). + 3732 :numberToDigits (3 7 3 2). }; r:evidence ( - [ a r:Fact; r:gives {(2732 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2732 1000) math:remainder 732}] + [ a r:Fact; r:gives {(3732 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3732 1000) math:remainder 732}] [ a r:Fact; r:gives {(732 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(732 100) math:remainder 32}] [ a r:Fact; r:gives {(32 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(32 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2732]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3732]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 732]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 32]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3151 a r:Inference; +skolem:lemma6476 a r:Inference; r:gives { - 2733 :numberToDigits (2 7 3 3). + 3733 :numberToDigits (3 7 3 3). }; r:evidence ( - [ a r:Fact; r:gives {(2733 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2733 1000) math:remainder 733}] + [ a r:Fact; r:gives {(3733 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3733 1000) math:remainder 733}] [ a r:Fact; r:gives {(733 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(733 100) math:remainder 33}] [ a r:Fact; r:gives {(33 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(33 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2733]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3733]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 733]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 33]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3152 a r:Inference; +skolem:lemma6477 a r:Inference; r:gives { - 2734 :numberToDigits (2 7 3 4). + 3734 :numberToDigits (3 7 3 4). }; r:evidence ( - [ a r:Fact; r:gives {(2734 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2734 1000) math:remainder 734}] + [ a r:Fact; r:gives {(3734 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3734 1000) math:remainder 734}] [ a r:Fact; r:gives {(734 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(734 100) math:remainder 34}] [ a r:Fact; r:gives {(34 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(34 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2734]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3734]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 734]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 34]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3153 a r:Inference; +skolem:lemma6478 a r:Inference; r:gives { - 2735 :numberToDigits (2 7 3 5). + 3735 :numberToDigits (3 7 3 5). }; r:evidence ( - [ a r:Fact; r:gives {(2735 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2735 1000) math:remainder 735}] + [ a r:Fact; r:gives {(3735 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3735 1000) math:remainder 735}] [ a r:Fact; r:gives {(735 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(735 100) math:remainder 35}] [ a r:Fact; r:gives {(35 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(35 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2735]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3735]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 735]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 35]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3154 a r:Inference; +skolem:lemma6479 a r:Inference; r:gives { - 2736 :numberToDigits (2 7 3 6). + 3736 :numberToDigits (3 7 3 6). }; r:evidence ( - [ a r:Fact; r:gives {(2736 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2736 1000) math:remainder 736}] + [ a r:Fact; r:gives {(3736 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3736 1000) math:remainder 736}] [ a r:Fact; r:gives {(736 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(736 100) math:remainder 36}] [ a r:Fact; r:gives {(36 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(36 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2736]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3736]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 736]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 36]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3155 a r:Inference; +skolem:lemma6480 a r:Inference; r:gives { - 2737 :numberToDigits (2 7 3 7). + 3737 :numberToDigits (3 7 3 7). }; r:evidence ( - [ a r:Fact; r:gives {(2737 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2737 1000) math:remainder 737}] + [ a r:Fact; r:gives {(3737 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3737 1000) math:remainder 737}] [ a r:Fact; r:gives {(737 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(737 100) math:remainder 37}] [ a r:Fact; r:gives {(37 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(37 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2737]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3737]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 737]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 37]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3156 a r:Inference; +skolem:lemma6481 a r:Inference; r:gives { - 2738 :numberToDigits (2 7 3 8). + 3738 :numberToDigits (3 7 3 8). }; r:evidence ( - [ a r:Fact; r:gives {(2738 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2738 1000) math:remainder 738}] + [ a r:Fact; r:gives {(3738 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3738 1000) math:remainder 738}] [ a r:Fact; r:gives {(738 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(738 100) math:remainder 38}] [ a r:Fact; r:gives {(38 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(38 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2738]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3738]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 738]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 38]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3157 a r:Inference; +skolem:lemma6482 a r:Inference; r:gives { - 2739 :numberToDigits (2 7 3 9). + 3739 :numberToDigits (3 7 3 9). }; r:evidence ( - [ a r:Fact; r:gives {(2739 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2739 1000) math:remainder 739}] + [ a r:Fact; r:gives {(3739 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3739 1000) math:remainder 739}] [ a r:Fact; r:gives {(739 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(739 100) math:remainder 39}] [ a r:Fact; r:gives {(39 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(39 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2739]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3739]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 739]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 39]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3158 a r:Inference; +skolem:lemma6483 a r:Inference; r:gives { - 2740 :numberToDigits (2 7 4 0). + 3740 :numberToDigits (3 7 4 0). }; r:evidence ( - [ a r:Fact; r:gives {(2740 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2740 1000) math:remainder 740}] + [ a r:Fact; r:gives {(3740 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3740 1000) math:remainder 740}] [ a r:Fact; r:gives {(740 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(740 100) math:remainder 40}] [ a r:Fact; r:gives {(40 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(40 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2740]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3740]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 740]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3159 a r:Inference; +skolem:lemma6484 a r:Inference; r:gives { - 2741 :numberToDigits (2 7 4 1). + 3741 :numberToDigits (3 7 4 1). }; r:evidence ( - [ a r:Fact; r:gives {(2741 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2741 1000) math:remainder 741}] + [ a r:Fact; r:gives {(3741 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3741 1000) math:remainder 741}] [ a r:Fact; r:gives {(741 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(741 100) math:remainder 41}] [ a r:Fact; r:gives {(41 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(41 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2741]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3741]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 741]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 41]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3160 a r:Inference; +skolem:lemma6485 a r:Inference; r:gives { - 2742 :numberToDigits (2 7 4 2). + 3742 :numberToDigits (3 7 4 2). }; r:evidence ( - [ a r:Fact; r:gives {(2742 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2742 1000) math:remainder 742}] + [ a r:Fact; r:gives {(3742 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3742 1000) math:remainder 742}] [ a r:Fact; r:gives {(742 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(742 100) math:remainder 42}] [ a r:Fact; r:gives {(42 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(42 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2742]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3742]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 742]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 42]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3161 a r:Inference; +skolem:lemma6486 a r:Inference; r:gives { - 2743 :numberToDigits (2 7 4 3). + 3743 :numberToDigits (3 7 4 3). }; r:evidence ( - [ a r:Fact; r:gives {(2743 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2743 1000) math:remainder 743}] + [ a r:Fact; r:gives {(3743 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3743 1000) math:remainder 743}] [ a r:Fact; r:gives {(743 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(743 100) math:remainder 43}] [ a r:Fact; r:gives {(43 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(43 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2743]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3743]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 743]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 43]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3162 a r:Inference; +skolem:lemma6487 a r:Inference; r:gives { - 2744 :numberToDigits (2 7 4 4). + 3744 :numberToDigits (3 7 4 4). }; r:evidence ( - [ a r:Fact; r:gives {(2744 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2744 1000) math:remainder 744}] + [ a r:Fact; r:gives {(3744 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3744 1000) math:remainder 744}] [ a r:Fact; r:gives {(744 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(744 100) math:remainder 44}] [ a r:Fact; r:gives {(44 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(44 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2744]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3744]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 744]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 44]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3163 a r:Inference; +skolem:lemma6488 a r:Inference; r:gives { - 2745 :numberToDigits (2 7 4 5). + 3745 :numberToDigits (3 7 4 5). }; r:evidence ( - [ a r:Fact; r:gives {(2745 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2745 1000) math:remainder 745}] + [ a r:Fact; r:gives {(3745 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3745 1000) math:remainder 745}] [ a r:Fact; r:gives {(745 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(745 100) math:remainder 45}] [ a r:Fact; r:gives {(45 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(45 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2745]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3745]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 745]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 45]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3164 a r:Inference; +skolem:lemma6489 a r:Inference; r:gives { - 2746 :numberToDigits (2 7 4 6). + 3746 :numberToDigits (3 7 4 6). }; r:evidence ( - [ a r:Fact; r:gives {(2746 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2746 1000) math:remainder 746}] + [ a r:Fact; r:gives {(3746 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3746 1000) math:remainder 746}] [ a r:Fact; r:gives {(746 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(746 100) math:remainder 46}] [ a r:Fact; r:gives {(46 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(46 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2746]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3746]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 746]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 46]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3165 a r:Inference; +skolem:lemma6490 a r:Inference; r:gives { - 2747 :numberToDigits (2 7 4 7). + 3747 :numberToDigits (3 7 4 7). }; r:evidence ( - [ a r:Fact; r:gives {(2747 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2747 1000) math:remainder 747}] + [ a r:Fact; r:gives {(3747 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3747 1000) math:remainder 747}] [ a r:Fact; r:gives {(747 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(747 100) math:remainder 47}] [ a r:Fact; r:gives {(47 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(47 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2747]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3747]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 747]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 47]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3166 a r:Inference; +skolem:lemma6491 a r:Inference; r:gives { - 2748 :numberToDigits (2 7 4 8). + 3748 :numberToDigits (3 7 4 8). }; r:evidence ( - [ a r:Fact; r:gives {(2748 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2748 1000) math:remainder 748}] + [ a r:Fact; r:gives {(3748 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3748 1000) math:remainder 748}] [ a r:Fact; r:gives {(748 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(748 100) math:remainder 48}] [ a r:Fact; r:gives {(48 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(48 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2748]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3748]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 748]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 48]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3167 a r:Inference; +skolem:lemma6492 a r:Inference; r:gives { - 2749 :numberToDigits (2 7 4 9). + 3749 :numberToDigits (3 7 4 9). }; r:evidence ( - [ a r:Fact; r:gives {(2749 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2749 1000) math:remainder 749}] + [ a r:Fact; r:gives {(3749 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3749 1000) math:remainder 749}] [ a r:Fact; r:gives {(749 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(749 100) math:remainder 49}] [ a r:Fact; r:gives {(49 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(49 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2749]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3749]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 749]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 49]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3168 a r:Inference; +skolem:lemma6493 a r:Inference; r:gives { - 2750 :numberToDigits (2 7 5 0). + 3750 :numberToDigits (3 7 5 0). }; r:evidence ( - [ a r:Fact; r:gives {(2750 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2750 1000) math:remainder 750}] + [ a r:Fact; r:gives {(3750 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3750 1000) math:remainder 750}] [ a r:Fact; r:gives {(750 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(750 100) math:remainder 50}] [ a r:Fact; r:gives {(50 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(50 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2750]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3750]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 750]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3169 a r:Inference; +skolem:lemma6494 a r:Inference; r:gives { - 2751 :numberToDigits (2 7 5 1). + 3751 :numberToDigits (3 7 5 1). }; r:evidence ( - [ a r:Fact; r:gives {(2751 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2751 1000) math:remainder 751}] + [ a r:Fact; r:gives {(3751 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3751 1000) math:remainder 751}] [ a r:Fact; r:gives {(751 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(751 100) math:remainder 51}] [ a r:Fact; r:gives {(51 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(51 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2751]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3751]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 751]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 51]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3170 a r:Inference; +skolem:lemma6495 a r:Inference; r:gives { - 2752 :numberToDigits (2 7 5 2). + 3752 :numberToDigits (3 7 5 2). }; r:evidence ( - [ a r:Fact; r:gives {(2752 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2752 1000) math:remainder 752}] + [ a r:Fact; r:gives {(3752 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3752 1000) math:remainder 752}] [ a r:Fact; r:gives {(752 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(752 100) math:remainder 52}] [ a r:Fact; r:gives {(52 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(52 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2752]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3752]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 752]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 52]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3171 a r:Inference; +skolem:lemma6496 a r:Inference; r:gives { - 2753 :numberToDigits (2 7 5 3). + 3753 :numberToDigits (3 7 5 3). }; r:evidence ( - [ a r:Fact; r:gives {(2753 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2753 1000) math:remainder 753}] + [ a r:Fact; r:gives {(3753 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3753 1000) math:remainder 753}] [ a r:Fact; r:gives {(753 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(753 100) math:remainder 53}] [ a r:Fact; r:gives {(53 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(53 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2753]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3753]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 753]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 53]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3172 a r:Inference; +skolem:lemma6497 a r:Inference; r:gives { - 2754 :numberToDigits (2 7 5 4). + 3754 :numberToDigits (3 7 5 4). }; r:evidence ( - [ a r:Fact; r:gives {(2754 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2754 1000) math:remainder 754}] + [ a r:Fact; r:gives {(3754 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3754 1000) math:remainder 754}] [ a r:Fact; r:gives {(754 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(754 100) math:remainder 54}] [ a r:Fact; r:gives {(54 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(54 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2754]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3754]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 754]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 54]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3173 a r:Inference; +skolem:lemma6498 a r:Inference; r:gives { - 2755 :numberToDigits (2 7 5 5). + 3755 :numberToDigits (3 7 5 5). }; r:evidence ( - [ a r:Fact; r:gives {(2755 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2755 1000) math:remainder 755}] + [ a r:Fact; r:gives {(3755 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3755 1000) math:remainder 755}] [ a r:Fact; r:gives {(755 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(755 100) math:remainder 55}] [ a r:Fact; r:gives {(55 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(55 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2755]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3755]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 755]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 55]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3174 a r:Inference; +skolem:lemma6499 a r:Inference; r:gives { - 2756 :numberToDigits (2 7 5 6). + 3756 :numberToDigits (3 7 5 6). }; r:evidence ( - [ a r:Fact; r:gives {(2756 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2756 1000) math:remainder 756}] + [ a r:Fact; r:gives {(3756 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3756 1000) math:remainder 756}] [ a r:Fact; r:gives {(756 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(756 100) math:remainder 56}] [ a r:Fact; r:gives {(56 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(56 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2756]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3756]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 756]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 56]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3175 a r:Inference; +skolem:lemma6500 a r:Inference; r:gives { - 2757 :numberToDigits (2 7 5 7). + 3757 :numberToDigits (3 7 5 7). }; r:evidence ( - [ a r:Fact; r:gives {(2757 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2757 1000) math:remainder 757}] + [ a r:Fact; r:gives {(3757 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3757 1000) math:remainder 757}] [ a r:Fact; r:gives {(757 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(757 100) math:remainder 57}] [ a r:Fact; r:gives {(57 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(57 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2757]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3757]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 757]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 57]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3176 a r:Inference; +skolem:lemma6501 a r:Inference; r:gives { - 2758 :numberToDigits (2 7 5 8). + 3758 :numberToDigits (3 7 5 8). }; r:evidence ( - [ a r:Fact; r:gives {(2758 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2758 1000) math:remainder 758}] + [ a r:Fact; r:gives {(3758 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3758 1000) math:remainder 758}] [ a r:Fact; r:gives {(758 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(758 100) math:remainder 58}] [ a r:Fact; r:gives {(58 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(58 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2758]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3758]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 758]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 58]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3177 a r:Inference; +skolem:lemma6502 a r:Inference; r:gives { - 2759 :numberToDigits (2 7 5 9). + 3759 :numberToDigits (3 7 5 9). }; r:evidence ( - [ a r:Fact; r:gives {(2759 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2759 1000) math:remainder 759}] + [ a r:Fact; r:gives {(3759 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3759 1000) math:remainder 759}] [ a r:Fact; r:gives {(759 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(759 100) math:remainder 59}] [ a r:Fact; r:gives {(59 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(59 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2759]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3759]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 759]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 59]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3178 a r:Inference; +skolem:lemma6503 a r:Inference; r:gives { - 2760 :numberToDigits (2 7 6 0). + 3760 :numberToDigits (3 7 6 0). }; r:evidence ( - [ a r:Fact; r:gives {(2760 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2760 1000) math:remainder 760}] + [ a r:Fact; r:gives {(3760 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3760 1000) math:remainder 760}] [ a r:Fact; r:gives {(760 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(760 100) math:remainder 60}] [ a r:Fact; r:gives {(60 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(60 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2760]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3760]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 760]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3179 a r:Inference; +skolem:lemma6504 a r:Inference; r:gives { - 2761 :numberToDigits (2 7 6 1). + 3761 :numberToDigits (3 7 6 1). }; r:evidence ( - [ a r:Fact; r:gives {(2761 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2761 1000) math:remainder 761}] + [ a r:Fact; r:gives {(3761 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3761 1000) math:remainder 761}] [ a r:Fact; r:gives {(761 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(761 100) math:remainder 61}] [ a r:Fact; r:gives {(61 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(61 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2761]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3761]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 761]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 61]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3180 a r:Inference; +skolem:lemma6505 a r:Inference; r:gives { - 2762 :numberToDigits (2 7 6 2). + 3762 :numberToDigits (3 7 6 2). }; r:evidence ( - [ a r:Fact; r:gives {(2762 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2762 1000) math:remainder 762}] + [ a r:Fact; r:gives {(3762 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3762 1000) math:remainder 762}] [ a r:Fact; r:gives {(762 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(762 100) math:remainder 62}] [ a r:Fact; r:gives {(62 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(62 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2762]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3762]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 762]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 62]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3181 a r:Inference; +skolem:lemma6506 a r:Inference; r:gives { - 2763 :numberToDigits (2 7 6 3). + 3763 :numberToDigits (3 7 6 3). }; r:evidence ( - [ a r:Fact; r:gives {(2763 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2763 1000) math:remainder 763}] + [ a r:Fact; r:gives {(3763 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3763 1000) math:remainder 763}] [ a r:Fact; r:gives {(763 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(763 100) math:remainder 63}] [ a r:Fact; r:gives {(63 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(63 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2763]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3763]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 763]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 63]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3182 a r:Inference; +skolem:lemma6507 a r:Inference; r:gives { - 2764 :numberToDigits (2 7 6 4). + 3764 :numberToDigits (3 7 6 4). }; r:evidence ( - [ a r:Fact; r:gives {(2764 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2764 1000) math:remainder 764}] + [ a r:Fact; r:gives {(3764 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3764 1000) math:remainder 764}] [ a r:Fact; r:gives {(764 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(764 100) math:remainder 64}] [ a r:Fact; r:gives {(64 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(64 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2764]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3764]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 764]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 64]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3183 a r:Inference; +skolem:lemma6508 a r:Inference; r:gives { - 2765 :numberToDigits (2 7 6 5). + 3765 :numberToDigits (3 7 6 5). }; r:evidence ( - [ a r:Fact; r:gives {(2765 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2765 1000) math:remainder 765}] + [ a r:Fact; r:gives {(3765 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3765 1000) math:remainder 765}] [ a r:Fact; r:gives {(765 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(765 100) math:remainder 65}] [ a r:Fact; r:gives {(65 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(65 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2765]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3765]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 765]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 65]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3184 a r:Inference; +skolem:lemma6509 a r:Inference; r:gives { - 2766 :numberToDigits (2 7 6 6). + 3766 :numberToDigits (3 7 6 6). }; r:evidence ( - [ a r:Fact; r:gives {(2766 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2766 1000) math:remainder 766}] + [ a r:Fact; r:gives {(3766 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3766 1000) math:remainder 766}] [ a r:Fact; r:gives {(766 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(766 100) math:remainder 66}] [ a r:Fact; r:gives {(66 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(66 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2766]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3766]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 766]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 66]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3185 a r:Inference; +skolem:lemma6510 a r:Inference; r:gives { - 2767 :numberToDigits (2 7 6 7). + 3767 :numberToDigits (3 7 6 7). }; r:evidence ( - [ a r:Fact; r:gives {(2767 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2767 1000) math:remainder 767}] + [ a r:Fact; r:gives {(3767 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3767 1000) math:remainder 767}] [ a r:Fact; r:gives {(767 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(767 100) math:remainder 67}] [ a r:Fact; r:gives {(67 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(67 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2767]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3767]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 767]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 67]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3186 a r:Inference; +skolem:lemma6511 a r:Inference; r:gives { - 2768 :numberToDigits (2 7 6 8). + 3768 :numberToDigits (3 7 6 8). }; r:evidence ( - [ a r:Fact; r:gives {(2768 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2768 1000) math:remainder 768}] + [ a r:Fact; r:gives {(3768 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3768 1000) math:remainder 768}] [ a r:Fact; r:gives {(768 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(768 100) math:remainder 68}] [ a r:Fact; r:gives {(68 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(68 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2768]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3768]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 768]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 68]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3187 a r:Inference; +skolem:lemma6512 a r:Inference; r:gives { - 2769 :numberToDigits (2 7 6 9). + 3769 :numberToDigits (3 7 6 9). }; r:evidence ( - [ a r:Fact; r:gives {(2769 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2769 1000) math:remainder 769}] + [ a r:Fact; r:gives {(3769 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3769 1000) math:remainder 769}] [ a r:Fact; r:gives {(769 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(769 100) math:remainder 69}] [ a r:Fact; r:gives {(69 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(69 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2769]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3769]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 769]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 69]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3188 a r:Inference; +skolem:lemma6513 a r:Inference; r:gives { - 2770 :numberToDigits (2 7 7 0). + 3770 :numberToDigits (3 7 7 0). }; r:evidence ( - [ a r:Fact; r:gives {(2770 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2770 1000) math:remainder 770}] + [ a r:Fact; r:gives {(3770 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3770 1000) math:remainder 770}] [ a r:Fact; r:gives {(770 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(770 100) math:remainder 70}] [ a r:Fact; r:gives {(70 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(70 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2770]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3770]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 770]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3189 a r:Inference; +skolem:lemma6514 a r:Inference; r:gives { - 2771 :numberToDigits (2 7 7 1). + 3771 :numberToDigits (3 7 7 1). }; r:evidence ( - [ a r:Fact; r:gives {(2771 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2771 1000) math:remainder 771}] + [ a r:Fact; r:gives {(3771 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3771 1000) math:remainder 771}] [ a r:Fact; r:gives {(771 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(771 100) math:remainder 71}] [ a r:Fact; r:gives {(71 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(71 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2771]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3771]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 771]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 71]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3190 a r:Inference; +skolem:lemma6515 a r:Inference; r:gives { - 2772 :numberToDigits (2 7 7 2). + 3772 :numberToDigits (3 7 7 2). }; r:evidence ( - [ a r:Fact; r:gives {(2772 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2772 1000) math:remainder 772}] + [ a r:Fact; r:gives {(3772 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3772 1000) math:remainder 772}] [ a r:Fact; r:gives {(772 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(772 100) math:remainder 72}] [ a r:Fact; r:gives {(72 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(72 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2772]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3772]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 772]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 72]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3191 a r:Inference; +skolem:lemma6516 a r:Inference; r:gives { - 2773 :numberToDigits (2 7 7 3). + 3773 :numberToDigits (3 7 7 3). }; r:evidence ( - [ a r:Fact; r:gives {(2773 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2773 1000) math:remainder 773}] + [ a r:Fact; r:gives {(3773 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3773 1000) math:remainder 773}] [ a r:Fact; r:gives {(773 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(773 100) math:remainder 73}] [ a r:Fact; r:gives {(73 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(73 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2773]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3773]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 773]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 73]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3192 a r:Inference; +skolem:lemma6517 a r:Inference; r:gives { - 2774 :numberToDigits (2 7 7 4). + 3774 :numberToDigits (3 7 7 4). }; r:evidence ( - [ a r:Fact; r:gives {(2774 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2774 1000) math:remainder 774}] + [ a r:Fact; r:gives {(3774 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3774 1000) math:remainder 774}] [ a r:Fact; r:gives {(774 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(774 100) math:remainder 74}] [ a r:Fact; r:gives {(74 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(74 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2774]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3774]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 774]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 74]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3193 a r:Inference; +skolem:lemma6518 a r:Inference; r:gives { - 2775 :numberToDigits (2 7 7 5). + 3775 :numberToDigits (3 7 7 5). }; r:evidence ( - [ a r:Fact; r:gives {(2775 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2775 1000) math:remainder 775}] + [ a r:Fact; r:gives {(3775 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3775 1000) math:remainder 775}] [ a r:Fact; r:gives {(775 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(775 100) math:remainder 75}] [ a r:Fact; r:gives {(75 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(75 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2775]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3775]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 775]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 75]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3194 a r:Inference; +skolem:lemma6519 a r:Inference; r:gives { - 2776 :numberToDigits (2 7 7 6). + 3776 :numberToDigits (3 7 7 6). }; r:evidence ( - [ a r:Fact; r:gives {(2776 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2776 1000) math:remainder 776}] + [ a r:Fact; r:gives {(3776 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3776 1000) math:remainder 776}] [ a r:Fact; r:gives {(776 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(776 100) math:remainder 76}] [ a r:Fact; r:gives {(76 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(76 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2776]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3776]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 776]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 76]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3195 a r:Inference; +skolem:lemma6520 a r:Inference; r:gives { - 2777 :numberToDigits (2 7 7 7). + 3777 :numberToDigits (3 7 7 7). }; r:evidence ( - [ a r:Fact; r:gives {(2777 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2777 1000) math:remainder 777}] + [ a r:Fact; r:gives {(3777 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3777 1000) math:remainder 777}] [ a r:Fact; r:gives {(777 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(777 100) math:remainder 77}] [ a r:Fact; r:gives {(77 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(77 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2777]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3777]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 777]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 77]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3196 a r:Inference; +skolem:lemma6521 a r:Inference; r:gives { - (2 7 7 7) :digitsToNumber 2777 . + (3 7 7 7) :digitsToNumber 3777 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(7 100) math:product 700}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(2000 700 70 7) math:sum 2777}] + [ a r:Fact; r:gives {(3000 700 70 7) math:sum 3777}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2777]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3777]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma3197 a r:Inference; +skolem:lemma6522 a r:Inference; r:gives { - (7 7 7 2) :digitsToNumber 7772 . + (7 7 7 3) :digitsToNumber 7773 . }; r:evidence ( [ a r:Fact; r:gives {(7 1000) math:product 7000}] [ a r:Fact; r:gives {(7 100) math:product 700}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(7000 700 70 2) math:sum 7772}] + [ a r:Fact; r:gives {(7000 700 70 3) math:sum 7773}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 7000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 7]; @@ -74710,60 +152199,60 @@ skolem:lemma3197 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7772]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 7773]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma3198 a r:Inference; +skolem:lemma6523 a r:Inference; r:gives { - 2778 :numberToDigits (2 7 7 8). + 3778 :numberToDigits (3 7 7 8). }; r:evidence ( - [ a r:Fact; r:gives {(2778 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2778 1000) math:remainder 778}] + [ a r:Fact; r:gives {(3778 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3778 1000) math:remainder 778}] [ a r:Fact; r:gives {(778 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(778 100) math:remainder 78}] [ a r:Fact; r:gives {(78 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(78 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2778]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3778]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 778]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 78]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3199 a r:Inference; +skolem:lemma6524 a r:Inference; r:gives { - (2 7 7 8) :digitsToNumber 2778 . + (3 7 7 8) :digitsToNumber 3778 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(7 100) math:product 700}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(2000 700 70 8) math:sum 2778}] + [ a r:Fact; r:gives {(3000 700 70 8) math:sum 3778}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2778]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3778]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma3200 a r:Inference; +skolem:lemma6525 a r:Inference; r:gives { - (8 7 7 2) :digitsToNumber 8772 . + (8 7 7 3) :digitsToNumber 8773 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(7 100) math:product 700}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(8000 700 70 2) math:sum 8772}] + [ a r:Fact; r:gives {(8000 700 70 3) math:sum 8773}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; @@ -74771,60 +152260,60 @@ skolem:lemma3200 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8772]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8773]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma3201 a r:Inference; +skolem:lemma6526 a r:Inference; r:gives { - 2779 :numberToDigits (2 7 7 9). + 3779 :numberToDigits (3 7 7 9). }; r:evidence ( - [ a r:Fact; r:gives {(2779 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2779 1000) math:remainder 779}] + [ a r:Fact; r:gives {(3779 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3779 1000) math:remainder 779}] [ a r:Fact; r:gives {(779 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(779 100) math:remainder 79}] [ a r:Fact; r:gives {(79 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(79 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2779]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3779]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 779]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 79]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3202 a r:Inference; +skolem:lemma6527 a r:Inference; r:gives { - (2 7 7 9) :digitsToNumber 2779 . + (3 7 7 9) :digitsToNumber 3779 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(7 100) math:product 700}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(2000 700 70 9) math:sum 2779}] + [ a r:Fact; r:gives {(3000 700 70 9) math:sum 3779}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2779]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3779]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma3203 a r:Inference; +skolem:lemma6528 a r:Inference; r:gives { - (9 7 7 2) :digitsToNumber 9772 . + (9 7 7 3) :digitsToNumber 9773 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(7 100) math:product 700}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(9000 700 70 2) math:sum 9772}] + [ a r:Fact; r:gives {(9000 700 70 3) math:sum 9773}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -74832,228 +152321,228 @@ skolem:lemma3203 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9772]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9773]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma3204 a r:Inference; +skolem:lemma6529 a r:Inference; r:gives { - 2780 :numberToDigits (2 7 8 0). + 3780 :numberToDigits (3 7 8 0). }; r:evidence ( - [ a r:Fact; r:gives {(2780 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2780 1000) math:remainder 780}] + [ a r:Fact; r:gives {(3780 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3780 1000) math:remainder 780}] [ a r:Fact; r:gives {(780 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(780 100) math:remainder 80}] [ a r:Fact; r:gives {(80 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(80 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2780]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3780]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 780]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3205 a r:Inference; +skolem:lemma6530 a r:Inference; r:gives { - 2781 :numberToDigits (2 7 8 1). + 3781 :numberToDigits (3 7 8 1). }; r:evidence ( - [ a r:Fact; r:gives {(2781 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2781 1000) math:remainder 781}] + [ a r:Fact; r:gives {(3781 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3781 1000) math:remainder 781}] [ a r:Fact; r:gives {(781 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(781 100) math:remainder 81}] [ a r:Fact; r:gives {(81 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(81 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2781]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3781]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 781]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 81]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3206 a r:Inference; +skolem:lemma6531 a r:Inference; r:gives { - 2782 :numberToDigits (2 7 8 2). + 3782 :numberToDigits (3 7 8 2). }; r:evidence ( - [ a r:Fact; r:gives {(2782 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2782 1000) math:remainder 782}] + [ a r:Fact; r:gives {(3782 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3782 1000) math:remainder 782}] [ a r:Fact; r:gives {(782 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(782 100) math:remainder 82}] [ a r:Fact; r:gives {(82 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(82 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2782]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3782]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 782]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 82]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3207 a r:Inference; +skolem:lemma6532 a r:Inference; r:gives { - 2783 :numberToDigits (2 7 8 3). + 3783 :numberToDigits (3 7 8 3). }; r:evidence ( - [ a r:Fact; r:gives {(2783 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2783 1000) math:remainder 783}] + [ a r:Fact; r:gives {(3783 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3783 1000) math:remainder 783}] [ a r:Fact; r:gives {(783 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(783 100) math:remainder 83}] [ a r:Fact; r:gives {(83 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(83 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2783]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3783]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 783]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 83]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3208 a r:Inference; +skolem:lemma6533 a r:Inference; r:gives { - 2784 :numberToDigits (2 7 8 4). + 3784 :numberToDigits (3 7 8 4). }; r:evidence ( - [ a r:Fact; r:gives {(2784 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2784 1000) math:remainder 784}] + [ a r:Fact; r:gives {(3784 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3784 1000) math:remainder 784}] [ a r:Fact; r:gives {(784 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(784 100) math:remainder 84}] [ a r:Fact; r:gives {(84 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(84 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2784]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3784]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 784]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 84]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3209 a r:Inference; +skolem:lemma6534 a r:Inference; r:gives { - 2785 :numberToDigits (2 7 8 5). + 3785 :numberToDigits (3 7 8 5). }; r:evidence ( - [ a r:Fact; r:gives {(2785 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2785 1000) math:remainder 785}] + [ a r:Fact; r:gives {(3785 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3785 1000) math:remainder 785}] [ a r:Fact; r:gives {(785 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(785 100) math:remainder 85}] [ a r:Fact; r:gives {(85 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(85 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2785]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3785]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 785]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 85]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3210 a r:Inference; +skolem:lemma6535 a r:Inference; r:gives { - 2786 :numberToDigits (2 7 8 6). + 3786 :numberToDigits (3 7 8 6). }; r:evidence ( - [ a r:Fact; r:gives {(2786 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2786 1000) math:remainder 786}] + [ a r:Fact; r:gives {(3786 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3786 1000) math:remainder 786}] [ a r:Fact; r:gives {(786 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(786 100) math:remainder 86}] [ a r:Fact; r:gives {(86 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(86 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2786]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3786]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 786]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 86]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3211 a r:Inference; +skolem:lemma6536 a r:Inference; r:gives { - 2787 :numberToDigits (2 7 8 7). + 3787 :numberToDigits (3 7 8 7). }; r:evidence ( - [ a r:Fact; r:gives {(2787 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2787 1000) math:remainder 787}] + [ a r:Fact; r:gives {(3787 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3787 1000) math:remainder 787}] [ a r:Fact; r:gives {(787 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(787 100) math:remainder 87}] [ a r:Fact; r:gives {(87 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(87 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2787]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3787]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 787]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 87]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3212 a r:Inference; +skolem:lemma6537 a r:Inference; r:gives { - 2788 :numberToDigits (2 7 8 8). + 3788 :numberToDigits (3 7 8 8). }; r:evidence ( - [ a r:Fact; r:gives {(2788 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2788 1000) math:remainder 788}] + [ a r:Fact; r:gives {(3788 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3788 1000) math:remainder 788}] [ a r:Fact; r:gives {(788 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(788 100) math:remainder 88}] [ a r:Fact; r:gives {(88 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(88 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2788]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3788]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 788]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 88]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3213 a r:Inference; +skolem:lemma6538 a r:Inference; r:gives { - (2 7 8 8) :digitsToNumber 2788 . + (3 7 8 8) :digitsToNumber 3788 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(7 100) math:product 700}] [ a r:Fact; r:gives {(8 10) math:product 80}] - [ a r:Fact; r:gives {(2000 700 80 8) math:sum 2788}] + [ a r:Fact; r:gives {(3000 700 80 8) math:sum 3788}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2788]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3788]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma3214 a r:Inference; +skolem:lemma6539 a r:Inference; r:gives { - (8 8 7 2) :digitsToNumber 8872 . + (8 8 7 3) :digitsToNumber 8873 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(8 100) math:product 800}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(8000 800 70 2) math:sum 8872}] + [ a r:Fact; r:gives {(8000 800 70 3) math:sum 8873}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; @@ -75061,60 +152550,60 @@ skolem:lemma3214 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8872]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8873]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma3215 a r:Inference; +skolem:lemma6540 a r:Inference; r:gives { - 2789 :numberToDigits (2 7 8 9). + 3789 :numberToDigits (3 7 8 9). }; r:evidence ( - [ a r:Fact; r:gives {(2789 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2789 1000) math:remainder 789}] + [ a r:Fact; r:gives {(3789 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3789 1000) math:remainder 789}] [ a r:Fact; r:gives {(789 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(789 100) math:remainder 89}] [ a r:Fact; r:gives {(89 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(89 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2789]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3789]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 789]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 89]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3216 a r:Inference; +skolem:lemma6541 a r:Inference; r:gives { - (2 7 8 9) :digitsToNumber 2789 . + (3 7 8 9) :digitsToNumber 3789 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(7 100) math:product 700}] [ a r:Fact; r:gives {(8 10) math:product 80}] - [ a r:Fact; r:gives {(2000 700 80 9) math:sum 2789}] + [ a r:Fact; r:gives {(3000 700 80 9) math:sum 3789}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2789]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3789]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma3217 a r:Inference; +skolem:lemma6542 a r:Inference; r:gives { - (9 8 7 2) :digitsToNumber 9872 . + (9 8 7 3) :digitsToNumber 9873 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(8 100) math:product 800}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(9000 800 70 2) math:sum 9872}] + [ a r:Fact; r:gives {(9000 800 70 3) math:sum 9873}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -75122,249 +152611,249 @@ skolem:lemma3217 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9872]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9873]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma3218 a r:Inference; +skolem:lemma6543 a r:Inference; r:gives { - 2790 :numberToDigits (2 7 9 0). + 3790 :numberToDigits (3 7 9 0). }; r:evidence ( - [ a r:Fact; r:gives {(2790 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2790 1000) math:remainder 790}] + [ a r:Fact; r:gives {(3790 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3790 1000) math:remainder 790}] [ a r:Fact; r:gives {(790 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(790 100) math:remainder 90}] [ a r:Fact; r:gives {(90 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(90 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2790]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3790]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 790]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 90]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3219 a r:Inference; +skolem:lemma6544 a r:Inference; r:gives { - 2791 :numberToDigits (2 7 9 1). + 3791 :numberToDigits (3 7 9 1). }; r:evidence ( - [ a r:Fact; r:gives {(2791 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2791 1000) math:remainder 791}] + [ a r:Fact; r:gives {(3791 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3791 1000) math:remainder 791}] [ a r:Fact; r:gives {(791 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(791 100) math:remainder 91}] [ a r:Fact; r:gives {(91 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(91 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2791]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3791]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 791]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 91]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3220 a r:Inference; +skolem:lemma6545 a r:Inference; r:gives { - 2792 :numberToDigits (2 7 9 2). + 3792 :numberToDigits (3 7 9 2). }; r:evidence ( - [ a r:Fact; r:gives {(2792 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2792 1000) math:remainder 792}] + [ a r:Fact; r:gives {(3792 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3792 1000) math:remainder 792}] [ a r:Fact; r:gives {(792 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(792 100) math:remainder 92}] [ a r:Fact; r:gives {(92 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(92 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2792]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3792]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 792]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 92]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3221 a r:Inference; +skolem:lemma6546 a r:Inference; r:gives { - 2793 :numberToDigits (2 7 9 3). + 3793 :numberToDigits (3 7 9 3). }; r:evidence ( - [ a r:Fact; r:gives {(2793 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2793 1000) math:remainder 793}] + [ a r:Fact; r:gives {(3793 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3793 1000) math:remainder 793}] [ a r:Fact; r:gives {(793 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(793 100) math:remainder 93}] [ a r:Fact; r:gives {(93 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(93 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2793]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3793]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 793]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 93]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3222 a r:Inference; +skolem:lemma6547 a r:Inference; r:gives { - 2794 :numberToDigits (2 7 9 4). + 3794 :numberToDigits (3 7 9 4). }; r:evidence ( - [ a r:Fact; r:gives {(2794 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2794 1000) math:remainder 794}] + [ a r:Fact; r:gives {(3794 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3794 1000) math:remainder 794}] [ a r:Fact; r:gives {(794 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(794 100) math:remainder 94}] [ a r:Fact; r:gives {(94 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(94 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2794]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3794]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 794]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 94]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3223 a r:Inference; +skolem:lemma6548 a r:Inference; r:gives { - 2795 :numberToDigits (2 7 9 5). + 3795 :numberToDigits (3 7 9 5). }; r:evidence ( - [ a r:Fact; r:gives {(2795 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2795 1000) math:remainder 795}] + [ a r:Fact; r:gives {(3795 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3795 1000) math:remainder 795}] [ a r:Fact; r:gives {(795 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(795 100) math:remainder 95}] [ a r:Fact; r:gives {(95 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(95 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2795]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3795]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 795]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 95]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3224 a r:Inference; +skolem:lemma6549 a r:Inference; r:gives { - 2796 :numberToDigits (2 7 9 6). + 3796 :numberToDigits (3 7 9 6). }; r:evidence ( - [ a r:Fact; r:gives {(2796 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2796 1000) math:remainder 796}] + [ a r:Fact; r:gives {(3796 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3796 1000) math:remainder 796}] [ a r:Fact; r:gives {(796 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(796 100) math:remainder 96}] [ a r:Fact; r:gives {(96 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(96 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2796]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3796]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 796]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 96]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3225 a r:Inference; +skolem:lemma6550 a r:Inference; r:gives { - 2797 :numberToDigits (2 7 9 7). + 3797 :numberToDigits (3 7 9 7). }; r:evidence ( - [ a r:Fact; r:gives {(2797 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2797 1000) math:remainder 797}] + [ a r:Fact; r:gives {(3797 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3797 1000) math:remainder 797}] [ a r:Fact; r:gives {(797 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(797 100) math:remainder 97}] [ a r:Fact; r:gives {(97 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(97 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2797]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3797]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 797]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 97]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3226 a r:Inference; +skolem:lemma6551 a r:Inference; r:gives { - 2798 :numberToDigits (2 7 9 8). + 3798 :numberToDigits (3 7 9 8). }; r:evidence ( - [ a r:Fact; r:gives {(2798 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2798 1000) math:remainder 798}] + [ a r:Fact; r:gives {(3798 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3798 1000) math:remainder 798}] [ a r:Fact; r:gives {(798 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(798 100) math:remainder 98}] [ a r:Fact; r:gives {(98 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(98 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2798]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3798]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 798]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 98]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3227 a r:Inference; +skolem:lemma6552 a r:Inference; r:gives { - 2799 :numberToDigits (2 7 9 9). + 3799 :numberToDigits (3 7 9 9). }; r:evidence ( - [ a r:Fact; r:gives {(2799 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2799 1000) math:remainder 799}] + [ a r:Fact; r:gives {(3799 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3799 1000) math:remainder 799}] [ a r:Fact; r:gives {(799 100) math:integerQuotient 7}] [ a r:Fact; r:gives {(799 100) math:remainder 99}] [ a r:Fact; r:gives {(99 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(99 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2799]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3799]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 799]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 99]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3228 a r:Inference; +skolem:lemma6553 a r:Inference; r:gives { - (2 7 9 9) :digitsToNumber 2799 . + (3 7 9 9) :digitsToNumber 3799 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(7 100) math:product 700}] [ a r:Fact; r:gives {(9 10) math:product 90}] - [ a r:Fact; r:gives {(2000 700 90 9) math:sum 2799}] + [ a r:Fact; r:gives {(3000 700 90 9) math:sum 3799}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 700]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 90]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2799]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3799]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma3229 a r:Inference; +skolem:lemma6554 a r:Inference; r:gives { - (9 9 7 2) :digitsToNumber 9972 . + (9 9 7 3) :digitsToNumber 9973 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(9 100) math:product 900}] [ a r:Fact; r:gives {(7 10) math:product 70}] - [ a r:Fact; r:gives {(9000 900 70 2) math:sum 9972}] + [ a r:Fact; r:gives {(9000 900 70 3) math:sum 9973}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -75372,1908 +152861,1908 @@ skolem:lemma3229 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9972]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9973]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma3230 a r:Inference; +skolem:lemma6555 a r:Inference; r:gives { - 2800 :numberToDigits (2 8 0 0). + 3800 :numberToDigits (3 8 0 0). }; r:evidence ( - [ a r:Fact; r:gives {(2800 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2800 1000) math:remainder 800}] + [ a r:Fact; r:gives {(3800 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3800 1000) math:remainder 800}] [ a r:Fact; r:gives {(800 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(800 100) math:remainder 0}] [ a r:Fact; r:gives {(0 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(0 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2800]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3800]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 800]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3231 a r:Inference; +skolem:lemma6556 a r:Inference; r:gives { - 2801 :numberToDigits (2 8 0 1). + 3801 :numberToDigits (3 8 0 1). }; r:evidence ( - [ a r:Fact; r:gives {(2801 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2801 1000) math:remainder 801}] + [ a r:Fact; r:gives {(3801 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3801 1000) math:remainder 801}] [ a r:Fact; r:gives {(801 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(801 100) math:remainder 1}] [ a r:Fact; r:gives {(1 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(1 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2801]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3801]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 801]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3232 a r:Inference; +skolem:lemma6557 a r:Inference; r:gives { - 2802 :numberToDigits (2 8 0 2). + 3802 :numberToDigits (3 8 0 2). }; r:evidence ( - [ a r:Fact; r:gives {(2802 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2802 1000) math:remainder 802}] + [ a r:Fact; r:gives {(3802 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3802 1000) math:remainder 802}] [ a r:Fact; r:gives {(802 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(802 100) math:remainder 2}] [ a r:Fact; r:gives {(2 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(2 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2802]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3802]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 802]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3233 a r:Inference; +skolem:lemma6558 a r:Inference; r:gives { - 2803 :numberToDigits (2 8 0 3). + 3803 :numberToDigits (3 8 0 3). }; r:evidence ( - [ a r:Fact; r:gives {(2803 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2803 1000) math:remainder 803}] + [ a r:Fact; r:gives {(3803 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3803 1000) math:remainder 803}] [ a r:Fact; r:gives {(803 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(803 100) math:remainder 3}] [ a r:Fact; r:gives {(3 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(3 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2803]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3803]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 803]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3234 a r:Inference; +skolem:lemma6559 a r:Inference; r:gives { - 2804 :numberToDigits (2 8 0 4). + 3804 :numberToDigits (3 8 0 4). }; r:evidence ( - [ a r:Fact; r:gives {(2804 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2804 1000) math:remainder 804}] + [ a r:Fact; r:gives {(3804 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3804 1000) math:remainder 804}] [ a r:Fact; r:gives {(804 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(804 100) math:remainder 4}] [ a r:Fact; r:gives {(4 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(4 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2804]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3804]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 804]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3235 a r:Inference; +skolem:lemma6560 a r:Inference; r:gives { - 2805 :numberToDigits (2 8 0 5). + 3805 :numberToDigits (3 8 0 5). }; r:evidence ( - [ a r:Fact; r:gives {(2805 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2805 1000) math:remainder 805}] + [ a r:Fact; r:gives {(3805 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3805 1000) math:remainder 805}] [ a r:Fact; r:gives {(805 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(805 100) math:remainder 5}] [ a r:Fact; r:gives {(5 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(5 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2805]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3805]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 805]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3236 a r:Inference; +skolem:lemma6561 a r:Inference; r:gives { - 2806 :numberToDigits (2 8 0 6). + 3806 :numberToDigits (3 8 0 6). }; r:evidence ( - [ a r:Fact; r:gives {(2806 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2806 1000) math:remainder 806}] + [ a r:Fact; r:gives {(3806 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3806 1000) math:remainder 806}] [ a r:Fact; r:gives {(806 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(806 100) math:remainder 6}] [ a r:Fact; r:gives {(6 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(6 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2806]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3806]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 806]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3237 a r:Inference; +skolem:lemma6562 a r:Inference; r:gives { - 2807 :numberToDigits (2 8 0 7). + 3807 :numberToDigits (3 8 0 7). }; r:evidence ( - [ a r:Fact; r:gives {(2807 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2807 1000) math:remainder 807}] + [ a r:Fact; r:gives {(3807 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3807 1000) math:remainder 807}] [ a r:Fact; r:gives {(807 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(807 100) math:remainder 7}] [ a r:Fact; r:gives {(7 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(7 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2807]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3807]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 807]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3238 a r:Inference; +skolem:lemma6563 a r:Inference; r:gives { - 2808 :numberToDigits (2 8 0 8). + 3808 :numberToDigits (3 8 0 8). }; r:evidence ( - [ a r:Fact; r:gives {(2808 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2808 1000) math:remainder 808}] + [ a r:Fact; r:gives {(3808 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3808 1000) math:remainder 808}] [ a r:Fact; r:gives {(808 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(808 100) math:remainder 8}] [ a r:Fact; r:gives {(8 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(8 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2808]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3808]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 808]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3239 a r:Inference; +skolem:lemma6564 a r:Inference; r:gives { - 2809 :numberToDigits (2 8 0 9). + 3809 :numberToDigits (3 8 0 9). }; r:evidence ( - [ a r:Fact; r:gives {(2809 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2809 1000) math:remainder 809}] + [ a r:Fact; r:gives {(3809 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3809 1000) math:remainder 809}] [ a r:Fact; r:gives {(809 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(809 100) math:remainder 9}] [ a r:Fact; r:gives {(9 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(9 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2809]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3809]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 809]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3240 a r:Inference; +skolem:lemma6565 a r:Inference; r:gives { - 2810 :numberToDigits (2 8 1 0). + 3810 :numberToDigits (3 8 1 0). }; r:evidence ( - [ a r:Fact; r:gives {(2810 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2810 1000) math:remainder 810}] + [ a r:Fact; r:gives {(3810 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3810 1000) math:remainder 810}] [ a r:Fact; r:gives {(810 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(810 100) math:remainder 10}] [ a r:Fact; r:gives {(10 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(10 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2810]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3810]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 810]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3241 a r:Inference; +skolem:lemma6566 a r:Inference; r:gives { - 2811 :numberToDigits (2 8 1 1). + 3811 :numberToDigits (3 8 1 1). }; r:evidence ( - [ a r:Fact; r:gives {(2811 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2811 1000) math:remainder 811}] + [ a r:Fact; r:gives {(3811 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3811 1000) math:remainder 811}] [ a r:Fact; r:gives {(811 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(811 100) math:remainder 11}] [ a r:Fact; r:gives {(11 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(11 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2811]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3811]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 811]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 11]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3242 a r:Inference; +skolem:lemma6567 a r:Inference; r:gives { - 2812 :numberToDigits (2 8 1 2). + 3812 :numberToDigits (3 8 1 2). }; r:evidence ( - [ a r:Fact; r:gives {(2812 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2812 1000) math:remainder 812}] + [ a r:Fact; r:gives {(3812 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3812 1000) math:remainder 812}] [ a r:Fact; r:gives {(812 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(812 100) math:remainder 12}] [ a r:Fact; r:gives {(12 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(12 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2812]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3812]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 812]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3243 a r:Inference; +skolem:lemma6568 a r:Inference; r:gives { - 2813 :numberToDigits (2 8 1 3). + 3813 :numberToDigits (3 8 1 3). }; r:evidence ( - [ a r:Fact; r:gives {(2813 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2813 1000) math:remainder 813}] + [ a r:Fact; r:gives {(3813 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3813 1000) math:remainder 813}] [ a r:Fact; r:gives {(813 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(813 100) math:remainder 13}] [ a r:Fact; r:gives {(13 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(13 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2813]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3813]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 813]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 13]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3244 a r:Inference; +skolem:lemma6569 a r:Inference; r:gives { - 2814 :numberToDigits (2 8 1 4). + 3814 :numberToDigits (3 8 1 4). }; r:evidence ( - [ a r:Fact; r:gives {(2814 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2814 1000) math:remainder 814}] + [ a r:Fact; r:gives {(3814 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3814 1000) math:remainder 814}] [ a r:Fact; r:gives {(814 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(814 100) math:remainder 14}] [ a r:Fact; r:gives {(14 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(14 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2814]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3814]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 814]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 14]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3245 a r:Inference; +skolem:lemma6570 a r:Inference; r:gives { - 2815 :numberToDigits (2 8 1 5). + 3815 :numberToDigits (3 8 1 5). }; r:evidence ( - [ a r:Fact; r:gives {(2815 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2815 1000) math:remainder 815}] + [ a r:Fact; r:gives {(3815 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3815 1000) math:remainder 815}] [ a r:Fact; r:gives {(815 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(815 100) math:remainder 15}] [ a r:Fact; r:gives {(15 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(15 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2815]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3815]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 815]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 15]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3246 a r:Inference; +skolem:lemma6571 a r:Inference; r:gives { - 2816 :numberToDigits (2 8 1 6). + 3816 :numberToDigits (3 8 1 6). }; r:evidence ( - [ a r:Fact; r:gives {(2816 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2816 1000) math:remainder 816}] + [ a r:Fact; r:gives {(3816 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3816 1000) math:remainder 816}] [ a r:Fact; r:gives {(816 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(816 100) math:remainder 16}] [ a r:Fact; r:gives {(16 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(16 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2816]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3816]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 816]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 16]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3247 a r:Inference; +skolem:lemma6572 a r:Inference; r:gives { - 2817 :numberToDigits (2 8 1 7). + 3817 :numberToDigits (3 8 1 7). }; r:evidence ( - [ a r:Fact; r:gives {(2817 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2817 1000) math:remainder 817}] + [ a r:Fact; r:gives {(3817 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3817 1000) math:remainder 817}] [ a r:Fact; r:gives {(817 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(817 100) math:remainder 17}] [ a r:Fact; r:gives {(17 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(17 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2817]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3817]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 817]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 17]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3248 a r:Inference; +skolem:lemma6573 a r:Inference; r:gives { - 2818 :numberToDigits (2 8 1 8). + 3818 :numberToDigits (3 8 1 8). }; r:evidence ( - [ a r:Fact; r:gives {(2818 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2818 1000) math:remainder 818}] + [ a r:Fact; r:gives {(3818 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3818 1000) math:remainder 818}] [ a r:Fact; r:gives {(818 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(818 100) math:remainder 18}] [ a r:Fact; r:gives {(18 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(18 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2818]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3818]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 818]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 18]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3249 a r:Inference; +skolem:lemma6574 a r:Inference; r:gives { - 2819 :numberToDigits (2 8 1 9). + 3819 :numberToDigits (3 8 1 9). }; r:evidence ( - [ a r:Fact; r:gives {(2819 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2819 1000) math:remainder 819}] + [ a r:Fact; r:gives {(3819 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3819 1000) math:remainder 819}] [ a r:Fact; r:gives {(819 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(819 100) math:remainder 19}] [ a r:Fact; r:gives {(19 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(19 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2819]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3819]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 819]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 19]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3250 a r:Inference; +skolem:lemma6575 a r:Inference; r:gives { - 2820 :numberToDigits (2 8 2 0). + 3820 :numberToDigits (3 8 2 0). }; r:evidence ( - [ a r:Fact; r:gives {(2820 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2820 1000) math:remainder 820}] + [ a r:Fact; r:gives {(3820 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3820 1000) math:remainder 820}] [ a r:Fact; r:gives {(820 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(820 100) math:remainder 20}] [ a r:Fact; r:gives {(20 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(20 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2820]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3820]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 820]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 20]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3251 a r:Inference; +skolem:lemma6576 a r:Inference; r:gives { - 2821 :numberToDigits (2 8 2 1). + 3821 :numberToDigits (3 8 2 1). }; r:evidence ( - [ a r:Fact; r:gives {(2821 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2821 1000) math:remainder 821}] + [ a r:Fact; r:gives {(3821 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3821 1000) math:remainder 821}] [ a r:Fact; r:gives {(821 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(821 100) math:remainder 21}] [ a r:Fact; r:gives {(21 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(21 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2821]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3821]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 821]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 21]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3252 a r:Inference; +skolem:lemma6577 a r:Inference; r:gives { - 2822 :numberToDigits (2 8 2 2). + 3822 :numberToDigits (3 8 2 2). }; r:evidence ( - [ a r:Fact; r:gives {(2822 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2822 1000) math:remainder 822}] + [ a r:Fact; r:gives {(3822 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3822 1000) math:remainder 822}] [ a r:Fact; r:gives {(822 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(822 100) math:remainder 22}] [ a r:Fact; r:gives {(22 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(22 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2822]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3822]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 822]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3253 a r:Inference; +skolem:lemma6578 a r:Inference; r:gives { - 2823 :numberToDigits (2 8 2 3). + 3823 :numberToDigits (3 8 2 3). }; r:evidence ( - [ a r:Fact; r:gives {(2823 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2823 1000) math:remainder 823}] + [ a r:Fact; r:gives {(3823 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3823 1000) math:remainder 823}] [ a r:Fact; r:gives {(823 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(823 100) math:remainder 23}] [ a r:Fact; r:gives {(23 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(23 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2823]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3823]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 823]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3254 a r:Inference; +skolem:lemma6579 a r:Inference; r:gives { - 2824 :numberToDigits (2 8 2 4). + 3824 :numberToDigits (3 8 2 4). }; r:evidence ( - [ a r:Fact; r:gives {(2824 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2824 1000) math:remainder 824}] + [ a r:Fact; r:gives {(3824 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3824 1000) math:remainder 824}] [ a r:Fact; r:gives {(824 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(824 100) math:remainder 24}] [ a r:Fact; r:gives {(24 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(24 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2824]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3824]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 824]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3255 a r:Inference; +skolem:lemma6580 a r:Inference; r:gives { - 2825 :numberToDigits (2 8 2 5). + 3825 :numberToDigits (3 8 2 5). }; r:evidence ( - [ a r:Fact; r:gives {(2825 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2825 1000) math:remainder 825}] + [ a r:Fact; r:gives {(3825 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3825 1000) math:remainder 825}] [ a r:Fact; r:gives {(825 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(825 100) math:remainder 25}] [ a r:Fact; r:gives {(25 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(25 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2825]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3825]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 825]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3256 a r:Inference; +skolem:lemma6581 a r:Inference; r:gives { - 2826 :numberToDigits (2 8 2 6). + 3826 :numberToDigits (3 8 2 6). }; r:evidence ( - [ a r:Fact; r:gives {(2826 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2826 1000) math:remainder 826}] + [ a r:Fact; r:gives {(3826 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3826 1000) math:remainder 826}] [ a r:Fact; r:gives {(826 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(826 100) math:remainder 26}] [ a r:Fact; r:gives {(26 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(26 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2826]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3826]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 826]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3257 a r:Inference; +skolem:lemma6582 a r:Inference; r:gives { - 2827 :numberToDigits (2 8 2 7). + 3827 :numberToDigits (3 8 2 7). }; r:evidence ( - [ a r:Fact; r:gives {(2827 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2827 1000) math:remainder 827}] + [ a r:Fact; r:gives {(3827 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3827 1000) math:remainder 827}] [ a r:Fact; r:gives {(827 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(827 100) math:remainder 27}] [ a r:Fact; r:gives {(27 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(27 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2827]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3827]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 827]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3258 a r:Inference; +skolem:lemma6583 a r:Inference; r:gives { - 2828 :numberToDigits (2 8 2 8). + 3828 :numberToDigits (3 8 2 8). }; r:evidence ( - [ a r:Fact; r:gives {(2828 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2828 1000) math:remainder 828}] + [ a r:Fact; r:gives {(3828 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3828 1000) math:remainder 828}] [ a r:Fact; r:gives {(828 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(828 100) math:remainder 28}] [ a r:Fact; r:gives {(28 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(28 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2828]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3828]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 828]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3259 a r:Inference; +skolem:lemma6584 a r:Inference; r:gives { - 2829 :numberToDigits (2 8 2 9). + 3829 :numberToDigits (3 8 2 9). }; r:evidence ( - [ a r:Fact; r:gives {(2829 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2829 1000) math:remainder 829}] + [ a r:Fact; r:gives {(3829 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3829 1000) math:remainder 829}] [ a r:Fact; r:gives {(829 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(829 100) math:remainder 29}] [ a r:Fact; r:gives {(29 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(29 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2829]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3829]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 829]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3260 a r:Inference; +skolem:lemma6585 a r:Inference; r:gives { - 2830 :numberToDigits (2 8 3 0). + 3830 :numberToDigits (3 8 3 0). }; r:evidence ( - [ a r:Fact; r:gives {(2830 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2830 1000) math:remainder 830}] + [ a r:Fact; r:gives {(3830 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3830 1000) math:remainder 830}] [ a r:Fact; r:gives {(830 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(830 100) math:remainder 30}] [ a r:Fact; r:gives {(30 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(30 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2830]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3830]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 830]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3261 a r:Inference; +skolem:lemma6586 a r:Inference; r:gives { - 2831 :numberToDigits (2 8 3 1). + 3831 :numberToDigits (3 8 3 1). }; r:evidence ( - [ a r:Fact; r:gives {(2831 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2831 1000) math:remainder 831}] + [ a r:Fact; r:gives {(3831 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3831 1000) math:remainder 831}] [ a r:Fact; r:gives {(831 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(831 100) math:remainder 31}] [ a r:Fact; r:gives {(31 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(31 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2831]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3831]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 831]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 31]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3262 a r:Inference; +skolem:lemma6587 a r:Inference; r:gives { - 2832 :numberToDigits (2 8 3 2). + 3832 :numberToDigits (3 8 3 2). }; r:evidence ( - [ a r:Fact; r:gives {(2832 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2832 1000) math:remainder 832}] + [ a r:Fact; r:gives {(3832 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3832 1000) math:remainder 832}] [ a r:Fact; r:gives {(832 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(832 100) math:remainder 32}] [ a r:Fact; r:gives {(32 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(32 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2832]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3832]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 832]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 32]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3263 a r:Inference; +skolem:lemma6588 a r:Inference; r:gives { - 2833 :numberToDigits (2 8 3 3). + 3833 :numberToDigits (3 8 3 3). }; r:evidence ( - [ a r:Fact; r:gives {(2833 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2833 1000) math:remainder 833}] + [ a r:Fact; r:gives {(3833 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3833 1000) math:remainder 833}] [ a r:Fact; r:gives {(833 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(833 100) math:remainder 33}] [ a r:Fact; r:gives {(33 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(33 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2833]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3833]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 833]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 33]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3264 a r:Inference; +skolem:lemma6589 a r:Inference; r:gives { - 2834 :numberToDigits (2 8 3 4). + 3834 :numberToDigits (3 8 3 4). }; r:evidence ( - [ a r:Fact; r:gives {(2834 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2834 1000) math:remainder 834}] + [ a r:Fact; r:gives {(3834 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3834 1000) math:remainder 834}] [ a r:Fact; r:gives {(834 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(834 100) math:remainder 34}] [ a r:Fact; r:gives {(34 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(34 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2834]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3834]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 834]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 34]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3265 a r:Inference; +skolem:lemma6590 a r:Inference; r:gives { - 2835 :numberToDigits (2 8 3 5). + 3835 :numberToDigits (3 8 3 5). }; r:evidence ( - [ a r:Fact; r:gives {(2835 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2835 1000) math:remainder 835}] + [ a r:Fact; r:gives {(3835 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3835 1000) math:remainder 835}] [ a r:Fact; r:gives {(835 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(835 100) math:remainder 35}] [ a r:Fact; r:gives {(35 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(35 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2835]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3835]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 835]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 35]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3266 a r:Inference; +skolem:lemma6591 a r:Inference; r:gives { - 2836 :numberToDigits (2 8 3 6). + 3836 :numberToDigits (3 8 3 6). }; r:evidence ( - [ a r:Fact; r:gives {(2836 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2836 1000) math:remainder 836}] + [ a r:Fact; r:gives {(3836 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3836 1000) math:remainder 836}] [ a r:Fact; r:gives {(836 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(836 100) math:remainder 36}] [ a r:Fact; r:gives {(36 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(36 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2836]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3836]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 836]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 36]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3267 a r:Inference; +skolem:lemma6592 a r:Inference; r:gives { - 2837 :numberToDigits (2 8 3 7). + 3837 :numberToDigits (3 8 3 7). }; r:evidence ( - [ a r:Fact; r:gives {(2837 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2837 1000) math:remainder 837}] + [ a r:Fact; r:gives {(3837 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3837 1000) math:remainder 837}] [ a r:Fact; r:gives {(837 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(837 100) math:remainder 37}] [ a r:Fact; r:gives {(37 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(37 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2837]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3837]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 837]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 37]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3268 a r:Inference; +skolem:lemma6593 a r:Inference; r:gives { - 2838 :numberToDigits (2 8 3 8). + 3838 :numberToDigits (3 8 3 8). }; r:evidence ( - [ a r:Fact; r:gives {(2838 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2838 1000) math:remainder 838}] + [ a r:Fact; r:gives {(3838 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3838 1000) math:remainder 838}] [ a r:Fact; r:gives {(838 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(838 100) math:remainder 38}] [ a r:Fact; r:gives {(38 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(38 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2838]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3838]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 838]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 38]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3269 a r:Inference; +skolem:lemma6594 a r:Inference; r:gives { - 2839 :numberToDigits (2 8 3 9). + 3839 :numberToDigits (3 8 3 9). }; r:evidence ( - [ a r:Fact; r:gives {(2839 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2839 1000) math:remainder 839}] + [ a r:Fact; r:gives {(3839 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3839 1000) math:remainder 839}] [ a r:Fact; r:gives {(839 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(839 100) math:remainder 39}] [ a r:Fact; r:gives {(39 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(39 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2839]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3839]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 839]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 39]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3270 a r:Inference; +skolem:lemma6595 a r:Inference; r:gives { - 2840 :numberToDigits (2 8 4 0). + 3840 :numberToDigits (3 8 4 0). }; r:evidence ( - [ a r:Fact; r:gives {(2840 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2840 1000) math:remainder 840}] + [ a r:Fact; r:gives {(3840 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3840 1000) math:remainder 840}] [ a r:Fact; r:gives {(840 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(840 100) math:remainder 40}] [ a r:Fact; r:gives {(40 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(40 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2840]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3840]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 840]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3271 a r:Inference; +skolem:lemma6596 a r:Inference; r:gives { - 2841 :numberToDigits (2 8 4 1). + 3841 :numberToDigits (3 8 4 1). }; r:evidence ( - [ a r:Fact; r:gives {(2841 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2841 1000) math:remainder 841}] + [ a r:Fact; r:gives {(3841 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3841 1000) math:remainder 841}] [ a r:Fact; r:gives {(841 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(841 100) math:remainder 41}] [ a r:Fact; r:gives {(41 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(41 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2841]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3841]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 841]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 41]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3272 a r:Inference; +skolem:lemma6597 a r:Inference; r:gives { - 2842 :numberToDigits (2 8 4 2). + 3842 :numberToDigits (3 8 4 2). }; r:evidence ( - [ a r:Fact; r:gives {(2842 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2842 1000) math:remainder 842}] + [ a r:Fact; r:gives {(3842 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3842 1000) math:remainder 842}] [ a r:Fact; r:gives {(842 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(842 100) math:remainder 42}] [ a r:Fact; r:gives {(42 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(42 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2842]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3842]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 842]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 42]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3273 a r:Inference; +skolem:lemma6598 a r:Inference; r:gives { - 2843 :numberToDigits (2 8 4 3). + 3843 :numberToDigits (3 8 4 3). }; r:evidence ( - [ a r:Fact; r:gives {(2843 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2843 1000) math:remainder 843}] + [ a r:Fact; r:gives {(3843 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3843 1000) math:remainder 843}] [ a r:Fact; r:gives {(843 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(843 100) math:remainder 43}] [ a r:Fact; r:gives {(43 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(43 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2843]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3843]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 843]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 43]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3274 a r:Inference; +skolem:lemma6599 a r:Inference; r:gives { - 2844 :numberToDigits (2 8 4 4). + 3844 :numberToDigits (3 8 4 4). }; r:evidence ( - [ a r:Fact; r:gives {(2844 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2844 1000) math:remainder 844}] + [ a r:Fact; r:gives {(3844 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3844 1000) math:remainder 844}] [ a r:Fact; r:gives {(844 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(844 100) math:remainder 44}] [ a r:Fact; r:gives {(44 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(44 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2844]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3844]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 844]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 44]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3275 a r:Inference; +skolem:lemma6600 a r:Inference; r:gives { - 2845 :numberToDigits (2 8 4 5). + 3845 :numberToDigits (3 8 4 5). }; r:evidence ( - [ a r:Fact; r:gives {(2845 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2845 1000) math:remainder 845}] + [ a r:Fact; r:gives {(3845 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3845 1000) math:remainder 845}] [ a r:Fact; r:gives {(845 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(845 100) math:remainder 45}] [ a r:Fact; r:gives {(45 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(45 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2845]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3845]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 845]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 45]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3276 a r:Inference; +skolem:lemma6601 a r:Inference; r:gives { - 2846 :numberToDigits (2 8 4 6). + 3846 :numberToDigits (3 8 4 6). }; r:evidence ( - [ a r:Fact; r:gives {(2846 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2846 1000) math:remainder 846}] + [ a r:Fact; r:gives {(3846 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3846 1000) math:remainder 846}] [ a r:Fact; r:gives {(846 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(846 100) math:remainder 46}] [ a r:Fact; r:gives {(46 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(46 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2846]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3846]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 846]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 46]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3277 a r:Inference; +skolem:lemma6602 a r:Inference; r:gives { - 2847 :numberToDigits (2 8 4 7). + 3847 :numberToDigits (3 8 4 7). }; r:evidence ( - [ a r:Fact; r:gives {(2847 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2847 1000) math:remainder 847}] + [ a r:Fact; r:gives {(3847 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3847 1000) math:remainder 847}] [ a r:Fact; r:gives {(847 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(847 100) math:remainder 47}] [ a r:Fact; r:gives {(47 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(47 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2847]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3847]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 847]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 47]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3278 a r:Inference; +skolem:lemma6603 a r:Inference; r:gives { - 2848 :numberToDigits (2 8 4 8). + 3848 :numberToDigits (3 8 4 8). }; r:evidence ( - [ a r:Fact; r:gives {(2848 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2848 1000) math:remainder 848}] + [ a r:Fact; r:gives {(3848 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3848 1000) math:remainder 848}] [ a r:Fact; r:gives {(848 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(848 100) math:remainder 48}] [ a r:Fact; r:gives {(48 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(48 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2848]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3848]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 848]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 48]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3279 a r:Inference; +skolem:lemma6604 a r:Inference; r:gives { - 2849 :numberToDigits (2 8 4 9). + 3849 :numberToDigits (3 8 4 9). }; r:evidence ( - [ a r:Fact; r:gives {(2849 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2849 1000) math:remainder 849}] + [ a r:Fact; r:gives {(3849 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3849 1000) math:remainder 849}] [ a r:Fact; r:gives {(849 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(849 100) math:remainder 49}] [ a r:Fact; r:gives {(49 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(49 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2849]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3849]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 849]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 49]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3280 a r:Inference; +skolem:lemma6605 a r:Inference; r:gives { - 2850 :numberToDigits (2 8 5 0). + 3850 :numberToDigits (3 8 5 0). }; r:evidence ( - [ a r:Fact; r:gives {(2850 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2850 1000) math:remainder 850}] + [ a r:Fact; r:gives {(3850 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3850 1000) math:remainder 850}] [ a r:Fact; r:gives {(850 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(850 100) math:remainder 50}] [ a r:Fact; r:gives {(50 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(50 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2850]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3850]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 850]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3281 a r:Inference; +skolem:lemma6606 a r:Inference; r:gives { - 2851 :numberToDigits (2 8 5 1). + 3851 :numberToDigits (3 8 5 1). }; r:evidence ( - [ a r:Fact; r:gives {(2851 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2851 1000) math:remainder 851}] + [ a r:Fact; r:gives {(3851 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3851 1000) math:remainder 851}] [ a r:Fact; r:gives {(851 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(851 100) math:remainder 51}] [ a r:Fact; r:gives {(51 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(51 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2851]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3851]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 851]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 51]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3282 a r:Inference; +skolem:lemma6607 a r:Inference; r:gives { - 2852 :numberToDigits (2 8 5 2). + 3852 :numberToDigits (3 8 5 2). }; r:evidence ( - [ a r:Fact; r:gives {(2852 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2852 1000) math:remainder 852}] + [ a r:Fact; r:gives {(3852 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3852 1000) math:remainder 852}] [ a r:Fact; r:gives {(852 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(852 100) math:remainder 52}] [ a r:Fact; r:gives {(52 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(52 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2852]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3852]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 852]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 52]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3283 a r:Inference; +skolem:lemma6608 a r:Inference; r:gives { - 2853 :numberToDigits (2 8 5 3). + 3853 :numberToDigits (3 8 5 3). }; r:evidence ( - [ a r:Fact; r:gives {(2853 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2853 1000) math:remainder 853}] + [ a r:Fact; r:gives {(3853 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3853 1000) math:remainder 853}] [ a r:Fact; r:gives {(853 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(853 100) math:remainder 53}] [ a r:Fact; r:gives {(53 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(53 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2853]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3853]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 853]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 53]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3284 a r:Inference; +skolem:lemma6609 a r:Inference; r:gives { - 2854 :numberToDigits (2 8 5 4). + 3854 :numberToDigits (3 8 5 4). }; r:evidence ( - [ a r:Fact; r:gives {(2854 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2854 1000) math:remainder 854}] + [ a r:Fact; r:gives {(3854 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3854 1000) math:remainder 854}] [ a r:Fact; r:gives {(854 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(854 100) math:remainder 54}] [ a r:Fact; r:gives {(54 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(54 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2854]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3854]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 854]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 54]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3285 a r:Inference; +skolem:lemma6610 a r:Inference; r:gives { - 2855 :numberToDigits (2 8 5 5). + 3855 :numberToDigits (3 8 5 5). }; r:evidence ( - [ a r:Fact; r:gives {(2855 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2855 1000) math:remainder 855}] + [ a r:Fact; r:gives {(3855 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3855 1000) math:remainder 855}] [ a r:Fact; r:gives {(855 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(855 100) math:remainder 55}] [ a r:Fact; r:gives {(55 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(55 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2855]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3855]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 855]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 55]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3286 a r:Inference; +skolem:lemma6611 a r:Inference; r:gives { - 2856 :numberToDigits (2 8 5 6). + 3856 :numberToDigits (3 8 5 6). }; r:evidence ( - [ a r:Fact; r:gives {(2856 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2856 1000) math:remainder 856}] + [ a r:Fact; r:gives {(3856 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3856 1000) math:remainder 856}] [ a r:Fact; r:gives {(856 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(856 100) math:remainder 56}] [ a r:Fact; r:gives {(56 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(56 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2856]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3856]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 856]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 56]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3287 a r:Inference; +skolem:lemma6612 a r:Inference; r:gives { - 2857 :numberToDigits (2 8 5 7). + 3857 :numberToDigits (3 8 5 7). }; r:evidence ( - [ a r:Fact; r:gives {(2857 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2857 1000) math:remainder 857}] + [ a r:Fact; r:gives {(3857 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3857 1000) math:remainder 857}] [ a r:Fact; r:gives {(857 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(857 100) math:remainder 57}] [ a r:Fact; r:gives {(57 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(57 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2857]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3857]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 857]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 57]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3288 a r:Inference; +skolem:lemma6613 a r:Inference; r:gives { - 2858 :numberToDigits (2 8 5 8). + 3858 :numberToDigits (3 8 5 8). }; r:evidence ( - [ a r:Fact; r:gives {(2858 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2858 1000) math:remainder 858}] + [ a r:Fact; r:gives {(3858 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3858 1000) math:remainder 858}] [ a r:Fact; r:gives {(858 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(858 100) math:remainder 58}] [ a r:Fact; r:gives {(58 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(58 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2858]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3858]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 858]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 58]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3289 a r:Inference; +skolem:lemma6614 a r:Inference; r:gives { - 2859 :numberToDigits (2 8 5 9). + 3859 :numberToDigits (3 8 5 9). }; r:evidence ( - [ a r:Fact; r:gives {(2859 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2859 1000) math:remainder 859}] + [ a r:Fact; r:gives {(3859 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3859 1000) math:remainder 859}] [ a r:Fact; r:gives {(859 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(859 100) math:remainder 59}] [ a r:Fact; r:gives {(59 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(59 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2859]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3859]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 859]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 59]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3290 a r:Inference; +skolem:lemma6615 a r:Inference; r:gives { - 2860 :numberToDigits (2 8 6 0). + 3860 :numberToDigits (3 8 6 0). }; r:evidence ( - [ a r:Fact; r:gives {(2860 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2860 1000) math:remainder 860}] + [ a r:Fact; r:gives {(3860 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3860 1000) math:remainder 860}] [ a r:Fact; r:gives {(860 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(860 100) math:remainder 60}] [ a r:Fact; r:gives {(60 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(60 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2860]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3860]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 860]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3291 a r:Inference; +skolem:lemma6616 a r:Inference; r:gives { - 2861 :numberToDigits (2 8 6 1). + 3861 :numberToDigits (3 8 6 1). }; r:evidence ( - [ a r:Fact; r:gives {(2861 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2861 1000) math:remainder 861}] + [ a r:Fact; r:gives {(3861 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3861 1000) math:remainder 861}] [ a r:Fact; r:gives {(861 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(861 100) math:remainder 61}] [ a r:Fact; r:gives {(61 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(61 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2861]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3861]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 861]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 61]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3292 a r:Inference; +skolem:lemma6617 a r:Inference; r:gives { - 2862 :numberToDigits (2 8 6 2). + 3862 :numberToDigits (3 8 6 2). }; r:evidence ( - [ a r:Fact; r:gives {(2862 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2862 1000) math:remainder 862}] + [ a r:Fact; r:gives {(3862 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3862 1000) math:remainder 862}] [ a r:Fact; r:gives {(862 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(862 100) math:remainder 62}] [ a r:Fact; r:gives {(62 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(62 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2862]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3862]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 862]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 62]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3293 a r:Inference; +skolem:lemma6618 a r:Inference; r:gives { - 2863 :numberToDigits (2 8 6 3). + 3863 :numberToDigits (3 8 6 3). }; r:evidence ( - [ a r:Fact; r:gives {(2863 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2863 1000) math:remainder 863}] + [ a r:Fact; r:gives {(3863 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3863 1000) math:remainder 863}] [ a r:Fact; r:gives {(863 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(863 100) math:remainder 63}] [ a r:Fact; r:gives {(63 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(63 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2863]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3863]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 863]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 63]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3294 a r:Inference; +skolem:lemma6619 a r:Inference; r:gives { - 2864 :numberToDigits (2 8 6 4). + 3864 :numberToDigits (3 8 6 4). }; r:evidence ( - [ a r:Fact; r:gives {(2864 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2864 1000) math:remainder 864}] + [ a r:Fact; r:gives {(3864 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3864 1000) math:remainder 864}] [ a r:Fact; r:gives {(864 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(864 100) math:remainder 64}] [ a r:Fact; r:gives {(64 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(64 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2864]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3864]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 864]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 64]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3295 a r:Inference; +skolem:lemma6620 a r:Inference; r:gives { - 2865 :numberToDigits (2 8 6 5). + 3865 :numberToDigits (3 8 6 5). }; r:evidence ( - [ a r:Fact; r:gives {(2865 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2865 1000) math:remainder 865}] + [ a r:Fact; r:gives {(3865 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3865 1000) math:remainder 865}] [ a r:Fact; r:gives {(865 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(865 100) math:remainder 65}] [ a r:Fact; r:gives {(65 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(65 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2865]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3865]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 865]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 65]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3296 a r:Inference; +skolem:lemma6621 a r:Inference; r:gives { - 2866 :numberToDigits (2 8 6 6). + 3866 :numberToDigits (3 8 6 6). }; r:evidence ( - [ a r:Fact; r:gives {(2866 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2866 1000) math:remainder 866}] + [ a r:Fact; r:gives {(3866 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3866 1000) math:remainder 866}] [ a r:Fact; r:gives {(866 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(866 100) math:remainder 66}] [ a r:Fact; r:gives {(66 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(66 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2866]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3866]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 866]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 66]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3297 a r:Inference; +skolem:lemma6622 a r:Inference; r:gives { - 2867 :numberToDigits (2 8 6 7). + 3867 :numberToDigits (3 8 6 7). }; r:evidence ( - [ a r:Fact; r:gives {(2867 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2867 1000) math:remainder 867}] + [ a r:Fact; r:gives {(3867 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3867 1000) math:remainder 867}] [ a r:Fact; r:gives {(867 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(867 100) math:remainder 67}] [ a r:Fact; r:gives {(67 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(67 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2867]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3867]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 867]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 67]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3298 a r:Inference; +skolem:lemma6623 a r:Inference; r:gives { - 2868 :numberToDigits (2 8 6 8). + 3868 :numberToDigits (3 8 6 8). }; r:evidence ( - [ a r:Fact; r:gives {(2868 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2868 1000) math:remainder 868}] + [ a r:Fact; r:gives {(3868 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3868 1000) math:remainder 868}] [ a r:Fact; r:gives {(868 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(868 100) math:remainder 68}] [ a r:Fact; r:gives {(68 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(68 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2868]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3868]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 868]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 68]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3299 a r:Inference; +skolem:lemma6624 a r:Inference; r:gives { - 2869 :numberToDigits (2 8 6 9). + 3869 :numberToDigits (3 8 6 9). }; r:evidence ( - [ a r:Fact; r:gives {(2869 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2869 1000) math:remainder 869}] + [ a r:Fact; r:gives {(3869 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3869 1000) math:remainder 869}] [ a r:Fact; r:gives {(869 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(869 100) math:remainder 69}] [ a r:Fact; r:gives {(69 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(69 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2869]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3869]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 869]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 69]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3300 a r:Inference; +skolem:lemma6625 a r:Inference; r:gives { - 2870 :numberToDigits (2 8 7 0). + 3870 :numberToDigits (3 8 7 0). }; r:evidence ( - [ a r:Fact; r:gives {(2870 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2870 1000) math:remainder 870}] + [ a r:Fact; r:gives {(3870 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3870 1000) math:remainder 870}] [ a r:Fact; r:gives {(870 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(870 100) math:remainder 70}] [ a r:Fact; r:gives {(70 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(70 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2870]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3870]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 870]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3301 a r:Inference; +skolem:lemma6626 a r:Inference; r:gives { - 2871 :numberToDigits (2 8 7 1). + 3871 :numberToDigits (3 8 7 1). }; r:evidence ( - [ a r:Fact; r:gives {(2871 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2871 1000) math:remainder 871}] + [ a r:Fact; r:gives {(3871 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3871 1000) math:remainder 871}] [ a r:Fact; r:gives {(871 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(871 100) math:remainder 71}] [ a r:Fact; r:gives {(71 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(71 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2871]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3871]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 871]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 71]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3302 a r:Inference; +skolem:lemma6627 a r:Inference; r:gives { - 2872 :numberToDigits (2 8 7 2). + 3872 :numberToDigits (3 8 7 2). }; r:evidence ( - [ a r:Fact; r:gives {(2872 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2872 1000) math:remainder 872}] + [ a r:Fact; r:gives {(3872 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3872 1000) math:remainder 872}] [ a r:Fact; r:gives {(872 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(872 100) math:remainder 72}] [ a r:Fact; r:gives {(72 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(72 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2872]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3872]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 872]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 72]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3303 a r:Inference; +skolem:lemma6628 a r:Inference; r:gives { - 2873 :numberToDigits (2 8 7 3). + 3873 :numberToDigits (3 8 7 3). }; r:evidence ( - [ a r:Fact; r:gives {(2873 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2873 1000) math:remainder 873}] + [ a r:Fact; r:gives {(3873 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3873 1000) math:remainder 873}] [ a r:Fact; r:gives {(873 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(873 100) math:remainder 73}] [ a r:Fact; r:gives {(73 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(73 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2873]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3873]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 873]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 73]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3304 a r:Inference; +skolem:lemma6629 a r:Inference; r:gives { - 2874 :numberToDigits (2 8 7 4). + 3874 :numberToDigits (3 8 7 4). }; r:evidence ( - [ a r:Fact; r:gives {(2874 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2874 1000) math:remainder 874}] + [ a r:Fact; r:gives {(3874 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3874 1000) math:remainder 874}] [ a r:Fact; r:gives {(874 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(874 100) math:remainder 74}] [ a r:Fact; r:gives {(74 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(74 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2874]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3874]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 874]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 74]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3305 a r:Inference; +skolem:lemma6630 a r:Inference; r:gives { - 2875 :numberToDigits (2 8 7 5). + 3875 :numberToDigits (3 8 7 5). }; r:evidence ( - [ a r:Fact; r:gives {(2875 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2875 1000) math:remainder 875}] + [ a r:Fact; r:gives {(3875 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3875 1000) math:remainder 875}] [ a r:Fact; r:gives {(875 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(875 100) math:remainder 75}] [ a r:Fact; r:gives {(75 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(75 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2875]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3875]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 875]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 75]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3306 a r:Inference; +skolem:lemma6631 a r:Inference; r:gives { - 2876 :numberToDigits (2 8 7 6). + 3876 :numberToDigits (3 8 7 6). }; r:evidence ( - [ a r:Fact; r:gives {(2876 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2876 1000) math:remainder 876}] + [ a r:Fact; r:gives {(3876 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3876 1000) math:remainder 876}] [ a r:Fact; r:gives {(876 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(876 100) math:remainder 76}] [ a r:Fact; r:gives {(76 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(76 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2876]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3876]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 876]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 76]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3307 a r:Inference; +skolem:lemma6632 a r:Inference; r:gives { - 2877 :numberToDigits (2 8 7 7). + 3877 :numberToDigits (3 8 7 7). }; r:evidence ( - [ a r:Fact; r:gives {(2877 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2877 1000) math:remainder 877}] + [ a r:Fact; r:gives {(3877 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3877 1000) math:remainder 877}] [ a r:Fact; r:gives {(877 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(877 100) math:remainder 77}] [ a r:Fact; r:gives {(77 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(77 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2877]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3877]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 877]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 77]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3308 a r:Inference; +skolem:lemma6633 a r:Inference; r:gives { - 2878 :numberToDigits (2 8 7 8). + 3878 :numberToDigits (3 8 7 8). }; r:evidence ( - [ a r:Fact; r:gives {(2878 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2878 1000) math:remainder 878}] + [ a r:Fact; r:gives {(3878 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3878 1000) math:remainder 878}] [ a r:Fact; r:gives {(878 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(878 100) math:remainder 78}] [ a r:Fact; r:gives {(78 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(78 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2878]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3878]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 878]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 78]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3309 a r:Inference; +skolem:lemma6634 a r:Inference; r:gives { - 2879 :numberToDigits (2 8 7 9). + 3879 :numberToDigits (3 8 7 9). }; r:evidence ( - [ a r:Fact; r:gives {(2879 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2879 1000) math:remainder 879}] + [ a r:Fact; r:gives {(3879 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3879 1000) math:remainder 879}] [ a r:Fact; r:gives {(879 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(879 100) math:remainder 79}] [ a r:Fact; r:gives {(79 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(79 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2879]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3879]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 879]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 79]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3310 a r:Inference; +skolem:lemma6635 a r:Inference; r:gives { - 2880 :numberToDigits (2 8 8 0). + 3880 :numberToDigits (3 8 8 0). }; r:evidence ( - [ a r:Fact; r:gives {(2880 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2880 1000) math:remainder 880}] + [ a r:Fact; r:gives {(3880 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3880 1000) math:remainder 880}] [ a r:Fact; r:gives {(880 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(880 100) math:remainder 80}] [ a r:Fact; r:gives {(80 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(80 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2880]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3880]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 880]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3311 a r:Inference; +skolem:lemma6636 a r:Inference; r:gives { - 2881 :numberToDigits (2 8 8 1). + 3881 :numberToDigits (3 8 8 1). }; r:evidence ( - [ a r:Fact; r:gives {(2881 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2881 1000) math:remainder 881}] + [ a r:Fact; r:gives {(3881 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3881 1000) math:remainder 881}] [ a r:Fact; r:gives {(881 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(881 100) math:remainder 81}] [ a r:Fact; r:gives {(81 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(81 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2881]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3881]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 881]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 81]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3312 a r:Inference; +skolem:lemma6637 a r:Inference; r:gives { - 2882 :numberToDigits (2 8 8 2). + 3882 :numberToDigits (3 8 8 2). }; r:evidence ( - [ a r:Fact; r:gives {(2882 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2882 1000) math:remainder 882}] + [ a r:Fact; r:gives {(3882 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3882 1000) math:remainder 882}] [ a r:Fact; r:gives {(882 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(882 100) math:remainder 82}] [ a r:Fact; r:gives {(82 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(82 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2882]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3882]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 882]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 82]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3313 a r:Inference; +skolem:lemma6638 a r:Inference; r:gives { - 2883 :numberToDigits (2 8 8 3). + 3883 :numberToDigits (3 8 8 3). }; r:evidence ( - [ a r:Fact; r:gives {(2883 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2883 1000) math:remainder 883}] + [ a r:Fact; r:gives {(3883 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3883 1000) math:remainder 883}] [ a r:Fact; r:gives {(883 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(883 100) math:remainder 83}] [ a r:Fact; r:gives {(83 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(83 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2883]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3883]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 883]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 83]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3314 a r:Inference; +skolem:lemma6639 a r:Inference; r:gives { - 2884 :numberToDigits (2 8 8 4). + 3884 :numberToDigits (3 8 8 4). }; r:evidence ( - [ a r:Fact; r:gives {(2884 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2884 1000) math:remainder 884}] + [ a r:Fact; r:gives {(3884 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3884 1000) math:remainder 884}] [ a r:Fact; r:gives {(884 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(884 100) math:remainder 84}] [ a r:Fact; r:gives {(84 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(84 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2884]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3884]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 884]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 84]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3315 a r:Inference; +skolem:lemma6640 a r:Inference; r:gives { - 2885 :numberToDigits (2 8 8 5). + 3885 :numberToDigits (3 8 8 5). }; r:evidence ( - [ a r:Fact; r:gives {(2885 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2885 1000) math:remainder 885}] + [ a r:Fact; r:gives {(3885 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3885 1000) math:remainder 885}] [ a r:Fact; r:gives {(885 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(885 100) math:remainder 85}] [ a r:Fact; r:gives {(85 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(85 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2885]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3885]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 885]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 85]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3316 a r:Inference; +skolem:lemma6641 a r:Inference; r:gives { - 2886 :numberToDigits (2 8 8 6). + 3886 :numberToDigits (3 8 8 6). }; r:evidence ( - [ a r:Fact; r:gives {(2886 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2886 1000) math:remainder 886}] + [ a r:Fact; r:gives {(3886 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3886 1000) math:remainder 886}] [ a r:Fact; r:gives {(886 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(886 100) math:remainder 86}] [ a r:Fact; r:gives {(86 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(86 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2886]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3886]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 886]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 86]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3317 a r:Inference; +skolem:lemma6642 a r:Inference; r:gives { - 2887 :numberToDigits (2 8 8 7). + 3887 :numberToDigits (3 8 8 7). }; r:evidence ( - [ a r:Fact; r:gives {(2887 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2887 1000) math:remainder 887}] + [ a r:Fact; r:gives {(3887 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3887 1000) math:remainder 887}] [ a r:Fact; r:gives {(887 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(887 100) math:remainder 87}] [ a r:Fact; r:gives {(87 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(87 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2887]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3887]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 887]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 87]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3318 a r:Inference; +skolem:lemma6643 a r:Inference; r:gives { - 2888 :numberToDigits (2 8 8 8). + 3888 :numberToDigits (3 8 8 8). }; r:evidence ( - [ a r:Fact; r:gives {(2888 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2888 1000) math:remainder 888}] + [ a r:Fact; r:gives {(3888 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3888 1000) math:remainder 888}] [ a r:Fact; r:gives {(888 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(888 100) math:remainder 88}] [ a r:Fact; r:gives {(88 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(88 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2888]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3888]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 888]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 88]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3319 a r:Inference; +skolem:lemma6644 a r:Inference; r:gives { - (2 8 8 8) :digitsToNumber 2888 . + (3 8 8 8) :digitsToNumber 3888 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(8 100) math:product 800}] [ a r:Fact; r:gives {(8 10) math:product 80}] - [ a r:Fact; r:gives {(2000 800 80 8) math:sum 2888}] + [ a r:Fact; r:gives {(3000 800 80 8) math:sum 3888}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2888]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3888]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma3320 a r:Inference; +skolem:lemma6645 a r:Inference; r:gives { - (8 8 8 2) :digitsToNumber 8882 . + (8 8 8 3) :digitsToNumber 8883 . }; r:evidence ( [ a r:Fact; r:gives {(8 1000) math:product 8000}] [ a r:Fact; r:gives {(8 100) math:product 800}] [ a r:Fact; r:gives {(8 10) math:product 80}] - [ a r:Fact; r:gives {(8000 800 80 2) math:sum 8882}] + [ a r:Fact; r:gives {(8000 800 80 3) math:sum 8883}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 8000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 8]; @@ -77281,60 +154770,60 @@ skolem:lemma3320 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8882]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 8883]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma3321 a r:Inference; +skolem:lemma6646 a r:Inference; r:gives { - 2889 :numberToDigits (2 8 8 9). + 3889 :numberToDigits (3 8 8 9). }; r:evidence ( - [ a r:Fact; r:gives {(2889 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2889 1000) math:remainder 889}] + [ a r:Fact; r:gives {(3889 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3889 1000) math:remainder 889}] [ a r:Fact; r:gives {(889 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(889 100) math:remainder 89}] [ a r:Fact; r:gives {(89 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(89 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2889]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3889]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 889]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 89]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3322 a r:Inference; +skolem:lemma6647 a r:Inference; r:gives { - (2 8 8 9) :digitsToNumber 2889 . + (3 8 8 9) :digitsToNumber 3889 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(8 100) math:product 800}] [ a r:Fact; r:gives {(8 10) math:product 80}] - [ a r:Fact; r:gives {(2000 800 80 9) math:sum 2889}] + [ a r:Fact; r:gives {(3000 800 80 9) math:sum 3889}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2889]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3889]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma3323 a r:Inference; +skolem:lemma6648 a r:Inference; r:gives { - (9 8 8 2) :digitsToNumber 9882 . + (9 8 8 3) :digitsToNumber 9883 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(8 100) math:product 800}] [ a r:Fact; r:gives {(8 10) math:product 80}] - [ a r:Fact; r:gives {(9000 800 80 2) math:sum 9882}] + [ a r:Fact; r:gives {(9000 800 80 3) math:sum 9883}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -77342,249 +154831,249 @@ skolem:lemma3323 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9882]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9883]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma3324 a r:Inference; +skolem:lemma6649 a r:Inference; r:gives { - 2890 :numberToDigits (2 8 9 0). + 3890 :numberToDigits (3 8 9 0). }; r:evidence ( - [ a r:Fact; r:gives {(2890 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2890 1000) math:remainder 890}] + [ a r:Fact; r:gives {(3890 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3890 1000) math:remainder 890}] [ a r:Fact; r:gives {(890 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(890 100) math:remainder 90}] [ a r:Fact; r:gives {(90 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(90 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2890]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3890]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 890]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 90]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3325 a r:Inference; +skolem:lemma6650 a r:Inference; r:gives { - 2891 :numberToDigits (2 8 9 1). + 3891 :numberToDigits (3 8 9 1). }; r:evidence ( - [ a r:Fact; r:gives {(2891 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2891 1000) math:remainder 891}] + [ a r:Fact; r:gives {(3891 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3891 1000) math:remainder 891}] [ a r:Fact; r:gives {(891 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(891 100) math:remainder 91}] [ a r:Fact; r:gives {(91 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(91 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2891]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3891]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 891]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 91]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3326 a r:Inference; +skolem:lemma6651 a r:Inference; r:gives { - 2892 :numberToDigits (2 8 9 2). + 3892 :numberToDigits (3 8 9 2). }; r:evidence ( - [ a r:Fact; r:gives {(2892 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2892 1000) math:remainder 892}] + [ a r:Fact; r:gives {(3892 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3892 1000) math:remainder 892}] [ a r:Fact; r:gives {(892 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(892 100) math:remainder 92}] [ a r:Fact; r:gives {(92 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(92 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2892]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3892]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 892]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 92]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3327 a r:Inference; +skolem:lemma6652 a r:Inference; r:gives { - 2893 :numberToDigits (2 8 9 3). + 3893 :numberToDigits (3 8 9 3). }; r:evidence ( - [ a r:Fact; r:gives {(2893 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2893 1000) math:remainder 893}] + [ a r:Fact; r:gives {(3893 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3893 1000) math:remainder 893}] [ a r:Fact; r:gives {(893 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(893 100) math:remainder 93}] [ a r:Fact; r:gives {(93 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(93 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2893]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3893]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 893]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 93]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3328 a r:Inference; +skolem:lemma6653 a r:Inference; r:gives { - 2894 :numberToDigits (2 8 9 4). + 3894 :numberToDigits (3 8 9 4). }; r:evidence ( - [ a r:Fact; r:gives {(2894 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2894 1000) math:remainder 894}] + [ a r:Fact; r:gives {(3894 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3894 1000) math:remainder 894}] [ a r:Fact; r:gives {(894 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(894 100) math:remainder 94}] [ a r:Fact; r:gives {(94 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(94 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2894]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3894]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 894]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 94]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3329 a r:Inference; +skolem:lemma6654 a r:Inference; r:gives { - 2895 :numberToDigits (2 8 9 5). + 3895 :numberToDigits (3 8 9 5). }; r:evidence ( - [ a r:Fact; r:gives {(2895 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2895 1000) math:remainder 895}] + [ a r:Fact; r:gives {(3895 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3895 1000) math:remainder 895}] [ a r:Fact; r:gives {(895 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(895 100) math:remainder 95}] [ a r:Fact; r:gives {(95 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(95 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2895]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3895]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 895]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 95]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3330 a r:Inference; +skolem:lemma6655 a r:Inference; r:gives { - 2896 :numberToDigits (2 8 9 6). + 3896 :numberToDigits (3 8 9 6). }; r:evidence ( - [ a r:Fact; r:gives {(2896 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2896 1000) math:remainder 896}] + [ a r:Fact; r:gives {(3896 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3896 1000) math:remainder 896}] [ a r:Fact; r:gives {(896 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(896 100) math:remainder 96}] [ a r:Fact; r:gives {(96 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(96 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2896]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3896]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 896]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 96]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3331 a r:Inference; +skolem:lemma6656 a r:Inference; r:gives { - 2897 :numberToDigits (2 8 9 7). + 3897 :numberToDigits (3 8 9 7). }; r:evidence ( - [ a r:Fact; r:gives {(2897 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2897 1000) math:remainder 897}] + [ a r:Fact; r:gives {(3897 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3897 1000) math:remainder 897}] [ a r:Fact; r:gives {(897 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(897 100) math:remainder 97}] [ a r:Fact; r:gives {(97 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(97 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2897]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3897]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 897]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 97]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3332 a r:Inference; +skolem:lemma6657 a r:Inference; r:gives { - 2898 :numberToDigits (2 8 9 8). + 3898 :numberToDigits (3 8 9 8). }; r:evidence ( - [ a r:Fact; r:gives {(2898 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2898 1000) math:remainder 898}] + [ a r:Fact; r:gives {(3898 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3898 1000) math:remainder 898}] [ a r:Fact; r:gives {(898 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(898 100) math:remainder 98}] [ a r:Fact; r:gives {(98 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(98 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2898]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3898]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 898]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 98]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3333 a r:Inference; +skolem:lemma6658 a r:Inference; r:gives { - 2899 :numberToDigits (2 8 9 9). + 3899 :numberToDigits (3 8 9 9). }; r:evidence ( - [ a r:Fact; r:gives {(2899 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2899 1000) math:remainder 899}] + [ a r:Fact; r:gives {(3899 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3899 1000) math:remainder 899}] [ a r:Fact; r:gives {(899 100) math:integerQuotient 8}] [ a r:Fact; r:gives {(899 100) math:remainder 99}] [ a r:Fact; r:gives {(99 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(99 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2899]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3899]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 899]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 99]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3334 a r:Inference; +skolem:lemma6659 a r:Inference; r:gives { - (2 8 9 9) :digitsToNumber 2899 . + (3 8 9 9) :digitsToNumber 3899 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(8 100) math:product 800}] [ a r:Fact; r:gives {(9 10) math:product 90}] - [ a r:Fact; r:gives {(2000 800 90 9) math:sum 2899}] + [ a r:Fact; r:gives {(3000 800 90 9) math:sum 3899}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 800]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 90]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2899]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3899]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma3335 a r:Inference; +skolem:lemma6660 a r:Inference; r:gives { - (9 9 8 2) :digitsToNumber 9982 . + (9 9 8 3) :digitsToNumber 9983 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(9 100) math:product 900}] [ a r:Fact; r:gives {(8 10) math:product 80}] - [ a r:Fact; r:gives {(9000 900 80 2) math:sum 9982}] + [ a r:Fact; r:gives {(9000 900 80 3) math:sum 9983}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -77592,2139 +155081,2139 @@ skolem:lemma3335 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9982]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9983]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma3336 a r:Inference; +skolem:lemma6661 a r:Inference; r:gives { - 2900 :numberToDigits (2 9 0 0). + 3900 :numberToDigits (3 9 0 0). }; r:evidence ( - [ a r:Fact; r:gives {(2900 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2900 1000) math:remainder 900}] + [ a r:Fact; r:gives {(3900 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3900 1000) math:remainder 900}] [ a r:Fact; r:gives {(900 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(900 100) math:remainder 0}] [ a r:Fact; r:gives {(0 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(0 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2900]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3900]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 900]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3337 a r:Inference; +skolem:lemma6662 a r:Inference; r:gives { - 2901 :numberToDigits (2 9 0 1). + 3901 :numberToDigits (3 9 0 1). }; r:evidence ( - [ a r:Fact; r:gives {(2901 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2901 1000) math:remainder 901}] + [ a r:Fact; r:gives {(3901 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3901 1000) math:remainder 901}] [ a r:Fact; r:gives {(901 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(901 100) math:remainder 1}] [ a r:Fact; r:gives {(1 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(1 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2901]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3901]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 901]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3338 a r:Inference; +skolem:lemma6663 a r:Inference; r:gives { - 2902 :numberToDigits (2 9 0 2). + 3902 :numberToDigits (3 9 0 2). }; r:evidence ( - [ a r:Fact; r:gives {(2902 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2902 1000) math:remainder 902}] + [ a r:Fact; r:gives {(3902 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3902 1000) math:remainder 902}] [ a r:Fact; r:gives {(902 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(902 100) math:remainder 2}] [ a r:Fact; r:gives {(2 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(2 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2902]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3902]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 902]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3339 a r:Inference; +skolem:lemma6664 a r:Inference; r:gives { - 2903 :numberToDigits (2 9 0 3). + 3903 :numberToDigits (3 9 0 3). }; r:evidence ( - [ a r:Fact; r:gives {(2903 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2903 1000) math:remainder 903}] + [ a r:Fact; r:gives {(3903 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3903 1000) math:remainder 903}] [ a r:Fact; r:gives {(903 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(903 100) math:remainder 3}] [ a r:Fact; r:gives {(3 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(3 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2903]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3903]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 903]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3340 a r:Inference; +skolem:lemma6665 a r:Inference; r:gives { - 2904 :numberToDigits (2 9 0 4). + 3904 :numberToDigits (3 9 0 4). }; r:evidence ( - [ a r:Fact; r:gives {(2904 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2904 1000) math:remainder 904}] + [ a r:Fact; r:gives {(3904 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3904 1000) math:remainder 904}] [ a r:Fact; r:gives {(904 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(904 100) math:remainder 4}] [ a r:Fact; r:gives {(4 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(4 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2904]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3904]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 904]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3341 a r:Inference; +skolem:lemma6666 a r:Inference; r:gives { - 2905 :numberToDigits (2 9 0 5). + 3905 :numberToDigits (3 9 0 5). }; r:evidence ( - [ a r:Fact; r:gives {(2905 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2905 1000) math:remainder 905}] + [ a r:Fact; r:gives {(3905 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3905 1000) math:remainder 905}] [ a r:Fact; r:gives {(905 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(905 100) math:remainder 5}] [ a r:Fact; r:gives {(5 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(5 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2905]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3905]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 905]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3342 a r:Inference; +skolem:lemma6667 a r:Inference; r:gives { - 2906 :numberToDigits (2 9 0 6). + 3906 :numberToDigits (3 9 0 6). }; r:evidence ( - [ a r:Fact; r:gives {(2906 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2906 1000) math:remainder 906}] + [ a r:Fact; r:gives {(3906 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3906 1000) math:remainder 906}] [ a r:Fact; r:gives {(906 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(906 100) math:remainder 6}] [ a r:Fact; r:gives {(6 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(6 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2906]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3906]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 906]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3343 a r:Inference; +skolem:lemma6668 a r:Inference; r:gives { - 2907 :numberToDigits (2 9 0 7). + 3907 :numberToDigits (3 9 0 7). }; r:evidence ( - [ a r:Fact; r:gives {(2907 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2907 1000) math:remainder 907}] + [ a r:Fact; r:gives {(3907 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3907 1000) math:remainder 907}] [ a r:Fact; r:gives {(907 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(907 100) math:remainder 7}] [ a r:Fact; r:gives {(7 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(7 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2907]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3907]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 907]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3344 a r:Inference; +skolem:lemma6669 a r:Inference; r:gives { - 2908 :numberToDigits (2 9 0 8). + 3908 :numberToDigits (3 9 0 8). }; r:evidence ( - [ a r:Fact; r:gives {(2908 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2908 1000) math:remainder 908}] + [ a r:Fact; r:gives {(3908 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3908 1000) math:remainder 908}] [ a r:Fact; r:gives {(908 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(908 100) math:remainder 8}] [ a r:Fact; r:gives {(8 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(8 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2908]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3908]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 908]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3345 a r:Inference; +skolem:lemma6670 a r:Inference; r:gives { - 2909 :numberToDigits (2 9 0 9). + 3909 :numberToDigits (3 9 0 9). }; r:evidence ( - [ a r:Fact; r:gives {(2909 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2909 1000) math:remainder 909}] + [ a r:Fact; r:gives {(3909 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3909 1000) math:remainder 909}] [ a r:Fact; r:gives {(909 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(909 100) math:remainder 9}] [ a r:Fact; r:gives {(9 10) math:integerQuotient 0}] [ a r:Fact; r:gives {(9 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2909]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3909]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 909]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 0]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3346 a r:Inference; +skolem:lemma6671 a r:Inference; r:gives { - 2910 :numberToDigits (2 9 1 0). + 3910 :numberToDigits (3 9 1 0). }; r:evidence ( - [ a r:Fact; r:gives {(2910 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2910 1000) math:remainder 910}] + [ a r:Fact; r:gives {(3910 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3910 1000) math:remainder 910}] [ a r:Fact; r:gives {(910 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(910 100) math:remainder 10}] [ a r:Fact; r:gives {(10 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(10 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2910]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3910]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 910]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 10]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3347 a r:Inference; +skolem:lemma6672 a r:Inference; r:gives { - 2911 :numberToDigits (2 9 1 1). + 3911 :numberToDigits (3 9 1 1). }; r:evidence ( - [ a r:Fact; r:gives {(2911 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2911 1000) math:remainder 911}] + [ a r:Fact; r:gives {(3911 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3911 1000) math:remainder 911}] [ a r:Fact; r:gives {(911 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(911 100) math:remainder 11}] [ a r:Fact; r:gives {(11 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(11 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2911]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3911]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 911]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 11]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3348 a r:Inference; +skolem:lemma6673 a r:Inference; r:gives { - 2912 :numberToDigits (2 9 1 2). + 3912 :numberToDigits (3 9 1 2). }; r:evidence ( - [ a r:Fact; r:gives {(2912 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2912 1000) math:remainder 912}] + [ a r:Fact; r:gives {(3912 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3912 1000) math:remainder 912}] [ a r:Fact; r:gives {(912 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(912 100) math:remainder 12}] [ a r:Fact; r:gives {(12 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(12 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2912]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3912]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 912]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 12]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3349 a r:Inference; +skolem:lemma6674 a r:Inference; r:gives { - 2913 :numberToDigits (2 9 1 3). + 3913 :numberToDigits (3 9 1 3). }; r:evidence ( - [ a r:Fact; r:gives {(2913 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2913 1000) math:remainder 913}] + [ a r:Fact; r:gives {(3913 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3913 1000) math:remainder 913}] [ a r:Fact; r:gives {(913 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(913 100) math:remainder 13}] [ a r:Fact; r:gives {(13 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(13 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2913]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3913]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 913]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 13]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3350 a r:Inference; +skolem:lemma6675 a r:Inference; r:gives { - 2914 :numberToDigits (2 9 1 4). + 3914 :numberToDigits (3 9 1 4). }; r:evidence ( - [ a r:Fact; r:gives {(2914 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2914 1000) math:remainder 914}] + [ a r:Fact; r:gives {(3914 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3914 1000) math:remainder 914}] [ a r:Fact; r:gives {(914 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(914 100) math:remainder 14}] [ a r:Fact; r:gives {(14 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(14 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2914]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3914]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 914]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 14]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3351 a r:Inference; +skolem:lemma6676 a r:Inference; r:gives { - 2915 :numberToDigits (2 9 1 5). + 3915 :numberToDigits (3 9 1 5). }; r:evidence ( - [ a r:Fact; r:gives {(2915 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2915 1000) math:remainder 915}] + [ a r:Fact; r:gives {(3915 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3915 1000) math:remainder 915}] [ a r:Fact; r:gives {(915 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(915 100) math:remainder 15}] [ a r:Fact; r:gives {(15 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(15 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2915]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3915]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 915]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 15]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3352 a r:Inference; +skolem:lemma6677 a r:Inference; r:gives { - 2916 :numberToDigits (2 9 1 6). + 3916 :numberToDigits (3 9 1 6). }; r:evidence ( - [ a r:Fact; r:gives {(2916 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2916 1000) math:remainder 916}] + [ a r:Fact; r:gives {(3916 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3916 1000) math:remainder 916}] [ a r:Fact; r:gives {(916 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(916 100) math:remainder 16}] [ a r:Fact; r:gives {(16 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(16 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2916]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3916]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 916]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 16]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3353 a r:Inference; +skolem:lemma6678 a r:Inference; r:gives { - 2917 :numberToDigits (2 9 1 7). + 3917 :numberToDigits (3 9 1 7). }; r:evidence ( - [ a r:Fact; r:gives {(2917 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2917 1000) math:remainder 917}] + [ a r:Fact; r:gives {(3917 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3917 1000) math:remainder 917}] [ a r:Fact; r:gives {(917 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(917 100) math:remainder 17}] [ a r:Fact; r:gives {(17 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(17 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2917]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3917]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 917]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 17]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3354 a r:Inference; +skolem:lemma6679 a r:Inference; r:gives { - 2918 :numberToDigits (2 9 1 8). + 3918 :numberToDigits (3 9 1 8). }; r:evidence ( - [ a r:Fact; r:gives {(2918 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2918 1000) math:remainder 918}] + [ a r:Fact; r:gives {(3918 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3918 1000) math:remainder 918}] [ a r:Fact; r:gives {(918 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(918 100) math:remainder 18}] [ a r:Fact; r:gives {(18 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(18 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2918]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3918]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 918]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 18]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3355 a r:Inference; +skolem:lemma6680 a r:Inference; r:gives { - 2919 :numberToDigits (2 9 1 9). + 3919 :numberToDigits (3 9 1 9). }; r:evidence ( - [ a r:Fact; r:gives {(2919 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2919 1000) math:remainder 919}] + [ a r:Fact; r:gives {(3919 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3919 1000) math:remainder 919}] [ a r:Fact; r:gives {(919 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(919 100) math:remainder 19}] [ a r:Fact; r:gives {(19 10) math:integerQuotient 1}] [ a r:Fact; r:gives {(19 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2919]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3919]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 919]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 19]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 1]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3356 a r:Inference; +skolem:lemma6681 a r:Inference; r:gives { - 2920 :numberToDigits (2 9 2 0). + 3920 :numberToDigits (3 9 2 0). }; r:evidence ( - [ a r:Fact; r:gives {(2920 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2920 1000) math:remainder 920}] + [ a r:Fact; r:gives {(3920 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3920 1000) math:remainder 920}] [ a r:Fact; r:gives {(920 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(920 100) math:remainder 20}] [ a r:Fact; r:gives {(20 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(20 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2920]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3920]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 920]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 20]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3357 a r:Inference; +skolem:lemma6682 a r:Inference; r:gives { - 2921 :numberToDigits (2 9 2 1). + 3921 :numberToDigits (3 9 2 1). }; r:evidence ( - [ a r:Fact; r:gives {(2921 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2921 1000) math:remainder 921}] + [ a r:Fact; r:gives {(3921 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3921 1000) math:remainder 921}] [ a r:Fact; r:gives {(921 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(921 100) math:remainder 21}] [ a r:Fact; r:gives {(21 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(21 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2921]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3921]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 921]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 21]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3358 a r:Inference; +skolem:lemma6683 a r:Inference; r:gives { - 2922 :numberToDigits (2 9 2 2). + 3922 :numberToDigits (3 9 2 2). }; r:evidence ( - [ a r:Fact; r:gives {(2922 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2922 1000) math:remainder 922}] + [ a r:Fact; r:gives {(3922 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3922 1000) math:remainder 922}] [ a r:Fact; r:gives {(922 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(922 100) math:remainder 22}] [ a r:Fact; r:gives {(22 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(22 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2922]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3922]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 922]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 22]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3359 a r:Inference; +skolem:lemma6684 a r:Inference; r:gives { - 2923 :numberToDigits (2 9 2 3). + 3923 :numberToDigits (3 9 2 3). }; r:evidence ( - [ a r:Fact; r:gives {(2923 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2923 1000) math:remainder 923}] + [ a r:Fact; r:gives {(3923 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3923 1000) math:remainder 923}] [ a r:Fact; r:gives {(923 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(923 100) math:remainder 23}] [ a r:Fact; r:gives {(23 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(23 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2923]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3923]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 923]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 23]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3360 a r:Inference; +skolem:lemma6685 a r:Inference; r:gives { - 2924 :numberToDigits (2 9 2 4). + 3924 :numberToDigits (3 9 2 4). }; r:evidence ( - [ a r:Fact; r:gives {(2924 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2924 1000) math:remainder 924}] + [ a r:Fact; r:gives {(3924 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3924 1000) math:remainder 924}] [ a r:Fact; r:gives {(924 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(924 100) math:remainder 24}] [ a r:Fact; r:gives {(24 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(24 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2924]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3924]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 924]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 24]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3361 a r:Inference; +skolem:lemma6686 a r:Inference; r:gives { - 2925 :numberToDigits (2 9 2 5). + 3925 :numberToDigits (3 9 2 5). }; r:evidence ( - [ a r:Fact; r:gives {(2925 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2925 1000) math:remainder 925}] + [ a r:Fact; r:gives {(3925 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3925 1000) math:remainder 925}] [ a r:Fact; r:gives {(925 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(925 100) math:remainder 25}] [ a r:Fact; r:gives {(25 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(25 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2925]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3925]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 925]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 25]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3362 a r:Inference; +skolem:lemma6687 a r:Inference; r:gives { - 2926 :numberToDigits (2 9 2 6). + 3926 :numberToDigits (3 9 2 6). }; r:evidence ( - [ a r:Fact; r:gives {(2926 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2926 1000) math:remainder 926}] + [ a r:Fact; r:gives {(3926 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3926 1000) math:remainder 926}] [ a r:Fact; r:gives {(926 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(926 100) math:remainder 26}] [ a r:Fact; r:gives {(26 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(26 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2926]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3926]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 926]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 26]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3363 a r:Inference; +skolem:lemma6688 a r:Inference; r:gives { - 2927 :numberToDigits (2 9 2 7). + 3927 :numberToDigits (3 9 2 7). }; r:evidence ( - [ a r:Fact; r:gives {(2927 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2927 1000) math:remainder 927}] + [ a r:Fact; r:gives {(3927 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3927 1000) math:remainder 927}] [ a r:Fact; r:gives {(927 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(927 100) math:remainder 27}] [ a r:Fact; r:gives {(27 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(27 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2927]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3927]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 927]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 27]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3364 a r:Inference; +skolem:lemma6689 a r:Inference; r:gives { - 2928 :numberToDigits (2 9 2 8). + 3928 :numberToDigits (3 9 2 8). }; r:evidence ( - [ a r:Fact; r:gives {(2928 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2928 1000) math:remainder 928}] + [ a r:Fact; r:gives {(3928 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3928 1000) math:remainder 928}] [ a r:Fact; r:gives {(928 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(928 100) math:remainder 28}] [ a r:Fact; r:gives {(28 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(28 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2928]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3928]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 928]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 28]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3365 a r:Inference; +skolem:lemma6690 a r:Inference; r:gives { - 2929 :numberToDigits (2 9 2 9). + 3929 :numberToDigits (3 9 2 9). }; r:evidence ( - [ a r:Fact; r:gives {(2929 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2929 1000) math:remainder 929}] + [ a r:Fact; r:gives {(3929 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3929 1000) math:remainder 929}] [ a r:Fact; r:gives {(929 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(929 100) math:remainder 29}] [ a r:Fact; r:gives {(29 10) math:integerQuotient 2}] [ a r:Fact; r:gives {(29 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2929]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3929]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 929]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 29]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 2]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3366 a r:Inference; +skolem:lemma6691 a r:Inference; r:gives { - 2930 :numberToDigits (2 9 3 0). + 3930 :numberToDigits (3 9 3 0). }; r:evidence ( - [ a r:Fact; r:gives {(2930 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2930 1000) math:remainder 930}] + [ a r:Fact; r:gives {(3930 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3930 1000) math:remainder 930}] [ a r:Fact; r:gives {(930 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(930 100) math:remainder 30}] [ a r:Fact; r:gives {(30 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(30 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2930]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3930]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 930]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 30]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3367 a r:Inference; +skolem:lemma6692 a r:Inference; r:gives { - 2931 :numberToDigits (2 9 3 1). + 3931 :numberToDigits (3 9 3 1). }; r:evidence ( - [ a r:Fact; r:gives {(2931 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2931 1000) math:remainder 931}] + [ a r:Fact; r:gives {(3931 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3931 1000) math:remainder 931}] [ a r:Fact; r:gives {(931 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(931 100) math:remainder 31}] [ a r:Fact; r:gives {(31 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(31 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2931]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3931]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 931]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 31]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3368 a r:Inference; +skolem:lemma6693 a r:Inference; r:gives { - 2932 :numberToDigits (2 9 3 2). + 3932 :numberToDigits (3 9 3 2). }; r:evidence ( - [ a r:Fact; r:gives {(2932 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2932 1000) math:remainder 932}] + [ a r:Fact; r:gives {(3932 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3932 1000) math:remainder 932}] [ a r:Fact; r:gives {(932 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(932 100) math:remainder 32}] [ a r:Fact; r:gives {(32 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(32 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2932]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3932]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 932]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 32]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3369 a r:Inference; +skolem:lemma6694 a r:Inference; r:gives { - 2933 :numberToDigits (2 9 3 3). + 3933 :numberToDigits (3 9 3 3). }; r:evidence ( - [ a r:Fact; r:gives {(2933 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2933 1000) math:remainder 933}] + [ a r:Fact; r:gives {(3933 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3933 1000) math:remainder 933}] [ a r:Fact; r:gives {(933 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(933 100) math:remainder 33}] [ a r:Fact; r:gives {(33 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(33 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2933]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3933]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 933]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 33]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3370 a r:Inference; +skolem:lemma6695 a r:Inference; r:gives { - 2934 :numberToDigits (2 9 3 4). + 3934 :numberToDigits (3 9 3 4). }; r:evidence ( - [ a r:Fact; r:gives {(2934 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2934 1000) math:remainder 934}] + [ a r:Fact; r:gives {(3934 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3934 1000) math:remainder 934}] [ a r:Fact; r:gives {(934 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(934 100) math:remainder 34}] [ a r:Fact; r:gives {(34 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(34 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2934]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3934]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 934]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 34]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3371 a r:Inference; +skolem:lemma6696 a r:Inference; r:gives { - 2935 :numberToDigits (2 9 3 5). + 3935 :numberToDigits (3 9 3 5). }; r:evidence ( - [ a r:Fact; r:gives {(2935 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2935 1000) math:remainder 935}] + [ a r:Fact; r:gives {(3935 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3935 1000) math:remainder 935}] [ a r:Fact; r:gives {(935 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(935 100) math:remainder 35}] [ a r:Fact; r:gives {(35 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(35 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2935]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3935]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 935]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 35]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3372 a r:Inference; +skolem:lemma6697 a r:Inference; r:gives { - 2936 :numberToDigits (2 9 3 6). + 3936 :numberToDigits (3 9 3 6). }; r:evidence ( - [ a r:Fact; r:gives {(2936 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2936 1000) math:remainder 936}] + [ a r:Fact; r:gives {(3936 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3936 1000) math:remainder 936}] [ a r:Fact; r:gives {(936 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(936 100) math:remainder 36}] [ a r:Fact; r:gives {(36 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(36 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2936]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3936]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 936]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 36]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3373 a r:Inference; +skolem:lemma6698 a r:Inference; r:gives { - 2937 :numberToDigits (2 9 3 7). + 3937 :numberToDigits (3 9 3 7). }; r:evidence ( - [ a r:Fact; r:gives {(2937 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2937 1000) math:remainder 937}] + [ a r:Fact; r:gives {(3937 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3937 1000) math:remainder 937}] [ a r:Fact; r:gives {(937 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(937 100) math:remainder 37}] [ a r:Fact; r:gives {(37 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(37 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2937]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3937]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 937]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 37]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3374 a r:Inference; +skolem:lemma6699 a r:Inference; r:gives { - 2938 :numberToDigits (2 9 3 8). + 3938 :numberToDigits (3 9 3 8). }; r:evidence ( - [ a r:Fact; r:gives {(2938 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2938 1000) math:remainder 938}] + [ a r:Fact; r:gives {(3938 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3938 1000) math:remainder 938}] [ a r:Fact; r:gives {(938 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(938 100) math:remainder 38}] [ a r:Fact; r:gives {(38 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(38 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2938]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3938]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 938]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 38]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3375 a r:Inference; +skolem:lemma6700 a r:Inference; r:gives { - 2939 :numberToDigits (2 9 3 9). + 3939 :numberToDigits (3 9 3 9). }; r:evidence ( - [ a r:Fact; r:gives {(2939 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2939 1000) math:remainder 939}] + [ a r:Fact; r:gives {(3939 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3939 1000) math:remainder 939}] [ a r:Fact; r:gives {(939 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(939 100) math:remainder 39}] [ a r:Fact; r:gives {(39 10) math:integerQuotient 3}] [ a r:Fact; r:gives {(39 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2939]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3939]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 939]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 39]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3376 a r:Inference; +skolem:lemma6701 a r:Inference; r:gives { - 2940 :numberToDigits (2 9 4 0). + 3940 :numberToDigits (3 9 4 0). }; r:evidence ( - [ a r:Fact; r:gives {(2940 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2940 1000) math:remainder 940}] + [ a r:Fact; r:gives {(3940 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3940 1000) math:remainder 940}] [ a r:Fact; r:gives {(940 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(940 100) math:remainder 40}] [ a r:Fact; r:gives {(40 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(40 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2940]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3940]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 940]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 40]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3377 a r:Inference; +skolem:lemma6702 a r:Inference; r:gives { - 2941 :numberToDigits (2 9 4 1). + 3941 :numberToDigits (3 9 4 1). }; r:evidence ( - [ a r:Fact; r:gives {(2941 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2941 1000) math:remainder 941}] + [ a r:Fact; r:gives {(3941 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3941 1000) math:remainder 941}] [ a r:Fact; r:gives {(941 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(941 100) math:remainder 41}] [ a r:Fact; r:gives {(41 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(41 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2941]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3941]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 941]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 41]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3378 a r:Inference; +skolem:lemma6703 a r:Inference; r:gives { - 2942 :numberToDigits (2 9 4 2). + 3942 :numberToDigits (3 9 4 2). }; r:evidence ( - [ a r:Fact; r:gives {(2942 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2942 1000) math:remainder 942}] + [ a r:Fact; r:gives {(3942 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3942 1000) math:remainder 942}] [ a r:Fact; r:gives {(942 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(942 100) math:remainder 42}] [ a r:Fact; r:gives {(42 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(42 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2942]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3942]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 942]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 42]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3379 a r:Inference; +skolem:lemma6704 a r:Inference; r:gives { - 2943 :numberToDigits (2 9 4 3). + 3943 :numberToDigits (3 9 4 3). }; r:evidence ( - [ a r:Fact; r:gives {(2943 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2943 1000) math:remainder 943}] + [ a r:Fact; r:gives {(3943 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3943 1000) math:remainder 943}] [ a r:Fact; r:gives {(943 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(943 100) math:remainder 43}] [ a r:Fact; r:gives {(43 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(43 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2943]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3943]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 943]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 43]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3380 a r:Inference; +skolem:lemma6705 a r:Inference; r:gives { - 2944 :numberToDigits (2 9 4 4). + 3944 :numberToDigits (3 9 4 4). }; r:evidence ( - [ a r:Fact; r:gives {(2944 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2944 1000) math:remainder 944}] + [ a r:Fact; r:gives {(3944 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3944 1000) math:remainder 944}] [ a r:Fact; r:gives {(944 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(944 100) math:remainder 44}] [ a r:Fact; r:gives {(44 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(44 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2944]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3944]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 944]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 44]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3381 a r:Inference; +skolem:lemma6706 a r:Inference; r:gives { - 2945 :numberToDigits (2 9 4 5). + 3945 :numberToDigits (3 9 4 5). }; r:evidence ( - [ a r:Fact; r:gives {(2945 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2945 1000) math:remainder 945}] + [ a r:Fact; r:gives {(3945 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3945 1000) math:remainder 945}] [ a r:Fact; r:gives {(945 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(945 100) math:remainder 45}] [ a r:Fact; r:gives {(45 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(45 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2945]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3945]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 945]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 45]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3382 a r:Inference; +skolem:lemma6707 a r:Inference; r:gives { - 2946 :numberToDigits (2 9 4 6). + 3946 :numberToDigits (3 9 4 6). }; r:evidence ( - [ a r:Fact; r:gives {(2946 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2946 1000) math:remainder 946}] + [ a r:Fact; r:gives {(3946 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3946 1000) math:remainder 946}] [ a r:Fact; r:gives {(946 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(946 100) math:remainder 46}] [ a r:Fact; r:gives {(46 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(46 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2946]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3946]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 946]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 46]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3383 a r:Inference; +skolem:lemma6708 a r:Inference; r:gives { - 2947 :numberToDigits (2 9 4 7). + 3947 :numberToDigits (3 9 4 7). }; r:evidence ( - [ a r:Fact; r:gives {(2947 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2947 1000) math:remainder 947}] + [ a r:Fact; r:gives {(3947 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3947 1000) math:remainder 947}] [ a r:Fact; r:gives {(947 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(947 100) math:remainder 47}] [ a r:Fact; r:gives {(47 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(47 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2947]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3947]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 947]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 47]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3384 a r:Inference; +skolem:lemma6709 a r:Inference; r:gives { - 2948 :numberToDigits (2 9 4 8). + 3948 :numberToDigits (3 9 4 8). }; r:evidence ( - [ a r:Fact; r:gives {(2948 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2948 1000) math:remainder 948}] + [ a r:Fact; r:gives {(3948 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3948 1000) math:remainder 948}] [ a r:Fact; r:gives {(948 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(948 100) math:remainder 48}] [ a r:Fact; r:gives {(48 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(48 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2948]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3948]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 948]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 48]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3385 a r:Inference; +skolem:lemma6710 a r:Inference; r:gives { - 2949 :numberToDigits (2 9 4 9). + 3949 :numberToDigits (3 9 4 9). }; r:evidence ( - [ a r:Fact; r:gives {(2949 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2949 1000) math:remainder 949}] + [ a r:Fact; r:gives {(3949 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3949 1000) math:remainder 949}] [ a r:Fact; r:gives {(949 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(949 100) math:remainder 49}] [ a r:Fact; r:gives {(49 10) math:integerQuotient 4}] [ a r:Fact; r:gives {(49 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2949]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3949]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 949]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 49]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 4]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3386 a r:Inference; +skolem:lemma6711 a r:Inference; r:gives { - 2950 :numberToDigits (2 9 5 0). + 3950 :numberToDigits (3 9 5 0). }; r:evidence ( - [ a r:Fact; r:gives {(2950 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2950 1000) math:remainder 950}] + [ a r:Fact; r:gives {(3950 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3950 1000) math:remainder 950}] [ a r:Fact; r:gives {(950 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(950 100) math:remainder 50}] [ a r:Fact; r:gives {(50 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(50 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2950]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3950]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 950]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 50]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3387 a r:Inference; +skolem:lemma6712 a r:Inference; r:gives { - 2951 :numberToDigits (2 9 5 1). + 3951 :numberToDigits (3 9 5 1). }; r:evidence ( - [ a r:Fact; r:gives {(2951 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2951 1000) math:remainder 951}] + [ a r:Fact; r:gives {(3951 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3951 1000) math:remainder 951}] [ a r:Fact; r:gives {(951 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(951 100) math:remainder 51}] [ a r:Fact; r:gives {(51 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(51 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2951]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3951]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 951]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 51]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3388 a r:Inference; +skolem:lemma6713 a r:Inference; r:gives { - 2952 :numberToDigits (2 9 5 2). + 3952 :numberToDigits (3 9 5 2). }; r:evidence ( - [ a r:Fact; r:gives {(2952 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2952 1000) math:remainder 952}] + [ a r:Fact; r:gives {(3952 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3952 1000) math:remainder 952}] [ a r:Fact; r:gives {(952 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(952 100) math:remainder 52}] [ a r:Fact; r:gives {(52 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(52 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2952]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3952]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 952]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 52]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3389 a r:Inference; +skolem:lemma6714 a r:Inference; r:gives { - 2953 :numberToDigits (2 9 5 3). + 3953 :numberToDigits (3 9 5 3). }; r:evidence ( - [ a r:Fact; r:gives {(2953 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2953 1000) math:remainder 953}] + [ a r:Fact; r:gives {(3953 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3953 1000) math:remainder 953}] [ a r:Fact; r:gives {(953 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(953 100) math:remainder 53}] [ a r:Fact; r:gives {(53 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(53 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2953]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3953]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 953]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 53]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3390 a r:Inference; +skolem:lemma6715 a r:Inference; r:gives { - 2954 :numberToDigits (2 9 5 4). + 3954 :numberToDigits (3 9 5 4). }; r:evidence ( - [ a r:Fact; r:gives {(2954 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2954 1000) math:remainder 954}] + [ a r:Fact; r:gives {(3954 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3954 1000) math:remainder 954}] [ a r:Fact; r:gives {(954 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(954 100) math:remainder 54}] [ a r:Fact; r:gives {(54 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(54 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2954]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3954]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 954]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 54]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3391 a r:Inference; +skolem:lemma6716 a r:Inference; r:gives { - 2955 :numberToDigits (2 9 5 5). + 3955 :numberToDigits (3 9 5 5). }; r:evidence ( - [ a r:Fact; r:gives {(2955 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2955 1000) math:remainder 955}] + [ a r:Fact; r:gives {(3955 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3955 1000) math:remainder 955}] [ a r:Fact; r:gives {(955 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(955 100) math:remainder 55}] [ a r:Fact; r:gives {(55 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(55 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2955]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3955]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 955]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 55]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3392 a r:Inference; +skolem:lemma6717 a r:Inference; r:gives { - 2956 :numberToDigits (2 9 5 6). + 3956 :numberToDigits (3 9 5 6). }; r:evidence ( - [ a r:Fact; r:gives {(2956 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2956 1000) math:remainder 956}] + [ a r:Fact; r:gives {(3956 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3956 1000) math:remainder 956}] [ a r:Fact; r:gives {(956 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(956 100) math:remainder 56}] [ a r:Fact; r:gives {(56 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(56 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2956]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3956]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 956]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 56]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3393 a r:Inference; +skolem:lemma6718 a r:Inference; r:gives { - 2957 :numberToDigits (2 9 5 7). + 3957 :numberToDigits (3 9 5 7). }; r:evidence ( - [ a r:Fact; r:gives {(2957 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2957 1000) math:remainder 957}] + [ a r:Fact; r:gives {(3957 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3957 1000) math:remainder 957}] [ a r:Fact; r:gives {(957 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(957 100) math:remainder 57}] [ a r:Fact; r:gives {(57 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(57 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2957]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3957]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 957]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 57]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3394 a r:Inference; +skolem:lemma6719 a r:Inference; r:gives { - 2958 :numberToDigits (2 9 5 8). + 3958 :numberToDigits (3 9 5 8). }; r:evidence ( - [ a r:Fact; r:gives {(2958 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2958 1000) math:remainder 958}] + [ a r:Fact; r:gives {(3958 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3958 1000) math:remainder 958}] [ a r:Fact; r:gives {(958 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(958 100) math:remainder 58}] [ a r:Fact; r:gives {(58 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(58 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2958]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3958]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 958]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 58]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3395 a r:Inference; +skolem:lemma6720 a r:Inference; r:gives { - 2959 :numberToDigits (2 9 5 9). + 3959 :numberToDigits (3 9 5 9). }; r:evidence ( - [ a r:Fact; r:gives {(2959 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2959 1000) math:remainder 959}] + [ a r:Fact; r:gives {(3959 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3959 1000) math:remainder 959}] [ a r:Fact; r:gives {(959 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(959 100) math:remainder 59}] [ a r:Fact; r:gives {(59 10) math:integerQuotient 5}] [ a r:Fact; r:gives {(59 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2959]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3959]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 959]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 59]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 5]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3396 a r:Inference; +skolem:lemma6721 a r:Inference; r:gives { - 2960 :numberToDigits (2 9 6 0). + 3960 :numberToDigits (3 9 6 0). }; r:evidence ( - [ a r:Fact; r:gives {(2960 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2960 1000) math:remainder 960}] + [ a r:Fact; r:gives {(3960 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3960 1000) math:remainder 960}] [ a r:Fact; r:gives {(960 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(960 100) math:remainder 60}] [ a r:Fact; r:gives {(60 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(60 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2960]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3960]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 960]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 60]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3397 a r:Inference; +skolem:lemma6722 a r:Inference; r:gives { - 2961 :numberToDigits (2 9 6 1). + 3961 :numberToDigits (3 9 6 1). }; r:evidence ( - [ a r:Fact; r:gives {(2961 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2961 1000) math:remainder 961}] + [ a r:Fact; r:gives {(3961 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3961 1000) math:remainder 961}] [ a r:Fact; r:gives {(961 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(961 100) math:remainder 61}] [ a r:Fact; r:gives {(61 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(61 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2961]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3961]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 961]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 61]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3398 a r:Inference; +skolem:lemma6723 a r:Inference; r:gives { - 2962 :numberToDigits (2 9 6 2). + 3962 :numberToDigits (3 9 6 2). }; r:evidence ( - [ a r:Fact; r:gives {(2962 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2962 1000) math:remainder 962}] + [ a r:Fact; r:gives {(3962 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3962 1000) math:remainder 962}] [ a r:Fact; r:gives {(962 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(962 100) math:remainder 62}] [ a r:Fact; r:gives {(62 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(62 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2962]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3962]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 962]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 62]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3399 a r:Inference; +skolem:lemma6724 a r:Inference; r:gives { - 2963 :numberToDigits (2 9 6 3). + 3963 :numberToDigits (3 9 6 3). }; r:evidence ( - [ a r:Fact; r:gives {(2963 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2963 1000) math:remainder 963}] + [ a r:Fact; r:gives {(3963 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3963 1000) math:remainder 963}] [ a r:Fact; r:gives {(963 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(963 100) math:remainder 63}] [ a r:Fact; r:gives {(63 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(63 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2963]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3963]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 963]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 63]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3400 a r:Inference; +skolem:lemma6725 a r:Inference; r:gives { - 2964 :numberToDigits (2 9 6 4). + 3964 :numberToDigits (3 9 6 4). }; r:evidence ( - [ a r:Fact; r:gives {(2964 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2964 1000) math:remainder 964}] + [ a r:Fact; r:gives {(3964 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3964 1000) math:remainder 964}] [ a r:Fact; r:gives {(964 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(964 100) math:remainder 64}] [ a r:Fact; r:gives {(64 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(64 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2964]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3964]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 964]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 64]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3401 a r:Inference; +skolem:lemma6726 a r:Inference; r:gives { - 2965 :numberToDigits (2 9 6 5). + 3965 :numberToDigits (3 9 6 5). }; r:evidence ( - [ a r:Fact; r:gives {(2965 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2965 1000) math:remainder 965}] + [ a r:Fact; r:gives {(3965 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3965 1000) math:remainder 965}] [ a r:Fact; r:gives {(965 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(965 100) math:remainder 65}] [ a r:Fact; r:gives {(65 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(65 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2965]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3965]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 965]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 65]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3402 a r:Inference; +skolem:lemma6727 a r:Inference; r:gives { - 2966 :numberToDigits (2 9 6 6). + 3966 :numberToDigits (3 9 6 6). }; r:evidence ( - [ a r:Fact; r:gives {(2966 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2966 1000) math:remainder 966}] + [ a r:Fact; r:gives {(3966 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3966 1000) math:remainder 966}] [ a r:Fact; r:gives {(966 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(966 100) math:remainder 66}] [ a r:Fact; r:gives {(66 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(66 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2966]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3966]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 966]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 66]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3403 a r:Inference; +skolem:lemma6728 a r:Inference; r:gives { - 2967 :numberToDigits (2 9 6 7). + 3967 :numberToDigits (3 9 6 7). }; r:evidence ( - [ a r:Fact; r:gives {(2967 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2967 1000) math:remainder 967}] + [ a r:Fact; r:gives {(3967 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3967 1000) math:remainder 967}] [ a r:Fact; r:gives {(967 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(967 100) math:remainder 67}] [ a r:Fact; r:gives {(67 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(67 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2967]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3967]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 967]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 67]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3404 a r:Inference; +skolem:lemma6729 a r:Inference; r:gives { - 2968 :numberToDigits (2 9 6 8). + 3968 :numberToDigits (3 9 6 8). }; r:evidence ( - [ a r:Fact; r:gives {(2968 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2968 1000) math:remainder 968}] + [ a r:Fact; r:gives {(3968 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3968 1000) math:remainder 968}] [ a r:Fact; r:gives {(968 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(968 100) math:remainder 68}] [ a r:Fact; r:gives {(68 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(68 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2968]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3968]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 968]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 68]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3405 a r:Inference; +skolem:lemma6730 a r:Inference; r:gives { - 2969 :numberToDigits (2 9 6 9). + 3969 :numberToDigits (3 9 6 9). }; r:evidence ( - [ a r:Fact; r:gives {(2969 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2969 1000) math:remainder 969}] + [ a r:Fact; r:gives {(3969 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3969 1000) math:remainder 969}] [ a r:Fact; r:gives {(969 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(969 100) math:remainder 69}] [ a r:Fact; r:gives {(69 10) math:integerQuotient 6}] [ a r:Fact; r:gives {(69 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2969]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3969]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 969]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 69]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 6]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3406 a r:Inference; +skolem:lemma6731 a r:Inference; r:gives { - 2970 :numberToDigits (2 9 7 0). + 3970 :numberToDigits (3 9 7 0). }; r:evidence ( - [ a r:Fact; r:gives {(2970 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2970 1000) math:remainder 970}] + [ a r:Fact; r:gives {(3970 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3970 1000) math:remainder 970}] [ a r:Fact; r:gives {(970 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(970 100) math:remainder 70}] [ a r:Fact; r:gives {(70 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(70 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2970]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3970]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 970]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 70]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3407 a r:Inference; +skolem:lemma6732 a r:Inference; r:gives { - 2971 :numberToDigits (2 9 7 1). + 3971 :numberToDigits (3 9 7 1). }; r:evidence ( - [ a r:Fact; r:gives {(2971 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2971 1000) math:remainder 971}] + [ a r:Fact; r:gives {(3971 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3971 1000) math:remainder 971}] [ a r:Fact; r:gives {(971 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(971 100) math:remainder 71}] [ a r:Fact; r:gives {(71 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(71 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2971]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3971]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 971]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 71]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3408 a r:Inference; +skolem:lemma6733 a r:Inference; r:gives { - 2972 :numberToDigits (2 9 7 2). + 3972 :numberToDigits (3 9 7 2). }; r:evidence ( - [ a r:Fact; r:gives {(2972 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2972 1000) math:remainder 972}] + [ a r:Fact; r:gives {(3972 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3972 1000) math:remainder 972}] [ a r:Fact; r:gives {(972 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(972 100) math:remainder 72}] [ a r:Fact; r:gives {(72 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(72 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2972]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3972]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 972]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 72]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3409 a r:Inference; +skolem:lemma6734 a r:Inference; r:gives { - 2973 :numberToDigits (2 9 7 3). + 3973 :numberToDigits (3 9 7 3). }; r:evidence ( - [ a r:Fact; r:gives {(2973 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2973 1000) math:remainder 973}] + [ a r:Fact; r:gives {(3973 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3973 1000) math:remainder 973}] [ a r:Fact; r:gives {(973 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(973 100) math:remainder 73}] [ a r:Fact; r:gives {(73 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(73 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2973]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3973]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 973]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 73]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3410 a r:Inference; +skolem:lemma6735 a r:Inference; r:gives { - 2974 :numberToDigits (2 9 7 4). + 3974 :numberToDigits (3 9 7 4). }; r:evidence ( - [ a r:Fact; r:gives {(2974 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2974 1000) math:remainder 974}] + [ a r:Fact; r:gives {(3974 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3974 1000) math:remainder 974}] [ a r:Fact; r:gives {(974 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(974 100) math:remainder 74}] [ a r:Fact; r:gives {(74 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(74 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2974]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3974]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 974]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 74]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3411 a r:Inference; +skolem:lemma6736 a r:Inference; r:gives { - 2975 :numberToDigits (2 9 7 5). + 3975 :numberToDigits (3 9 7 5). }; r:evidence ( - [ a r:Fact; r:gives {(2975 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2975 1000) math:remainder 975}] + [ a r:Fact; r:gives {(3975 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3975 1000) math:remainder 975}] [ a r:Fact; r:gives {(975 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(975 100) math:remainder 75}] [ a r:Fact; r:gives {(75 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(75 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2975]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3975]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 975]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 75]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3412 a r:Inference; +skolem:lemma6737 a r:Inference; r:gives { - 2976 :numberToDigits (2 9 7 6). + 3976 :numberToDigits (3 9 7 6). }; r:evidence ( - [ a r:Fact; r:gives {(2976 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2976 1000) math:remainder 976}] + [ a r:Fact; r:gives {(3976 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3976 1000) math:remainder 976}] [ a r:Fact; r:gives {(976 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(976 100) math:remainder 76}] [ a r:Fact; r:gives {(76 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(76 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2976]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3976]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 976]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 76]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3413 a r:Inference; +skolem:lemma6738 a r:Inference; r:gives { - 2977 :numberToDigits (2 9 7 7). + 3977 :numberToDigits (3 9 7 7). }; r:evidence ( - [ a r:Fact; r:gives {(2977 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2977 1000) math:remainder 977}] + [ a r:Fact; r:gives {(3977 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3977 1000) math:remainder 977}] [ a r:Fact; r:gives {(977 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(977 100) math:remainder 77}] [ a r:Fact; r:gives {(77 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(77 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2977]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3977]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 977]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 77]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3414 a r:Inference; +skolem:lemma6739 a r:Inference; r:gives { - 2978 :numberToDigits (2 9 7 8). + 3978 :numberToDigits (3 9 7 8). }; r:evidence ( - [ a r:Fact; r:gives {(2978 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2978 1000) math:remainder 978}] + [ a r:Fact; r:gives {(3978 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3978 1000) math:remainder 978}] [ a r:Fact; r:gives {(978 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(978 100) math:remainder 78}] [ a r:Fact; r:gives {(78 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(78 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2978]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3978]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 978]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 78]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3415 a r:Inference; +skolem:lemma6740 a r:Inference; r:gives { - 2979 :numberToDigits (2 9 7 9). + 3979 :numberToDigits (3 9 7 9). }; r:evidence ( - [ a r:Fact; r:gives {(2979 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2979 1000) math:remainder 979}] + [ a r:Fact; r:gives {(3979 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3979 1000) math:remainder 979}] [ a r:Fact; r:gives {(979 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(979 100) math:remainder 79}] [ a r:Fact; r:gives {(79 10) math:integerQuotient 7}] [ a r:Fact; r:gives {(79 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2979]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3979]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 979]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 79]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 7]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3416 a r:Inference; +skolem:lemma6741 a r:Inference; r:gives { - 2980 :numberToDigits (2 9 8 0). + 3980 :numberToDigits (3 9 8 0). }; r:evidence ( - [ a r:Fact; r:gives {(2980 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2980 1000) math:remainder 980}] + [ a r:Fact; r:gives {(3980 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3980 1000) math:remainder 980}] [ a r:Fact; r:gives {(980 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(980 100) math:remainder 80}] [ a r:Fact; r:gives {(80 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(80 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2980]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3980]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 980]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 80]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3417 a r:Inference; +skolem:lemma6742 a r:Inference; r:gives { - 2981 :numberToDigits (2 9 8 1). + 3981 :numberToDigits (3 9 8 1). }; r:evidence ( - [ a r:Fact; r:gives {(2981 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2981 1000) math:remainder 981}] + [ a r:Fact; r:gives {(3981 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3981 1000) math:remainder 981}] [ a r:Fact; r:gives {(981 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(981 100) math:remainder 81}] [ a r:Fact; r:gives {(81 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(81 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2981]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3981]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 981]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 81]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3418 a r:Inference; +skolem:lemma6743 a r:Inference; r:gives { - 2982 :numberToDigits (2 9 8 2). + 3982 :numberToDigits (3 9 8 2). }; r:evidence ( - [ a r:Fact; r:gives {(2982 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2982 1000) math:remainder 982}] + [ a r:Fact; r:gives {(3982 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3982 1000) math:remainder 982}] [ a r:Fact; r:gives {(982 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(982 100) math:remainder 82}] [ a r:Fact; r:gives {(82 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(82 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2982]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3982]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 982]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 82]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3419 a r:Inference; +skolem:lemma6744 a r:Inference; r:gives { - 2983 :numberToDigits (2 9 8 3). + 3983 :numberToDigits (3 9 8 3). }; r:evidence ( - [ a r:Fact; r:gives {(2983 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2983 1000) math:remainder 983}] + [ a r:Fact; r:gives {(3983 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3983 1000) math:remainder 983}] [ a r:Fact; r:gives {(983 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(983 100) math:remainder 83}] [ a r:Fact; r:gives {(83 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(83 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2983]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3983]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 983]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 83]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3420 a r:Inference; +skolem:lemma6745 a r:Inference; r:gives { - 2984 :numberToDigits (2 9 8 4). + 3984 :numberToDigits (3 9 8 4). }; r:evidence ( - [ a r:Fact; r:gives {(2984 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2984 1000) math:remainder 984}] + [ a r:Fact; r:gives {(3984 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3984 1000) math:remainder 984}] [ a r:Fact; r:gives {(984 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(984 100) math:remainder 84}] [ a r:Fact; r:gives {(84 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(84 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2984]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3984]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 984]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 84]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3421 a r:Inference; +skolem:lemma6746 a r:Inference; r:gives { - 2985 :numberToDigits (2 9 8 5). + 3985 :numberToDigits (3 9 8 5). }; r:evidence ( - [ a r:Fact; r:gives {(2985 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2985 1000) math:remainder 985}] + [ a r:Fact; r:gives {(3985 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3985 1000) math:remainder 985}] [ a r:Fact; r:gives {(985 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(985 100) math:remainder 85}] [ a r:Fact; r:gives {(85 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(85 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2985]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3985]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 985]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 85]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3422 a r:Inference; +skolem:lemma6747 a r:Inference; r:gives { - 2986 :numberToDigits (2 9 8 6). + 3986 :numberToDigits (3 9 8 6). }; r:evidence ( - [ a r:Fact; r:gives {(2986 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2986 1000) math:remainder 986}] + [ a r:Fact; r:gives {(3986 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3986 1000) math:remainder 986}] [ a r:Fact; r:gives {(986 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(986 100) math:remainder 86}] [ a r:Fact; r:gives {(86 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(86 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2986]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3986]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 986]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 86]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3423 a r:Inference; +skolem:lemma6748 a r:Inference; r:gives { - 2987 :numberToDigits (2 9 8 7). + 3987 :numberToDigits (3 9 8 7). }; r:evidence ( - [ a r:Fact; r:gives {(2987 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2987 1000) math:remainder 987}] + [ a r:Fact; r:gives {(3987 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3987 1000) math:remainder 987}] [ a r:Fact; r:gives {(987 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(987 100) math:remainder 87}] [ a r:Fact; r:gives {(87 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(87 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2987]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3987]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 987]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 87]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3424 a r:Inference; +skolem:lemma6749 a r:Inference; r:gives { - 2988 :numberToDigits (2 9 8 8). + 3988 :numberToDigits (3 9 8 8). }; r:evidence ( - [ a r:Fact; r:gives {(2988 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2988 1000) math:remainder 988}] + [ a r:Fact; r:gives {(3988 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3988 1000) math:remainder 988}] [ a r:Fact; r:gives {(988 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(988 100) math:remainder 88}] [ a r:Fact; r:gives {(88 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(88 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2988]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3988]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 988]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 88]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3425 a r:Inference; +skolem:lemma6750 a r:Inference; r:gives { - 2989 :numberToDigits (2 9 8 9). + 3989 :numberToDigits (3 9 8 9). }; r:evidence ( - [ a r:Fact; r:gives {(2989 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2989 1000) math:remainder 989}] + [ a r:Fact; r:gives {(3989 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3989 1000) math:remainder 989}] [ a r:Fact; r:gives {(989 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(989 100) math:remainder 89}] [ a r:Fact; r:gives {(89 10) math:integerQuotient 8}] [ a r:Fact; r:gives {(89 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2989]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3989]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 989]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 89]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 8]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3426 a r:Inference; +skolem:lemma6751 a r:Inference; r:gives { - 2990 :numberToDigits (2 9 9 0). + 3990 :numberToDigits (3 9 9 0). }; r:evidence ( - [ a r:Fact; r:gives {(2990 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2990 1000) math:remainder 990}] + [ a r:Fact; r:gives {(3990 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3990 1000) math:remainder 990}] [ a r:Fact; r:gives {(990 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(990 100) math:remainder 90}] [ a r:Fact; r:gives {(90 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(90 10) math:remainder 0}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2990]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3990]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 990]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 90]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 0]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3427 a r:Inference; +skolem:lemma6752 a r:Inference; r:gives { - 2991 :numberToDigits (2 9 9 1). + 3991 :numberToDigits (3 9 9 1). }; r:evidence ( - [ a r:Fact; r:gives {(2991 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2991 1000) math:remainder 991}] + [ a r:Fact; r:gives {(3991 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3991 1000) math:remainder 991}] [ a r:Fact; r:gives {(991 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(991 100) math:remainder 91}] [ a r:Fact; r:gives {(91 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(91 10) math:remainder 1}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2991]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3991]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 991]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 91]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 1]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3428 a r:Inference; +skolem:lemma6753 a r:Inference; r:gives { - 2992 :numberToDigits (2 9 9 2). + 3992 :numberToDigits (3 9 9 2). }; r:evidence ( - [ a r:Fact; r:gives {(2992 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2992 1000) math:remainder 992}] + [ a r:Fact; r:gives {(3992 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3992 1000) math:remainder 992}] [ a r:Fact; r:gives {(992 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(992 100) math:remainder 92}] [ a r:Fact; r:gives {(92 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(92 10) math:remainder 2}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2992]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3992]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 992]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 92]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3429 a r:Inference; +skolem:lemma6754 a r:Inference; r:gives { - 2993 :numberToDigits (2 9 9 3). + 3993 :numberToDigits (3 9 9 3). }; r:evidence ( - [ a r:Fact; r:gives {(2993 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2993 1000) math:remainder 993}] + [ a r:Fact; r:gives {(3993 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3993 1000) math:remainder 993}] [ a r:Fact; r:gives {(993 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(993 100) math:remainder 93}] [ a r:Fact; r:gives {(93 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(93 10) math:remainder 3}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3993]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 993]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 93]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3430 a r:Inference; +skolem:lemma6755 a r:Inference; r:gives { - 2994 :numberToDigits (2 9 9 4). + 3994 :numberToDigits (3 9 9 4). }; r:evidence ( - [ a r:Fact; r:gives {(2994 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2994 1000) math:remainder 994}] + [ a r:Fact; r:gives {(3994 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3994 1000) math:remainder 994}] [ a r:Fact; r:gives {(994 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(994 100) math:remainder 94}] [ a r:Fact; r:gives {(94 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(94 10) math:remainder 4}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2994]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3994]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 994]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 94]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 4]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3431 a r:Inference; +skolem:lemma6756 a r:Inference; r:gives { - 2995 :numberToDigits (2 9 9 5). + 3995 :numberToDigits (3 9 9 5). }; r:evidence ( - [ a r:Fact; r:gives {(2995 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2995 1000) math:remainder 995}] + [ a r:Fact; r:gives {(3995 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3995 1000) math:remainder 995}] [ a r:Fact; r:gives {(995 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(995 100) math:remainder 95}] [ a r:Fact; r:gives {(95 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(95 10) math:remainder 5}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2995]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3995]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 995]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 95]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 5]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3432 a r:Inference; +skolem:lemma6757 a r:Inference; r:gives { - 2996 :numberToDigits (2 9 9 6). + 3996 :numberToDigits (3 9 9 6). }; r:evidence ( - [ a r:Fact; r:gives {(2996 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2996 1000) math:remainder 996}] + [ a r:Fact; r:gives {(3996 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3996 1000) math:remainder 996}] [ a r:Fact; r:gives {(996 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(996 100) math:remainder 96}] [ a r:Fact; r:gives {(96 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(96 10) math:remainder 6}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2996]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3996]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 996]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 96]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 6]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3433 a r:Inference; +skolem:lemma6758 a r:Inference; r:gives { - 2997 :numberToDigits (2 9 9 7). + 3997 :numberToDigits (3 9 9 7). }; r:evidence ( - [ a r:Fact; r:gives {(2997 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2997 1000) math:remainder 997}] + [ a r:Fact; r:gives {(3997 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3997 1000) math:remainder 997}] [ a r:Fact; r:gives {(997 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(997 100) math:remainder 97}] [ a r:Fact; r:gives {(97 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(97 10) math:remainder 7}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2997]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3997]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 997]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 97]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 7]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3434 a r:Inference; +skolem:lemma6759 a r:Inference; r:gives { - 2998 :numberToDigits (2 9 9 8). + 3998 :numberToDigits (3 9 9 8). }; r:evidence ( - [ a r:Fact; r:gives {(2998 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2998 1000) math:remainder 998}] + [ a r:Fact; r:gives {(3998 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3998 1000) math:remainder 998}] [ a r:Fact; r:gives {(998 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(998 100) math:remainder 98}] [ a r:Fact; r:gives {(98 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(98 10) math:remainder 8}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2998]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3998]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 998]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 98]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 8]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3435 a r:Inference; +skolem:lemma6760 a r:Inference; r:gives { - 2999 :numberToDigits (2 9 9 9). + 3999 :numberToDigits (3 9 9 9). }; r:evidence ( - [ a r:Fact; r:gives {(2999 1000) math:integerQuotient 2}] - [ a r:Fact; r:gives {(2999 1000) math:remainder 999}] + [ a r:Fact; r:gives {(3999 1000) math:integerQuotient 3}] + [ a r:Fact; r:gives {(3999 1000) math:remainder 999}] [ a r:Fact; r:gives {(999 100) math:integerQuotient 9}] [ a r:Fact; r:gives {(999 100) math:remainder 99}] [ a r:Fact; r:gives {(99 10) math:integerQuotient 9}] [ a r:Fact; r:gives {(99 10) math:remainder 9}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3999]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 999]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 99]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3438. + r:rule skolem:lemma6763. -skolem:lemma3436 a r:Inference; +skolem:lemma6761 a r:Inference; r:gives { - (2 9 9 9) :digitsToNumber 2999 . + (3 9 9 9) :digitsToNumber 3999 . }; r:evidence ( - [ a r:Fact; r:gives {(2 1000) math:product 2000}] + [ a r:Fact; r:gives {(3 1000) math:product 3000}] [ a r:Fact; r:gives {(9 100) math:product 900}] [ a r:Fact; r:gives {(9 10) math:product 90}] - [ a r:Fact; r:gives {(2000 900 90 9) math:sum 2999}] + [ a r:Fact; r:gives {(3000 900 90 9) math:sum 3999}] ); - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 2000]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 2]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 3000]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 3]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_3"]; r:boundTo 900]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 90]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 2999]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 3999]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 9]; - r:rule skolem:lemma3439. + r:rule skolem:lemma6764. -skolem:lemma3437 a r:Inference; +skolem:lemma6762 a r:Inference; r:gives { - (9 9 9 2) :digitsToNumber 9992 . + (9 9 9 3) :digitsToNumber 9993 . }; r:evidence ( [ a r:Fact; r:gives {(9 1000) math:product 9000}] [ a r:Fact; r:gives {(9 100) math:product 900}] [ a r:Fact; r:gives {(9 10) math:product 90}] - [ a r:Fact; r:gives {(9000 900 90 2) math:sum 9992}] + [ a r:Fact; r:gives {(9000 900 90 3) math:sum 9993}] ); r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_1"]; r:boundTo 9000]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_0"]; r:boundTo 9]; @@ -79732,11 +157221,11 @@ skolem:lemma3437 a r:Inference; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_2"]; r:boundTo 9]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_5"]; r:boundTo 90]; r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_4"]; r:boundTo 9]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9992]; - r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 2]; - r:rule skolem:lemma3439. + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_7"]; r:boundTo 9993]; + r:binding [ r:variable [ n3:uri "http://www.w3.org/2000/10/swap/var#x_6"]; r:boundTo 3]; + r:rule skolem:lemma6764. -skolem:lemma3438 a r:Extraction; +skolem:lemma6763 a r:Extraction; r:gives { @forAll var:x_0, var:x_1, var:x_2, var:x_3, var:x_4, var:x_5, var:x_6. { var:x_0 :numberToDigits (var:x_1 var:x_3 var:x_5 var:x_6). @@ -79751,7 +157240,7 @@ skolem:lemma3438 a r:Extraction; }; r:because [ a r:Parsing; r:source ]. -skolem:lemma3439 a r:Extraction; +skolem:lemma6764 a r:Extraction; r:gives { @forAll var:x_0, var:x_1, var:x_2, var:x_3, var:x_4, var:x_5, var:x_6, var:x_7. { (var:x_0 var:x_2 var:x_4 var:x_6) :digitsToNumber var:x_7. diff --git a/reasoning/proof-by-recursion/example2-query.n3 b/reasoning/proof-by-recursion/example2-query.n3 index 01249d7d4..b2102fb90 100644 --- a/reasoning/proof-by-recursion/example2-query.n3 +++ b/reasoning/proof-by-recursion/example2-query.n3 @@ -4,7 +4,7 @@ # query { - 1000 log:repeat ?A. + 2000 log:repeat ?A. (?A 2000) math:sum ?B. ?B :kaprekar (0 ?C). } => {